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Chapter 13: Capital Structure and Leverage
o
A firm's business risk is largely determined by the financial characteristics of its industry, especially by the amount of debt the average firm in the industry uses. o
True
o
False
ANSWER: False
o
Financial risk refers to the extra risk borne by stockholders as a result of a firm's use of debt as compared with their risk if the firm had used no debt. o
True
o
False
ANSWER: True
o
A firm's capital structure does not affect its free cash flows as discussed in the text, because FCF reflects only operating cash flows, which are available to service debt, to pay dividends to stockholders, and for other purposes. o
True
o
False
ANSWER: True
o
If a firm borrows money, it is using financial leverage. o
True
o
False
ANSWER: True
o
Other things held constant, an increase in financial leverage will increase a firm's market (or systematic) risk as measured by its beta coefficient. o
True
o
False
ANSWER: True
o
The graphical probability distribution of ROE for a firm that uses financial leverage would tend to be more peaked than the distribution if the firm used no leverage, other things held constant. o
True
o
False
ANSWER: False
o
Provided a firm does not use an extreme amount of debt, operating leverage typically affects only EPS, while financial leverage affects both EPS and EBIT. o
True
o
False
ANSWER: False o
The trade-off theory states that capital structure decisions involve a tradeoff between the costs and benefits of debt financing. o
True
o
False
ANSWER: True
o
Different borrowers have different risks of bankruptcy, and if a borrower goes bankrupt, its lenders will probably not get back the full amount of funds that they loaned. Therefore, lenders charge higher rates to borrowers judged to be more likely to go bankrupt. o
True
o
False
ANSWER: True
o
Modigliani and Miller (MM) won Nobel Prizes for their work on capital structure theory. o
True
o
False
ANSWER: True
o
Modigliani and Miller's first article led to the conclusion that capital structure is "irrelevant" because it has no effect on a firm's value. o
True
o
False
ANSWER: True
o
Modigliani and Miller's first article led to the conclusion that capital structure is extremely important, and that every firm has an optimal capital structure that maximizes its value and minimizes its cost of capital. o
True
o
False
ANSWER: False
o
It is possible for Firms A and B to have identical financial and operating leverage, yet for Firm A to have more risk as measured by the variability of EPS. This would occur if Firm A has more business risk than Firm B. o
True
o
False
ANSWER:
True
RATIONALE: If Firm A's sales are more volatile than those of Firm B, then A would have greater EPS variability in spite of identical financial and operating leverage. Operating leverage is only one factor that affects business risk. o
As the text indicates, a firm's financial risk can and should be divided into separate market and diversifiable risk components. o
True
o
False
ANSWER: False
o
If two firms have the same expected earnings per share (EPS) and the same standard deviation of expected EPS, then they must have the same amount of business risk. o
True
o
False
ANSWER: False
o
In a world with no taxes, Modigliani and Miller (MM) show that a firm's capital structure does not affect its value. However, when taxes are considered, MM show a positive relationship between debt and value, i.e., the firm's value rises as it uses more and more debt, other things held constant. o
True
o
False
ANSWER: True
o
According to Modigliani and Miller (MM), in a world without taxes the optimal capital structure for a firm is approximately 100% debt financing. o
True
o
False
ANSWER: False
o
According to Modigliani and Miller (MM), in a world with corporate income taxes the optimal capital structure calls for approximately 100% debt financing. o
True
o
False
ANSWER: True
o
According to Modigliani and Miller (MM), in a world without corporate income taxes the use of debt has no effect on the firm's value. o
True
o
False
ANSWER: True
o
Modigliani and Miller's first article led to the conclusion that capital structure is "irrelevant" because it has no effect on a firm's value. However, that article was criticized because it assumed that no taxes existed. MM then revised their original article to include corporate taxes, and this model led to the conclusion that a firm's value would be maximized if it used (almost) 100% debt. o
True
o
False
ANSWER: True o
Modigliani and Miller's second article, which assumed the existence of corporate income taxes, led to the conclusion that a firm's value would be maximized, and its cost of capital minimized, if it used (almost) 100% debt. However, this model did not take of bankruptcy costs. The existence of bankruptcy costs leads to the assumption of an optimal capital structure where the debt ratio is less than 100%. o
True
o
False
ANSWER: True
o
The Miller model begins with the Modigliani and Miller (MM) model with corporate taxes and then adds personal taxes. o
True
o
False
ANSWER: True
o
The Miller model begins with the Modigliani and Miller (MM) model without corporate taxes and then adds personal taxes. o
True
o
False
ANSWER: False
o
The Modigliani and Miller (MM) articles implicitly assumed that bankruptcy did not exist. That led to the development of the "trade-off" model, where the firm's value first rises with the use of debt due to the tax shelter of debt, but later falls as more debt is added because the potential costs of bankruptcy begin to more than offset the tax shelter benefits. Under the trade-off theory, an optimal capital structure exists. o
True
o
False
ANSWER: True
o
Modigliani and Miller (MM), in their second article, took of taxes, bankruptcy, and other factors that were assumed away in their original article. Once they took of all these assumptions, they concluded that every firm has a unique optimal capital structure. Moreover, a manager can use the second MM model to determine his or her firm's optimal debt ratio. o
True
o
False
ANSWER: False
o
Some people—including the former chairman of the Federal Reserve Board of Governors (Ben Bernanke)—have argued that one advantage of corporate debt from the stockholders' standpoint is that the existence of debt forces managers to focus on cash flow and to refrain from spending too much of the firm's money on private plane and other "perks." This is one of the factors that led to the rise of LBOs and private equity firms. o
True
o
False
ANSWER: True
o
The Modigliani and Miller (MM) articles implicitly assumed, among other things, that outside stockholders have the same information about a firm's future prospects as its managers. That was called "symmetric information," and it is questionable. The introduction of "asymmetric information" led to the development of the "signaling" theory of capital structure, which postulated that firms are reluctant to issue new stock because investors will interpret such an act as a signal that the firm's managers are worried about its future. Other actions give off different signals, and the end result is that capital structure is affected by managers' perceptions about how their financing decisions will affect investors' views of the firm and thus its value. o
True
o
False
ANSWER: True
o
According to the signaling theory of capital structure, firms first use common equity for their capital, then use debt if and only if they can raise no more equity on "reasonable" . This occurs because the use of debt financing signals to investors that the firm's managers think that the future does not look good. o
True
o
False
ANSWER: False
o
Other things held constant, firms with more stable and predictable sales tend to use more debt than firms with less stable sales. o
True
o
False
ANSWER: True
o
Other things held constant, firms that use assets that can be sold easily (like trucks) tend to use more debt than firms whose assets are harder to sell (like those engaged in research and development). o
True
o
False
ANSWER: True
o
Other things held constant, the lower a firm's tax rate, the more logical it is for the firm to use debt. o
True
o
False
ANSWER:
False
RATIONALE: This is false. The lower the tax rate, the less valuable the tax shelter from debt. Think about the cost of debt in the WACC: rd(1 − T). If T is low, then the cost of debt is not reduced as much as when T is high.
o
A firm's treasurer likes to be in a position to raise funds to operations whenever such funds are needed, even in "bad times." This is called "financial flexibility," and the lower the firm's debt ratio, the greater its financial flexibility, other things held constant. o
True
o
False
ANSWER:
True
RATIONALE: This is true, because if times are bad which is when financial flexibility is important investors are much more willing to lend a firm money than to buy its stock, because if the firm fails, debt holders are first in line to get their money back.
o
If a firm utilizes debt financing, a 10% decline in earnings before interest and taxes (EBIT) will result in a decline in earnings per share that is larger than 10%, and the higher the debt ratio, the larger this difference will be. o
True
o
False
ANSWER: True
o
An increase in the debt ratio will generally have no effect on which of these items? o
Business risk.
o
Total risk.
o
Financial risk.
o
Market risk.
o
The firm's beta.
ANSWER: a
o
Business risk is affected by a firm's operations. Which of the following is NOT directly associated with (or does not directly contribute to) business risk? o
Demand variability.
o
Sales price variability.
o
The extent to which operating costs are fixed.
o
The extent to which interest rates on the firm's debt fluctuate.
o
Input price variability.
ANSWER: d
o
Which of the following statements is CORRECT? o
Since debt financing raises the firm's financial risk, increasing the target debt ratio will always increase the WACC.
o
Since debt financing is cheaper than equity financing, raising a company's debt ratio will always reduce its WACC.
o
Increasing a company's debt ratio will typically reduce the marginal costs of both debt and equity financing. However, this action still may raise the company's WACC.
o
Increasing a company's debt ratio will typically increase the marginal costs of both debt and equity financing. However, this action still may lower the company's WACC.
o
Since a firm's beta coefficient is not affected by its use of financial leverage, leverage does not affect the cost of equity.
ANSWER: d o
Which of the following statements is CORRECT? o
The capital structure that maximizes expected EPS also maximizes the price per share of common stock.
o
The capital structure that minimizes the interest rate on debt also maximizes the expected EPS.
o
The capital structure that minimizes the required return on equity also maximizes the stock price.
o
The capital structure that minimizes the WACC also maximizes the price per share of common stock.
o
The capital structure that gives the firm the best bond rating also maximizes the stock price.
ANSWER: d
o
Based on the information below, what is the firm's optimal capital structure? o
Debt = 40%; Equity = 60%; EPS = $2.95; Stock price = $26.50.
o
Debt = 50%; Equity = 50%; EPS = $3.05; Stock price = $28.90.
o
Debt = 60%; Equity = 40%; EPS = $3.18; Stock price = $31.20.
o
Debt = 80%; Equity = 20%; EPS = $3.42; Stock price = $30.40.
o
Debt = 70%; Equity = 30%; EPS = $3.31; Stock price = $30.00.
ANSWER: c
o
Which of the following statements best describes the optimal capital structure? o
The optimal capital structure is the mix of debt, equity, and preferred stock that maximizes the company's earnings per share (EPS).
o
The optimal capital structure is the mix of debt, equity, and preferred stock that maximizes the company's stock price.
o
The optimal capital structure is the mix of debt, equity, and preferred stock that minimizes the company's cost of equity.
o
The optimal capital structure is the mix of debt, equity, and preferred stock that minimizes the company's cost of debt.
o
The optimal capital structure is the mix of debt, equity, and preferred stock that minimizes the company's cost of preferred stock.
ANSWER: b
o
Which of the following events is likely to encourage a company to raise its target debt ratio, other things held constant? o
An increase in the corporate tax rate.
o
An increase in the personal tax rate.
o
An increase in the company's operating leverage.
o
The Federal Reserve tightens interest rates in an effort to fight inflation.
o
The company's stock price hits a new high.
ANSWER: a
o
Which of the following would tend to increase a firm's target debt ratio, other things held constant? o
The costs associated with filing for bankruptcy increase.
o
The corporate tax rate is increased.
o
The personal tax rate is increased.
o
The Federal Reserve tightens interest rates in an effort to fight inflation.
o
The company's stock price hits a new low.
ANSWER: b
o
Which of the following statements is CORRECT? o
As a rule, the optimal capital structure is found by determining the debt-equity mix that maximizes expected EPS.
o
The optimal capital structure simultaneously maximizes EPS and minimizes the WACC.
o
The optimal capital structure minimizes the cost of equity, which is a necessary condition for maximizing the stock price.
o
The optimal capital structure simultaneously minimizes the cost of debt, the cost of equity, and the WACC.
o
The optimal capital structure simultaneously maximizes the stock price and minimizes the WACC.
ANSWER: e
o
The firm's target capital structure should do which of the following? o
Maximize the earnings per share (EPS).
o
Minimize the cost of debt (rd).
o
Obtain the highest possible bond rating.
o
Minimize the cost of equity (rs).
o
Minimize the weighted average cost of capital (WACC).
ANSWER: e
o
Which of the following statements is CORRECT? o
A firm's business risk is determined solely by the financial characteristics of its industry.
o
The factors that affect a firm's business risk include industry characteristics and economic conditions, both of which are generally beyond the firm's control.
o
One of the benefits to a firm of being at or near its target capital structure is that this generally minimizes the risk of bankruptcy.
o
A firm's financial risk can be minimized by diversification.
o
The amount of debt in its capital structure can under no circumstances affect a company's EBIT and business risk.
ANSWER: b
o
Which of the following statements is CORRECT? As a firm increases the operating leverage used to produce a given quantity of output, this o
normally leads to an increase in its fixed assets turnover ratio.
o
normally leads to a decrease in its business risk.
o
normally leads to a decrease in the standard deviation of its expected EBIT.
o
normally leads to a decrease in the variability of its expected EPS.
o
ANSWER:
normally leads to a reduction in its fixed assets turnover ratio.
e
RATIONALE: More operating leverage generally means a greater use of automation, which means more fixed assets. If fixed assets increase proportionately more than sales, then the fixed assets turnover (S/FA) will decline. o
A firm's CFO is considering increasing the target debt ratio, which would also increase the company's interest expense. New bonds would be issued and the proceeds would be used to buy back shares of common stock. Neither total assets nor operating income would change, but expected earnings per share (EPS) would increase. Assuming the CFO's estimates are correct, which of the following statements is CORRECT? o
Since the proposed plan increases the firm's financial risk, the stock price might fall even if EPS increases.
o
If the plan reduces the WACC, the stock price is likely to decline.
o
Since the plan is expected to increase EPS, this implies that net income is also expected to increase.
o
If the plan does increase the EPS, the stock price will automatically increase at the same rate.
o
Under the plan there will be more bonds outstanding, and that will increase their liquidity and thus lower the interest rate on the currently outstanding bonds.
ANSWER: a
o
Which of the following statements is CORRECT?
o
Increasing its use of financial leverage is one way to increase a firm's return on investors' capital (ROIC).
o
If a firm lowered its fixed costs but increased its variable costs by just enough to hold total costs at the present level of sales constant, this would increase its operating leverage.
o
The debt ratio that maximizes expected EPS generally exceeds the debt ratio that maximizes share price.
o
If a company were to issue debt and use the money to repurchase common stock, this would reduce its return on investors' capital (ROIC). (Assume that the repurchase has no impact on the company's operating income.)
o
If a change in the bankruptcy code made bankruptcy less costly to corporations, this would tend to reduce corporations' debt ratios.
ANSWER: c
o
Your firm has $500 million of investor-supplied capital, its return on investors' capital (ROIC) is 15%, and it currently has no debt in its capital structure (i.e., wd = 0). The CFO is contemplating a recapitalization where it would issue debt at an after-tax cost of 10% and use the proceeds to buy back some of its common stock, such that the percentage of common equity in the capital structure (wc) is 1 − wd. If the company goes ahead with the recapitalization, its operating income, the size of the firm (i.e., total assets), total investor-supplied capital, and tax rate would remain unchanged. Which of the following is most likely to occur as a result of the recapitalization? o
The ROA would increase.
o
The ROA would remain unchanged.
o
The return on investors' capital would decline.
o
The return on investors' capital would increase.
o
The ROE would increase.
ANSWER: e
o
Companies HD and LD have identical tax rates, total assets, total investor-supplied capital, and returns on investors' capital (ROIC), and their ROICs exceed their after-tax costs of debt, rd(1 − T). However, Company HD has a higher debt ratio and thus more interest expense than Company LD. Which of the following statements is CORRECT? o
Company HD has a higher net income than Company LD.
o
Company HD has a lower ROA than Company LD.
o
Company HD has a lower ROE than Company LD.
o
The two companies have the same ROA.
o
The two companies have the same ROE.
ANSWER: b
o
Firms U and L each have the same amount of assets, investor-supplied capital, and both have a return on investors' capital (ROIC) of 12%. Firm U is unleveraged, i.e., it is 100% equity financed, while Firm L is financed with 50% debt and 50% equity. Firm L's debt has an after-tax cost of 8%. Both firms have positive net income and a 35% tax rate. Which of the following statements is CORRECT? o
The two companies have the same times interest earned (TIE) ratio.
o
Firm L has a lower ROA than Firm U.
o
Firm L has a lower ROE than Firm U.
o
Firm L has the higher times interest earned (TIE) ratio.
o
Firm L has a higher EBIT than Firm U.
ANSWER: b
o
Your firm is currently 100% equity financed. The CFO is considering a recapitalization plan under which the firm would issue long-term debt with an after-tax yield of 9% and use the proceeds to repurchase some of its common stock. The recapitalization would not change the company's total investor-supplied capital, the size of the firm (i.e., total assets), and it would not affect the firm's return on investors' capital (ROIC), which is 15%. The CFO believes that this recapitalization would reduce the firm's WACC and increase its stock price. Which of the following would be likely to occur if the company goes ahead with the recapitalization plan? o
The company's net income would increase.
o
The company's earnings per share would decline.
o
The company's cost of equity would increase.
o
The company's ROA would increase.
o
The company's ROE would decline.
ANSWER: c
o
A major contribution of the Miller model is that it demonstrates, other things held constant, that o
personal taxes increase the value of using corporate debt.
o
personal taxes lower the value of using corporate debt.
o
personal taxes have no effect on the value of using corporate debt.
o
financial distress and agency costs reduce the value of using corporate debt.
o
debt costs increase with financial leverage.
ANSWER: b
o
Which of the following statements is CORRECT, holding other things constant? o
Firms whose assets are relatively liquid tend to have relatively low bankruptcy costs, hence they tend to use relatively little debt.
o
An increase in the personal tax rate is likely to increase the debt ratio of the average corporation.
o
If changes in the bankruptcy code make bankruptcy less costly to corporations, then this would likely lead to lower debt ratios for corporations.
o
An increase in the company's degree of operating leverage would tend to encourage the firm to use more debt in its capital structure so as to keep its total risk unchanged.
o
An increase in the corporate tax rate would in theory encourage companies to use more debt in their capital structures.
ANSWER: e
o
Other things held constant, which of the following events would be most likely to encourage a firm to increase the amount of debt in its capital structure? o
Its sales are projected to become less stable in the future.
o
The bankruptcy laws are changed in a way that would make bankruptcy more costly to the firm and its stockholders.
o
Management believes that the firm's stock is currently overvalued.
o
The firm decides to automate its factory with specialized equipment and thus increase its use of operating leverage.
o
The corporate tax rate is increased.
ANSWER: e o
Which of the following statements is CORRECT? o
A firm can use retained earnings without paying a flotation cost. Therefore, while the cost of retained earnings is not zero, its cost is generally lower than the after-tax cost of debt.
o
The capital structure that minimizes a firm's weighted average cost of capital is also the capital structure that maximizes its stock price.
o
The capital structure that minimizes the firm's weighted average cost of capital is also the capital structure that maximizes its earnings per share.
o
If a firm finds that the cost of debt is less than the cost of equity, increasing its debt ratio must reduce its WACC.
o
Other things held constant, if corporate tax rates declined, then the Modigliani-Miller tax-adjusted theory would suggest that firms should increase their use of debt.
ANSWER: b
o
Which of the following statements is CORRECT? o
The capital structure that maximizes the stock price is also the capital structure that minimizes the cost of equity from retained earnings (rs).
o
The capital structure that maximizes the stock price is also the capital structure that maximizes earnings per share.
o
The capital structure that maximizes the stock price is also the capital structure that maximizes the firm's times interest earned (TIE) ratio.
o
If a company increases its debt ratio, this will typically increase the marginal costs of both debt and equity, but it still may reduce the company's WACC.
o
If Congress were to legislation that increases the personal tax rate but decreases the corporate tax rate, this would encourage companies to increase their debt ratios.
ANSWER: d
o
Which of the following statements is CORRECT? o
In general, a firm with low operating leverage also has a small proportion of its total costs in the form of fixed costs.
o
There is no reason to think that changes in the personal tax rate would affect firms' capital structure decisions.
o
A firm with a relatively high business risk is more likely to increase its use of financial leverage than a firm with low business risk, assuming all else equal.
o
If a firm's after-tax cost of equity exceeds its after-tax cost of debt, it can always reduce its WACC by increasing its use of debt.
o
Suppose a firm has less than its optimal amount of debt. Increasing its use of debt to the point where it is at its optimal capital structure will decrease the costs of both debt and equity.
ANSWER: a
o
Companies HD and LD have identical amounts of assets, investorsupplied capital, operating income (EBIT), tax rates, and business risk. Company HD, however, has a higher debt ratio than LD. Company HD's return on investors' capital (ROIC) exceeds its after-tax cost of debt, rd(1 − T). Which of the following statements is CORRECT? o
Company HD has a higher return on assets (ROA) than Company LD.
o
Company HD has a higher times interest earned (TIE) ratio than Company LD.
o
Company HD has a higher return on equity (ROE) than Company LD, and its risk as measured by the standard deviation of ROE is also higher than LD's.
o
The two companies have the same ROE.
o
Company HD's ROE would be higher if it had no debt.
ANSWER: c
o
Companies HD and LD have the same total assets, total investor-supplied capital, operating income (EBIT), tax rate, and business risk. Company HD, however, has a much higher debt ratio than LD. Also, both companies' returns on investors' capital (ROIC) exceed their after-tax costs of debt, rd(1 − T). Which of the following statements is CORRECT? o
HD should have a higher return on assets (ROA) than LD.
o
HD should have a higher times interest earned (TIE) ratio than LD.
o
HD should have a higher return on equity (ROE) than LD, but its risk, as measured by the standard deviation of ROE, should also be higher than LD's.
o
Given that ROIC > rd(1 − T), HD's stock price must exceed that of LD.
o
Given that ROIC > rd(1 − T), LD's stock price must exceed that of HD.
ANSWER: c
o
Which of the following statements is CORRECT? o
If Congress lowered corporate tax rates while other things were held constant, and if the Modigliani-Miller tax-adjusted theory of capital structure were correct, this would tend to cause corporations to decrease their use of debt.
o
A change in the personal tax rate should not affect firms' capital structure decisions.
o
"Business risk" is differentiated from "financial risk" by the fact that financial risk reflects only the use of debt, while business risk reflects both the use of debt and such factors as sales variability, cost variability, and operating leverage.
o
The optimal capital structure is the one that simultaneously (1) maximizes the price of the firm's stock, (2) minimizes its WACC, and (3) maximizes its EPS.
o
If changes in the bankruptcy code made bankruptcy less costly to corporations, this would likely reduce the average corporation's debt ratio.
ANSWER: a
o
Which of the following statements is CORRECT? o
When a company increases its debt ratio, the costs of equity and debt both increase. Therefore, the WACC must also increase.
o
The capital structure that maximizes the stock price is generally the capital structure that also maximizes earnings per share.
o
All else equal, an increase in the corporate tax rate would tend to encourage companies to increase their debt ratios.
o
Since debt financing raises the firm's financial risk, increasing a company's debt ratio will always increase its WACC.
o
Since the cost of debt is generally fixed, increasing the debt ratio tends to stabilize net income.
ANSWER: c
o
Which of the following statements is CORRECT? o
Generally, debt ratios do not vary much among different industries, although they do vary among firms within a given industry.
o
Electric utilities generally have very high common equity ratios because their revenues are more volatile than those of firms in most other industries.
o
Airline companies tend to have very volatile earnings, and as a result they generally have high target debt-to- equity ratios.
o
Wide variations in capital structures exist both between industries and among individual firms within given industries. These differences are caused by differing business risks and also managerial attitudes.
o
Since most stocks sell at or very close to their book values, book value capital structures are typically adequate for use in estimating firms' weighted average costs of capital.
ANSWER: d
o
Longstreet Inc. has fixed operating costs of $470,000, variable costs of $2.80 per unit produced, and its product sells for $4.00 per unit. What is the company's break-even point, i.e., at what unit sales volume would income equal costs?
o
391,667
o
411,250
o
431,813
o
453,403
o
476,073
ANSWER:
a
RATIONALE: Fixed operating costs (F)
$470,000
Variable costs per unit (V)
$2.80
Sales price per unit (P)
$4.00
QBE = F/(P − V) = 391,667
o
Your uncle is considering investing in a new company that will produce high quality stereo speakers. The sales price would be set at 1.5 times the variable cost per unit; the variable cost per unit is estimated to be $75.00; and fixed costs are estimated at $1,200,000. What sales volume would be required to break even, i.e., to have EBIT = zero?
o
28,880
o
30,400
o
32,000
o
33,600
o
35,280
ANSWER:
c
RATIONALE: Variable costs per unit (V)
$75.00
Price multiple over VC
1.50
Sales price per unit (P)
$112.50
Fixed costs (F) $1,200,000 QBE = F/(P − V) = 32,000
o
Southwest U's campus book store sells course packs for $15 each, the variable cost per pack is $9, fixed costs to produce the packs are $200,000, and expected annual sales are 50,000 What are the pre-tax profits from sales of course packs?
o
$ 72,900
o
$ 81,000
o
$ 90,000
o
$100,000
o
e. $110,000
ANSWER:
d
RATIONALE: Sales price per unit (P)
$15.00
Variable costs per unit (V) Annual sales (Q) Fixed costs (F)
$9.00 50,000 $200,000
Profit = PQ − VQ − F = EBIT = $750,000 − $450,000 − $200,000 = $100,000
o
Southwest U's campus book store sells course packs for $16 The variable cost per pack is $10, and at current annual sales of 50,000 packs, the store earns $75,000 before taxes on course packs. How much are the fixed costs of producing the course packs?
o
a. $164,025
o
$182,250
o
c. $202,500
o
$225,000
o
e. $247,500
ANSWER:
d
RATIONALE: Sales price per unit (P) Variable costs per unit (V) Annual sales (Q) Profit = PQ − VQ − F
$16.00 $10.00 50,000 $75,000
F = PQ − VQ − EBIT = $800,000 − $500,000 − 75000 = $225,000
o
Assume that you and your brother plan to open a business that will make and sell a newly designed type of Two robotic machines are available to make the sandals, Machine A and Machine B. The price per pair will be $20.00 regardless of which machine is used. The fixed and variable costs associated with the two machines are shown below. What is the difference between the break-even points for Machines A and B? (Hint: Find BEB− BEA)
Machine A
Machine B
Price per pair (P)
$20.00
$20.00
Fixed costs (F)
$25,000
$100,000
Variable cost/unit (V)
$7.00
$4.00
o
3,154
o
3,505
o
3,894
o
4,327
o
4,760
ANSWER:
d
RATIONALE:
MachineA Machine B
Sales price per pair (P)
$20.00
$20.00
Fixed costs (F)
$25,000
$100,000
Variable costs per unit (V)
$7.00
$4.00
QBE = F/(P − V)
1,923
6,250
Difference = BEB − BEA = 4,327
o
Your company plans to produce a new product, a wireless computer mouse. Two machines can be used to make the mouse, Machines A and B. The price per mouse will be $25.00 regardless of which machine is used. The fixed and variable costs associated with the two machines are shown below. At the expected sales level of 75,000 units, how much higher or lower will the firm's expected EBIT be if it uses Machine B with high fixed costs rather than Machine A with low fixed costs, i.e., what is EBITB− EBITA?
Machine A
Machine B
Price per mouse (P)
$25.00
$25.00
Fixed costs (F)
$100,000
$400,000
Variable cost/unit (V)
$15.25
$9.00
Exp. unit sales (Q)
75,000
75,000
o
a. $123,019
o
$136,688
o
c. $151,875
o
$168,750
o
e. $185,625
ANSWER:
d
RATIONALE:
MachineA Machine B
Sale price per mouse (P)
$25.00
$25.00
Fixed costs (F)
$100,000
$400,000
Variable costs per unit (V)
$15.25
$9.00
Expected unit sales (Q)
75,000
75,000
Expected EBIT = (P − V)Q − F
$631,250
$800,000
Difference = EBITB − EBITA = $168,750
o
Your company, which is financed entirely with common equity, plans to manufacture a new product, a cell phone that can be worn like a Two robotic machines are available to make the phone, Machine A and Machine B. The price per phone will be $250.00 regardless of which machine is used to make it. The fixed and variable costs associated with the two machines are shown below, along with the capital (all equity) that must be invested to purchase each machine. The expected sales level is 25,000 units. Your company has tax loss carry-forwards that will cause its tax rate to be zero for the life of the project, so T = 0. How much higher or lower will the project's ROE be if you select the machine that produces the higher ROE, i.e., what is ROEB− ROEA? (Hint: Since the firm uses no debt and its tax rate is zero, ROE = EBIT/Required investment.)
Machine A
Machine B
Price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$2,000,000
Variable cost/unit (V)
$200.00
$150.00
Expected unit sales (Q)
25,000
25,000
Required equity investment
$2,500,000
$3,000,000
o
6.00%
o
6.67%
o
7.00%
o
7.35%
o
7.72%
ANSWER:
b
RATIONALE:
MachineA Machine B
Sales price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$2,000,000
Variable costs per unit (V)
$200.00
$150.00
Expected unit sales (Q)
25,000
25,000
Required equity investment
$2,500,000
$3,000,000
Exp. profit = EBIT = (P − V)Q − F $250,000
$500,000
Return on investment = ROE
16.67%
10.00%
Difference = ROEB − ROEA = 6.67%
o
You work for the CEO of a new company that plans to manufacture and sell a new product, a watch that has an embedded TV set and a magnifying glass The issue now is how to finance the company, with only equity or with a mix of debt and equity. Expected operating income is $400,000. Other data for the firm are shown below. How much higher or lower will the firm's expected ROE be if it uses some debt rather than all equity, i.e., what is ROEL − ROEU? 0% Debt, U
60% Debt, L
Oper. income (EBIT)
$400,000
$400,000
Required investment
$2,500,000
$2,500,000
% Debt
0.0%
60.0%
$ of Debt
$0.00
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35%
35%
o
5.85%
o
6.14%
o
6.45%
o
6.77%
o
7.11%
ANSWER:
a
RATIONALE: 0% Debt, U
60% Debt, L
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
$ of Debt
$0
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
Operating income (EBIT)
$400,000
$400,000
Interest Taxable income
0
150,000
$400,000
$250,000
140,000
87,500
Net Income
$260,000
$162,500
ROE
10.40%
16.25%
Taxes
Difference in ROEs = 5.85%
o
You work for the CEO of a new company that plans to manufacture and sell a new type of laptop The issue now is how to finance the company, with only equity or with a mix of debt and equity. Expected operating income is $600,000. Other data for the firm are shown below. How much higher or lower will the firm's expected EPS be if it uses some debt rather than only equity, i.e., what is EPSL− EPSU?
0% Debt, U
60% Debt, L
Oper. income (EBIT)
$600,000
$600,000
Required investment
$2,500,000
$2,500,000
% Debt
0.0%
60.0%
$ of Debt
$0.00
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Shares issued, $10/share
250,000
100,000
Interest rate
NA
10.00%
Tax rate
35%
35%
o
$1.00
o
$1.11
o
$1.23
o
$1.37
o
$1.50
ANSWER: d RATIONALE: 0% Debt, U
60% Debt, L
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
$ of Debt
$0
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Shares issued at $10/share
250,000
100,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
Operating income (EBIT)
$600,000
$600,000
Interest
0
Taxable income Taxes Net income
150,000
$600,000
$450,000
210,000
157,500
$390,000
$292,500
Earnings per share (EPS)
$1.56
$2.93
Difference in EPS = $1.37
o
Confu expects to have the following data during the coming year. What is the firm's expected ROE?
Capital
$200,000
Debt/Capital, book value 65% EBIT
o
$25,000
12.51%
Interest rate
8%
Tax rate
40%
o
13.14%
o
13.80%
o
14.49%
o
15.21%
ANSWER:
a
RATIONALE: Capital
$200,000
Debt/Capital =
EBIT
$25,000
− Interest = rate × debt
65% 10,400
EBIT taxes
$25,000 Earnings before $14,600
Interest rate
− Taxes
8%
Tax rate
40%
Debt = (Debt/Capital)) × Capital =
$130,000
5,840
Net Income $ 8,760 NI/Equity = ROE =
12.51%
Equity = Assets − Debt = $70,000
o
Senate Inc. is considering two alternative methods for producing playing cards. Method 1 involves using a machine with a fixed cost (mainly depreciation) of $12,000 and variable costs of $1.00 per deck of cards. Method 2 would use a less expensive machine with a fixed cost of only $5,000, but it would require a variable cost of $1.50 per deck. The sales price per deck would be the same under each method. At what unit output level would the two methods provide the same operating income (EBIT)?
o
12,600
o
14,000
o
c. 15,400
o
16,940
o
e. 18,634 b Method 1
Method 2
Price/unit (P)
$2.00
$2.00
V
$1.00
$1.50
F
$12,000
$5,000
ANSWER: RATIONALE:
EBIT = PQ − VQ − F Insert data for Methods 1 and 2, then set the 2 equations equal to one another, and then solve for Q. EBIT1 = PQ − Q(V1) − F1 EBIT2 = PQ − Q(V2) − F2
The PQs cancel, divide by −1, and we are left with: Q(V1) + F1 = Q(V2) + F2 This reduces to: Q(V2 − V1) = F1 − F2 Q = (F1 − F2)/(V2 − V1) = 14,000 o
A group of venture investors is considering putting money into Lemma Books, which wants to produce a new reader for electronic books. The variable cost per unit is estimated at $250, the sales price would be set at twice the VC/unit, or $500, and fixed costs are estimated at $750,000. The investors will put up the funds if the project is likely to have an operating income of $500,000 or more. What sales volume would be required in order to meet the minimum profit goal? (Hint: Use the break-even formula, but include the required profit in the numerator.)
o
4,513
o
4,750
o
5,000
o
5,250
o
5,513
ANSWER:
c
RATIONALE: Variable costs per unit (V)
$250
Sale price per unit (P) Fixed costs (F) Required minimum profit
$500 $750,000 $500,000
Volume (units) required to meet profit goal = (F + Profit)/(P − V) = 5,000
Check: Op profit = (P − V) × Units − F = $500,000
o
El Capitan Foods has a capital structure of 40% debt and 60% equity, its tax rate is 35%, and its beta (leveraged) is 25. Based on the Hamada equation, what would the firm's beta be if it used no debt, i.e., what is its unlevered beta, bU?
o
0.71
o
0.75
o
0.79
o
0.83
o
0.87
ANSWER:
e
RATIONALE: bL wd
1.25 0.40
Tax rate
35%
D/E = wd/(1 − wd)
0.67
bU = bL/(1 + (D/E) ×(1 − T))
0.87
o
Gator Fabrics Inc. currently has zero debt (i.e., wd = 0). It is a zero growth company, and additional firm data are shown below. Now the company is considering using some debt, moving to the new capital structure indicated The money raised would be used to repurchase stock at the current price. It is estimated that the increase in risk resulting
from the additional leverage would cause the required rate of return on equity to rise somewhat, as indicated below. If this plan were carried out, by how much would the WACC change, i.e., what is WACCOld − WACCNew?
wd %
55%
Orig. cost of equity, rs
wc rs
45%
New cost of equity =
10.0
11.0%
Interest rate new = rd rate
o
2.74%
o
3.01%
o
3.32%
o
3.65%
o
4.01%
ANSWER:
7.0%
Tax
40%
a
RATIONALE: wd
55%
Interest rate = rd
wc
45%
New cost of equity =
rs 11.0%
equity
Tax rate 10.0%
40%
Old cost of
7.0%
WACCOLD = wd(1 − T)rd + wcrs = 0.00% + 10.00% = 10.00% WACCNEW = wd(1 − T)rd + wcrs = 2.31% + 4.95% = 7.26% Change in WACC = WACC Old − WACC New = 2.74%
o
As a consultant to First Responder Inc., you have obtained the following data (dollars in millions). The company plans to pay out all of its earnings as dividends, hence g = 0. Also, no net new investment in operating capital is needed because growth is zero. The CFO believes that a move from zero debt to 20.0% debt would cause the cost of equity to increase from 10.0% to 12.0%, and the interest rate on the new debt would be 8.0%. What would the firm's total market value be if it makes this change? Hints: Find the FCF, which is equal to NOPAT = EBIT(1 − T) because no new operating capital is needed, and then divide by (WACC − g).
Oper. income (EBIT)
$800
New cost of equity (rs)
12.00%
Interest rate (rd)
8.00%
o
a. $2,982
o
$3,314
o
c. $3,682
o
$4,091
o
e. $4,545
Tax rate New wd
40.0% 20.0%
ANSWER:
e
RATIONALE: Operating income (EBIT)
$800
Tax rate
40.0%
New cost of equity (rs)
12.00%
New wd
20.0%
Interest rate (rd)
8.00%
New WACC
= wd × rd(1 − T) + wc × rs = 0.96% + 9.60% = 10.56%
FCF = EBIT(1 − T) because there is no investment in new operating capital. FCF = EBIT(1 − T) = $800 × 0.6 = $480.0 Firm value = FCF/(WACC − g) = $480.0/10.56% = $4,545.45
o
You plan to invest in one of two home delivery pizza companies, High and Low, that were recently founded and are about to commence operations. They are identical except for their use of debt (wd) and the interest rates on their debt—High uses more debt and thus must pay a higher interest rate. Based on the data given below, how much higher or lower will High's expected EPS be versus that of Low, i.e., what is EPSHigh − EPSLow?
Applicable to Both Firms
Firm High's Data
Firm Low's Data
Capital
$3,000,000 wd
70%
wd
20%
EBIT
$500,000
90,000
Shares
240,000
Shares
Tax rate 35%
Int. rate
12%
Int. rate
10%
a. $0.49 b. $0.54 c. $0.60 d. $0.66 e. $0.73
ANSWER: c RATIONALE: Applicable to Both Firms Data Firm Low's Data
Firm High's
Capital
$3,000,000 wd
70%
wd
20%
EBIT
$500,000
90,000
Shares
240,000
Tax rate 35%
Shares
Int. rate 12% Debt
Int. rate 10%
$2,100,000 Debt
$600,000
EBIT
$500,000
$500,000
Interest = I = Debt × rate
252,000
60,000
Taxable income = EBIT − I
$248,000
$440,000
86,800
154,000
$161,200
$286,000
Taxes NI
EPS = NI/Shares outstanding
$1.79
$1.19
Difference in EPS = $0.60
o
Firms HD and LD are identical except for their use of debt and the interest rates they pay HD has more debt and thus must pay a higher interest Based on the data given below, how much higher or lower will HD's ROE be versus that of LD, i.e., what is ROEHD − ROELD?
Applicable to Both Firms
Firm HD's Data
Firm LD's Data
Capital
$3,000,000 wd
70%
wd
20%
EBIT
$500,000
12%
Int. rate
10%
Tax rate
35%
Int. rate
a. 5.41% b. 5.69% c. 5.99% d. 6.29% e. 6.61% ANSWER: c RATIONALE: Applicable to Both Firms D's Data
Firm HD's Data
Capital
wd
$3,000,000 wd 70%
20%
Firm L
EBIT rate
$500,000 Int.
Tax rate
35% Debt
12%
Int. rate
10%
$2,100,000 Debt
$600,000
EBIT
$500,000
$500,000
Interest = I = Debt × Rate
252,000
60,000
Taxable income = EBIT − I
$248,000
$440,000
86,800
154,000
NI
$161,200
$286,000
Equity = (1 − wd)(Capital)
$900,000
$400,000
ROE = NI/Equity
17.91%
11.92%
Taxes
Difference in ROEs = 5.99%
o
Firm A is very aggressive in its use of debt to leverage up its earnings for common stockholders, whereas Firm NA is not aggressive and uses no debt. The two firms' operations are identical they have the same total investor-supplied capital, sales, operating costs, and EBIT. Thus, they differ only in their use of financial leverage (wd). Based on the following data, how much higher or lower is A's ROE than that of NA, i.e., what is ROEA − ROENA?
Applicable to Both Firms Capital
$150,000
wd
Firm A's Data 50%
wd
Firm NA's Data 0%
EBIT
$40,000
Int. rate
12%
Int. rate
10%
Tax rate 35%
o
8.60%
o
9.06%
o
9.53%
o
10.01%
o
10.51%
ANSWER: RATIONALE: NA's Data
c Applicable to Both Firms
Capital EBIT Tax rate
$150,000 $40,000 35%
wd
Int. rate Debt
EBIT
Firm A's Data
50% 12% $75,000 $40,000
Interest = I = Debt × Rate
9,000
Taxable income = EBIT − I
$31,000
Taxes NI = (Taxable Income)(1 − T) Equity = (1 − wd)(Capital) ROE = NI/Equity
10,850 $20,150 $75,000 26.87%
Firm
wd
0%
Int. rate
10%
Debt
$0
$40,000 0 $40,000 14,000 $26,000 $150,000 17.33%
Difference in ROEs = 9.53%
o
Your firm's debt ratio is only 5.00%, but the new CFO thinks that more debt should be employed. She wants to sell bonds and use the proceeds to buy back and retire common shares so the percentage of common equity in the capital structure (wc) = 1 − wd. Other things held constant, and based on the data below, if the firm increases the percentage of debt in its capital structure (wd) to 60.0%, by how much would the ROE change, i.e., what is ROENew − ROEOld?
Operating Data Capital
$150,000
ROIC = EBIT(1 − T)/Capital rate
Other Data
13.00%
Old wd
5%
Old interest
10%
Tax rate
35%
New wd New interest rate
o
6.73%
o
7.09%
o
7.46%
o
7.83%
o
8.22%
ANSWER:
c
60% 12%
RATIONALE:
Operating Data
Capital wd
$150,000 60%
ROIC = EBIT(1 − T)/Capital Tax rate rate
Other Data
New
13.00% 35% 12%
Old wd
5%
New interest
Old interest rate
10%
New wd wd Debt
$90,000
EBIT = (ROIC × Capital)/(1 – T)
$30,000
Interest = Rate × Debt
10,800
Taxable income = EBIT – I
$19,200
$7,500 $30,000 750 $29,250
Taxes
6,720
NI
$12,480
$19,013
Equity = (1 − wd)(Capital)
$60,000
$142,500
ROE = NI/Equity
Difference in ROEs = 7.46%
20.80%
10,238
13.34%
Old
o
You have been hired by a new firm that is just being The CFO wants to finance with 60% debt, but the president thinks it would be better to hold the percentage of debt in the capital structure (wd) to only 10%. Other things held constant, and based on the data below, if the firm uses more debt, by how much would the ROE change, i.e., what is ROENew − ROEOld?
Operating Data
Other Data
Capital
$4,000
ROIC = EBIT(1 − T)/Capital
13.00%
rate
Higher wd
60%
Higher interest
13%
Tax rate
35%
Lower wd
10%
Lower interest rate
o
5.44%
o
5.73%
o
6.03%
o
6.33%
o
6.65%
ANSWER: RATIONALE:
9%
c Operating Data
Capital
$4,000
ROIC = EBIT(1 − T)/Capital
13.00%
Other Data
Higher wd New interest rate
60% 13%
Tax rate
35%
Lower wd
10%
Old interest rate
Lower wd Debt
9%
Higher wd
$400
$2,400
EBIT = (ROIC × Capital)/(1 − T)
$800.00
$800.00
Interest = Rate × Debt
36.00
312.00
Taxable income = EBIT − I
$764.00
Taxes
$488.00
267.40 170.80
NI
$496.60
$317.20
Equity = (1 − wd)(Capital) ROE = NI/Equity %
$3,600.00
13.79%
$1,600.00
19.83
Difference in ROEs = 6.03%
o
Your girlfriend plans to start a new company to make a new type of cat Her father will finance the operation, but she will have to pay him back. You are helping her, and the issue now is how to finance the company,
with equity only or with a mix of debt and equity. The price per unit will be $10.00 regardless of how the firm is financed. The expected fixed and variable operating costs, along with other information, are shown below. How much higher or lower will the firm's expected EPS be if it uses some debt rather than only equity, i.e., what is EPSL− EPSU?
0% Debt, U
60% Debt, L
Expected unit sales
225,000
225,000
Price per unit
$10.00
$10.00
Fixed costs
$1,000,000
$1,000,000
Variable cost/unit
$3.50
$3.50
Required investment
$2,500,000
$2,500,000
Shares issued at $10/share
250,000
100,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
o
$0.54
o
$0.60
o
$0.67
o
$0.75
o
$0.83
ANSWER:
e
RATIONALE:
sales
0% Debt, U Expected unit 225,000
60% Debt, L
225,000
Price per unit
$10.00
$10.00
costs
Fixed operating $1,000,000
$1,000,000
cost/unit
Variable operating $3.50
$3.50
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
equity
$ of common $2,500,000
$10/share
Shares of stock issued at 250,000 100,000 Interest rate Tax rate
$1,000,000
NA
10.00%
35.00%
35.00%
Sales revenues
$2,250,000
$2,250,000
1,000,000
1,000,000
Fixed costs Variable costs
787,500
787,500
Operating income
$ 462,500
$ 462,500
Interest
0
150,000
Taxable income
$ 462,500
$ 312,500
Taxes
161,875
109,375
Net income
$ 300,625 Earnings per share $1.20
(EPS)
$ 203,125
$2.03
Difference in EPS = $0.83 o
Southeast U's campus book store sells course packs for $15.00 each, the variable cost per pack is $11.00, fixed costs for this operation are $300,000, and annual sales are 100,000 The unit variable cost consists of a $4.00 royalty payment, VR, per pack to professors plus other variable costs of VO = $7.00. The royalty payment is negotiable. The book store's directors believe that the store should earn a profit margin of 10% on sales, and they want the store's managers to pay a royalty rate that will produce that profit margin. What royalty per pack would permit the store to earn a 10% profit margin on course packs, other things held constant?
o
$2.55
o
$2.84
o
$3.15
o
$3.50
o
$3.85
d Sales price (P) $15.00 Target profit margin
10%
Current royalty component of variable costs (VR)
$4.00
Other variable costs (VO)
7.00
Total variable costs (V)
$11.00
Annual sales (Q)
100,000
Fixed costs (F)
$300,000
ANSWER: RATIONALE:
Current profit = PQ − VRQ − VOQ − F = $1,500,000 − $400,000 − $700,000 − $300,000 = $100,000
Target profit (TP) = 0.10(PQ) = $150,000 Target profit (TP) = PQ − VR Q − VO Q − F = 0.10(PQ) = $150,000 Target VR = P − 0.1P − VO − F/Q = 0.9P − VO − F/Q = $3.50
Check: Profit with VR = P × Q − VR × Q − VO × Q − FC = 10% of Sales = $1,500,000 − $350,000 − $700,000 − $300,000 = $150,000
o
Dye Industries currently uses no debt, but its new CFO is considering changing the capital structure to 0% debt (wd) by issuing bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity in the capital structure (wc) = 1 − wd. Given the data shown below, by how much would this recapitalization change the firm's cost of equity, i.e., what is rL − rU?
Risk-free rate, rRF
6.00%
Market risk , RPM 4.00%
Tax rate, T
40%
Current wd
0%
Current beta, bU
1.15
Target wd
40%
a. 1.66% b. 1.84% c. 2.02% d. 2.23% e. 2.45% ANSWER:
b
RATIONALE: Risk-free rate, rRF T Market risk , RPM wd
6.00% Tax rate, 40% 4.00% Current 0%
Current beta, bU wd
1.15 Target 40%
Target D/E = wd/(1 − wd)
0.67
bL = bU[(1 + (D/E)(1 − T)]
1.61
rsU = rRF + bU(RPM )
10.60%
r sL = rRF + bL(RPM ) 12.44% Change in equity cost = 1.84%
o
Dyson currently finances with 20.0% debt (i.e., wd = 20%), but its new CFO is considering changing the capital structure so wd = 60.0% by issuing additional bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity in the capital structure (wc) = 1 − wd. Given the data shown below, by how much would this recapitalization change the firm's cost of equity? (Hint: You must unlever the current beta and then use the unlevered beta to solve the problem.)
Risk-free rate, rRF
5.00% Tax rate, T
40%
Market risk , RPM
6.00% Current wd
20%
Current beta, bL1
1.15
Target wd
60%
RATIONALE: Risk-free rate, rRF
5.00%
Tax rate, T
40%
Market risk , RPM
6.00%
Current wd
20%
Current beta, bL1
1.15
a. 4.05% b. 4.50% c. 4.95% d. 5.45% e. 5.99% ANSWER:
b
Current D/E = wd/(1 − wd)
Target wd
60%
0.25
Target D/E using target wd = wd/(1 − wd)
1.50
Unleveraged beta: Found with current data: bU = bL1/[1 + (1 − T)(D/E)]
1.00
Beta at new capital structure = bL2 = bU[(1 + (D/E)(1 − T)]
1.900
Original cost of equity = rsL1 = rRF + bL1(RPM ) 11.90% New cost of equity = rsL2 = rRF + bL2(RPM ) 16.40% Change in equity cost = 4.50%
o
Monroe Inc. is an all-equity firm with 500,000 shares outstanding. It has $2,000,000 of EBIT, and EBIT is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per shares (DPS), and its tax rate is 40%. The company is considering issuing $5,000,000 of 9.00% bonds and using the proceeds to repurchase stock. The risk-free rate is 4.5%, the market risk is 5.0%, and the firm's beta is currently 0.90. However, the CFO believes the beta would rise to 1.10 if the recapitalization occurs. Assuming the shares could be repurchased at the price that existed prior to the recapitalization, what would the price per share be following the recapitalization? (Hint: P0 = EPS/rs because EPS = DPS.)
o
$28.27
o
$29.76
o
$31.25
o
$32.81
o
$34.45
ANSWER: b
RATIONALE: Interest rate initially 500,000
rRF
9%
Risk-free rate, 4.5% EBIT
Shares outstanding
$2,000,000
Market risk , RPM
5.0%
Dividend payout ratio
Beta, before recap
0.90
Tax rate
Beta, after recap
1.10
Bonds issued = stock
40%
repurchased
$5,000,000
Before the recapitalization DPS = EPS = (EBIT)(1 − T)/Shares $2.40 rs = rRF + bold(RPM )
9.00%
P0 = DPS/rs
$26.67
Shares repurchased = Bonds issued/P0
187,500
After the recapitalization DPS = EPS = (EBIT − rd × Bonds)(1 − T)/Shares $2.98 rs = rRF + bNew(RPM )
100%
10.00%
P0 = DPS/rs
o
$29.76
You were hired as the CFO of a new company that was founded by three professors at your university. The company plans to manufacture and sell a new product, a cell phone that can be worn like a wrist watch. The issue now is how to finance the company, with equity only or with a mix of debt and equity. The price per phone will be $250.00 regardless of how the firm is financed. The expected fixed and variable operating costs, along with other data, are shown below. How much higher or lower will the firm's expected ROE be if it uses 60% debt rather than only equity, i.e., what is ROEL − ROEU?
0% Debt, U
60% Debt, L
Expected unit sales (Q)
28,500
28,500
Price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$1,000,000
Variable cost/unit (V)
$200.00
$200.00
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
o
5.68%
o
5.94%
o
6.22%
o
6.52%
o
6.83%
e 0% Debt, U
60% Debt, L
Expected unit sales
28,500
28,500
Price per phone
$250.00
$250.00
Fixed operating costs
$1,000,000
$1,000,000
Variable operating cost/unit
$200.00
$200.00
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
Sales revenues
$7,125,000
$7,125,000
Fixed costs
1,000,000
Variable costs
5,700,000
5,700,000
Operating income
$ 425,000
$ 425,000
Interest Taxable income Taxes
0 $ 425,000 148,750
1,000,000
150,000 $ 275,000 96,250
Net income
$ 276,250
$ 178,750
ROE
11.05%
17.88%
Difference in ROEs = 6.83%
ANSWER: RATIONALE:
o
A firm's business risk is largely determined by the financial characteristics of its industry, especially by the amount of debt the average firm in the industry uses. o
True
o
False
ANSWER: False
o
Financial risk refers to the extra risk borne by stockholders as a result of a firm's use of debt as compared with their risk if the firm had used no debt. o
True
o
False
ANSWER: True
o
A firm's capital structure does not affect its free cash flows as discussed in the text, because FCF reflects only operating cash flows, which are available to service debt, to pay dividends to stockholders, and for other purposes. o
True
o
False
ANSWER: True
o
If a firm borrows money, it is using financial leverage. o
True
o
False
ANSWER: True
o
Other things held constant, an increase in financial leverage will increase a firm's market (or systematic) risk as measured by its beta coefficient. o
True
o
False
ANSWER: True
o
The graphical probability distribution of ROE for a firm that uses financial leverage would tend to be more peaked than the distribution if the firm used no leverage, other things held constant. o
True
o
False
ANSWER: False
o
Provided a firm does not use an extreme amount of debt, operating leverage typically affects only EPS, while financial leverage affects both EPS and EBIT. o
True
o
False
ANSWER: False o
The trade-off theory states that capital structure decisions involve a tradeoff between the costs and benefits of debt financing. o
True
o
False
ANSWER: True
o
Different borrowers have different risks of bankruptcy, and if a borrower goes bankrupt, its lenders will probably not get back the full amount of funds that they loaned. Therefore, lenders charge higher rates to borrowers judged to be more likely to go bankrupt. o
True
o
False
ANSWER: True
o
Modigliani and Miller (MM) won Nobel Prizes for their work on capital structure theory. o
True
o
False
ANSWER: True
o
Modigliani and Miller's first article led to the conclusion that capital structure is "irrelevant" because it has no effect on a firm's value. o
True
o
False
ANSWER: True
o
Modigliani and Miller's first article led to the conclusion that capital structure is extremely important, and that every firm has an optimal capital structure that maximizes its value and minimizes its cost of capital. o
True
o
False
ANSWER: False
o
It is possible for Firms A and B to have identical financial and operating leverage, yet for Firm A to have more risk as measured by the variability of EPS. This would occur if Firm A has more business risk than Firm B. o
True
o
False
ANSWER:
True
RATIONALE: If Firm A's sales are more volatile than those of Firm B, then A would have greater EPS variability in spite of identical financial and operating leverage. Operating leverage is only one factor that affects business risk. o
As the text indicates, a firm's financial risk can and should be divided into separate market and diversifiable risk components. o
True
o
False
ANSWER: False
o
If two firms have the same expected earnings per share (EPS) and the same standard deviation of expected EPS, then they must have the same amount of business risk. o
True
o
False
ANSWER: False
o
In a world with no taxes, Modigliani and Miller (MM) show that a firm's capital structure does not affect its value. However, when taxes are considered, MM show a positive relationship between debt and value, i.e., the firm's value rises as it uses more and more debt, other things held constant. o
True
o
False
ANSWER: True
o
According to Modigliani and Miller (MM), in a world without taxes the optimal capital structure for a firm is approximately 100% debt financing. o
True
o
False
ANSWER: False
o
According to Modigliani and Miller (MM), in a world with corporate income taxes the optimal capital structure calls for approximately 100% debt financing. o
True
o
False
ANSWER: True
o
According to Modigliani and Miller (MM), in a world without corporate income taxes the use of debt has no effect on the firm's value. o
True
o
False
ANSWER: True
o
Modigliani and Miller's first article led to the conclusion that capital structure is "irrelevant" because it has no effect on a firm's value. However, that article was criticized because it assumed that no taxes existed. MM then revised their original article to include corporate taxes, and this model led to the conclusion that a firm's value would be maximized if it used (almost) 100% debt. o
True
o
False
ANSWER: True o
Modigliani and Miller's second article, which assumed the existence of corporate income taxes, led to the conclusion that a firm's value would be maximized, and its cost of capital minimized, if it used (almost) 100% debt. However, this model did not take of bankruptcy costs. The existence of bankruptcy costs leads to the assumption of an optimal capital structure where the debt ratio is less than 100%. o
True
o
False
ANSWER: True
o
The Miller model begins with the Modigliani and Miller (MM) model with corporate taxes and then adds personal taxes. o
True
o
False
ANSWER: True
o
The Miller model begins with the Modigliani and Miller (MM) model without corporate taxes and then adds personal taxes. o
True
o
False
ANSWER: False
o
The Modigliani and Miller (MM) articles implicitly assumed that bankruptcy did not exist. That led to the development of the "trade-off" model, where the firm's value first rises with the use of debt due to the tax shelter of debt, but later falls as more debt is added because the potential costs of bankruptcy begin to more than offset the tax shelter benefits. Under the trade-off theory, an optimal capital structure exists. o
True
o
False
ANSWER: True
o
Modigliani and Miller (MM), in their second article, took of taxes, bankruptcy, and other factors that were assumed away in their original article. Once they took of all these assumptions, they concluded that every firm has a unique optimal capital structure. Moreover, a manager can use the second MM model to determine his or her firm's optimal debt ratio. o
True
o
False
ANSWER: False
o
Some people—including the former chairman of the Federal Reserve Board of Governors (Ben Bernanke)—have argued that one advantage of corporate debt from the stockholders' standpoint is that the existence of debt forces managers to focus on cash flow and to refrain from spending too much of the firm's money on private plane and other "perks." This is one of the factors that led to the rise of LBOs and private equity firms. o
True
o
False
ANSWER: True
o
The Modigliani and Miller (MM) articles implicitly assumed, among other things, that outside stockholders have the same information about a firm's future prospects as its managers. That was called "symmetric information," and it is questionable. The introduction of "asymmetric information" led to the development of the "signaling" theory of capital structure, which postulated that firms are reluctant to issue new stock because investors will interpret such an act as a signal that the firm's managers are worried about its future. Other actions give off different signals, and the end result is that capital structure is affected by managers' perceptions about how their financing decisions will affect investors' views of the firm and thus its value. o
True
o
False
ANSWER: True
o
According to the signaling theory of capital structure, firms first use common equity for their capital, then use debt if and only if they can raise no more equity on "reasonable" . This occurs because the use of debt financing signals to investors that the firm's managers think that the future does not look good. o
True
o
False
ANSWER: False
o
Other things held constant, firms with more stable and predictable sales tend to use more debt than firms with less stable sales. o
True
o
False
ANSWER: True
o
Other things held constant, firms that use assets that can be sold easily (like trucks) tend to use more debt than firms whose assets are harder to sell (like those engaged in research and development). o
True
o
False
ANSWER: True
o
Other things held constant, the lower a firm's tax rate, the more logical it is for the firm to use debt. o
True
o
False
ANSWER:
False
RATIONALE: This is false. The lower the tax rate, the less valuable the tax shelter from debt. Think about the cost of debt in the WACC: rd(1 − T). If T is low, then the cost of debt is not reduced as much as when T is high.
o
A firm's treasurer likes to be in a position to raise funds to operations whenever such funds are needed, even in "bad times." This is called "financial flexibility," and the lower the firm's debt ratio, the greater its financial flexibility, other things held constant. o
True
o
False
ANSWER:
True
RATIONALE: This is true, because if times are bad which is when financial flexibility is important investors are much more willing to lend a firm money than to buy its stock, because if the firm fails, debt holders are first in line to get their money back.
o
If a firm utilizes debt financing, a 10% decline in earnings before interest and taxes (EBIT) will result in a decline in earnings per share that is larger than 10%, and the higher the debt ratio, the larger this difference will be. o
True
o
False
ANSWER: True
o
An increase in the debt ratio will generally have no effect on which of these items? o
Business risk.
o
Total risk.
o
Financial risk.
o
Market risk.
o
The firm's beta.
ANSWER: a
o
Business risk is affected by a firm's operations. Which of the following is NOT directly associated with (or does not directly contribute to) business risk? o
Demand variability.
o
Sales price variability.
o
The extent to which operating costs are fixed.
o
The extent to which interest rates on the firm's debt fluctuate.
o
Input price variability.
ANSWER: d
o
Which of the following statements is CORRECT? o
Since debt financing raises the firm's financial risk, increasing the target debt ratio will always increase the WACC.
o
Since debt financing is cheaper than equity financing, raising a company's debt ratio will always reduce its WACC.
o
Increasing a company's debt ratio will typically reduce the marginal costs of both debt and equity financing. However, this action still may raise the company's WACC.
o
Increasing a company's debt ratio will typically increase the marginal costs of both debt and equity financing. However, this action still may lower the company's WACC.
o
Since a firm's beta coefficient is not affected by its use of financial leverage, leverage does not affect the cost of equity.
ANSWER: d o
Which of the following statements is CORRECT? o
The capital structure that maximizes expected EPS also maximizes the price per share of common stock.
o
The capital structure that minimizes the interest rate on debt also maximizes the expected EPS.
o
The capital structure that minimizes the required return on equity also maximizes the stock price.
o
The capital structure that minimizes the WACC also maximizes the price per share of common stock.
o
The capital structure that gives the firm the best bond rating also maximizes the stock price.
ANSWER: d
o
Based on the information below, what is the firm's optimal capital structure? o
Debt = 40%; Equity = 60%; EPS = $2.95; Stock price = $26.50.
o
Debt = 50%; Equity = 50%; EPS = $3.05; Stock price = $28.90.
o
Debt = 60%; Equity = 40%; EPS = $3.18; Stock price = $31.20.
o
Debt = 80%; Equity = 20%; EPS = $3.42; Stock price = $30.40.
o
Debt = 70%; Equity = 30%; EPS = $3.31; Stock price = $30.00.
ANSWER: c
o
Which of the following statements best describes the optimal capital structure? o
The optimal capital structure is the mix of debt, equity, and preferred stock that maximizes the company's earnings per share (EPS).
o
The optimal capital structure is the mix of debt, equity, and preferred stock that maximizes the company's stock price.
o
The optimal capital structure is the mix of debt, equity, and preferred stock that minimizes the company's cost of equity.
o
The optimal capital structure is the mix of debt, equity, and preferred stock that minimizes the company's cost of debt.
o
The optimal capital structure is the mix of debt, equity, and preferred stock that minimizes the company's cost of preferred stock.
ANSWER: b
o
Which of the following events is likely to encourage a company to raise its target debt ratio, other things held constant? o
An increase in the corporate tax rate.
o
An increase in the personal tax rate.
o
An increase in the company's operating leverage.
o
The Federal Reserve tightens interest rates in an effort to fight inflation.
o
The company's stock price hits a new high.
ANSWER: a
o
Which of the following would tend to increase a firm's target debt ratio, other things held constant? o
The costs associated with filing for bankruptcy increase.
o
The corporate tax rate is increased.
o
The personal tax rate is increased.
o
The Federal Reserve tightens interest rates in an effort to fight inflation.
o
The company's stock price hits a new low.
ANSWER: b
o
Which of the following statements is CORRECT? o
As a rule, the optimal capital structure is found by determining the debt-equity mix that maximizes expected EPS.
o
The optimal capital structure simultaneously maximizes EPS and minimizes the WACC.
o
The optimal capital structure minimizes the cost of equity, which is a necessary condition for maximizing the stock price.
o
The optimal capital structure simultaneously minimizes the cost of debt, the cost of equity, and the WACC.
o
The optimal capital structure simultaneously maximizes the stock price and minimizes the WACC.
ANSWER: e
o
The firm's target capital structure should do which of the following? o
Maximize the earnings per share (EPS).
o
Minimize the cost of debt (rd).
o
Obtain the highest possible bond rating.
o
Minimize the cost of equity (rs).
o
Minimize the weighted average cost of capital (WACC).
ANSWER: e
o
Which of the following statements is CORRECT? o
A firm's business risk is determined solely by the financial characteristics of its industry.
o
The factors that affect a firm's business risk include industry characteristics and economic conditions, both of which are generally beyond the firm's control.
o
One of the benefits to a firm of being at or near its target capital structure is that this generally minimizes the risk of bankruptcy.
o
A firm's financial risk can be minimized by diversification.
o
The amount of debt in its capital structure can under no circumstances affect a company's EBIT and business risk.
ANSWER: b
o
Which of the following statements is CORRECT? As a firm increases the operating leverage used to produce a given quantity of output, this o
normally leads to an increase in its fixed assets turnover ratio.
o
normally leads to a decrease in its business risk.
o
normally leads to a decrease in the standard deviation of its expected EBIT.
o
normally leads to a decrease in the variability of its expected EPS.
o
ANSWER:
normally leads to a reduction in its fixed assets turnover ratio.
e
RATIONALE: More operating leverage generally means a greater use of automation, which means more fixed assets. If fixed assets increase proportionately more than sales, then the fixed assets turnover (S/FA) will decline. o
A firm's CFO is considering increasing the target debt ratio, which would also increase the company's interest expense. New bonds would be issued and the proceeds would be used to buy back shares of common stock. Neither total assets nor operating income would change, but expected earnings per share (EPS) would increase. Assuming the CFO's estimates are correct, which of the following statements is CORRECT? o
Since the proposed plan increases the firm's financial risk, the stock price might fall even if EPS increases.
o
If the plan reduces the WACC, the stock price is likely to decline.
o
Since the plan is expected to increase EPS, this implies that net income is also expected to increase.
o
If the plan does increase the EPS, the stock price will automatically increase at the same rate.
o
Under the plan there will be more bonds outstanding, and that will increase their liquidity and thus lower the interest rate on the currently outstanding bonds.
ANSWER: a
o
Which of the following statements is CORRECT?
o
Increasing its use of financial leverage is one way to increase a firm's return on investors' capital (ROIC).
o
If a firm lowered its fixed costs but increased its variable costs by just enough to hold total costs at the present level of sales constant, this would increase its operating leverage.
o
The debt ratio that maximizes expected EPS generally exceeds the debt ratio that maximizes share price.
o
If a company were to issue debt and use the money to repurchase common stock, this would reduce its return on investors' capital (ROIC). (Assume that the repurchase has no impact on the company's operating income.)
o
If a change in the bankruptcy code made bankruptcy less costly to corporations, this would tend to reduce corporations' debt ratios.
ANSWER: c
o
Your firm has $500 million of investor-supplied capital, its return on investors' capital (ROIC) is 15%, and it currently has no debt in its capital structure (i.e., wd = 0). The CFO is contemplating a recapitalization where it would issue debt at an after-tax cost of 10% and use the proceeds to buy back some of its common stock, such that the percentage of common equity in the capital structure (wc) is 1 − wd. If the company goes ahead with the recapitalization, its operating income, the size of the firm (i.e., total assets), total investor-supplied capital, and tax rate would remain unchanged. Which of the following is most likely to occur as a result of the recapitalization? o
The ROA would increase.
o
The ROA would remain unchanged.
o
The return on investors' capital would decline.
o
The return on investors' capital would increase.
o
The ROE would increase.
ANSWER: e
o
Companies HD and LD have identical tax rates, total assets, total investor-supplied capital, and returns on investors' capital (ROIC), and their ROICs exceed their after-tax costs of debt, rd(1 − T). However, Company HD has a higher debt ratio and thus more interest expense than Company LD. Which of the following statements is CORRECT? o
Company HD has a higher net income than Company LD.
o
Company HD has a lower ROA than Company LD.
o
Company HD has a lower ROE than Company LD.
o
The two companies have the same ROA.
o
The two companies have the same ROE.
ANSWER: b
o
Firms U and L each have the same amount of assets, investor-supplied capital, and both have a return on investors' capital (ROIC) of 12%. Firm U is unleveraged, i.e., it is 100% equity financed, while Firm L is financed with 50% debt and 50% equity. Firm L's debt has an after-tax cost of 8%. Both firms have positive net income and a 35% tax rate. Which of the following statements is CORRECT? o
The two companies have the same times interest earned (TIE) ratio.
o
Firm L has a lower ROA than Firm U.
o
Firm L has a lower ROE than Firm U.
o
Firm L has the higher times interest earned (TIE) ratio.
o
Firm L has a higher EBIT than Firm U.
ANSWER: b
o
Your firm is currently 100% equity financed. The CFO is considering a recapitalization plan under which the firm would issue long-term debt with an after-tax yield of 9% and use the proceeds to repurchase some of its common stock. The recapitalization would not change the company's total investor-supplied capital, the size of the firm (i.e., total assets), and it would not affect the firm's return on investors' capital (ROIC), which is 15%. The CFO believes that this recapitalization would reduce the firm's WACC and increase its stock price. Which of the following would be likely to occur if the company goes ahead with the recapitalization plan? o
The company's net income would increase.
o
The company's earnings per share would decline.
o
The company's cost of equity would increase.
o
The company's ROA would increase.
o
The company's ROE would decline.
ANSWER: c
o
A major contribution of the Miller model is that it demonstrates, other things held constant, that o
personal taxes increase the value of using corporate debt.
o
personal taxes lower the value of using corporate debt.
o
personal taxes have no effect on the value of using corporate debt.
o
financial distress and agency costs reduce the value of using corporate debt.
o
debt costs increase with financial leverage.
ANSWER: b
o
Which of the following statements is CORRECT, holding other things constant? o
Firms whose assets are relatively liquid tend to have relatively low bankruptcy costs, hence they tend to use relatively little debt.
o
An increase in the personal tax rate is likely to increase the debt ratio of the average corporation.
o
If changes in the bankruptcy code make bankruptcy less costly to corporations, then this would likely lead to lower debt ratios for corporations.
o
An increase in the company's degree of operating leverage would tend to encourage the firm to use more debt in its capital structure so as to keep its total risk unchanged.
o
An increase in the corporate tax rate would in theory encourage companies to use more debt in their capital structures.
ANSWER: e
o
Other things held constant, which of the following events would be most likely to encourage a firm to increase the amount of debt in its capital structure? o
Its sales are projected to become less stable in the future.
o
The bankruptcy laws are changed in a way that would make bankruptcy more costly to the firm and its stockholders.
o
Management believes that the firm's stock is currently overvalued.
o
The firm decides to automate its factory with specialized equipment and thus increase its use of operating leverage.
o
The corporate tax rate is increased.
ANSWER: e o
Which of the following statements is CORRECT? o
A firm can use retained earnings without paying a flotation cost. Therefore, while the cost of retained earnings is not zero, its cost is generally lower than the after-tax cost of debt.
o
The capital structure that minimizes a firm's weighted average cost of capital is also the capital structure that maximizes its stock price.
o
The capital structure that minimizes the firm's weighted average cost of capital is also the capital structure that maximizes its earnings per share.
o
If a firm finds that the cost of debt is less than the cost of equity, increasing its debt ratio must reduce its WACC.
o
Other things held constant, if corporate tax rates declined, then the Modigliani-Miller tax-adjusted theory would suggest that firms should increase their use of debt.
ANSWER: b
o
Which of the following statements is CORRECT? o
The capital structure that maximizes the stock price is also the capital structure that minimizes the cost of equity from retained earnings (rs).
o
The capital structure that maximizes the stock price is also the capital structure that maximizes earnings per share.
o
The capital structure that maximizes the stock price is also the capital structure that maximizes the firm's times interest earned (TIE) ratio.
o
If a company increases its debt ratio, this will typically increase the marginal costs of both debt and equity, but it still may reduce the company's WACC.
o
If Congress were to legislation that increases the personal tax rate but decreases the corporate tax rate, this would encourage companies to increase their debt ratios.
ANSWER: d
o
Which of the following statements is CORRECT? o
In general, a firm with low operating leverage also has a small proportion of its total costs in the form of fixed costs.
o
There is no reason to think that changes in the personal tax rate would affect firms' capital structure decisions.
o
A firm with a relatively high business risk is more likely to increase its use of financial leverage than a firm with low business risk, assuming all else equal.
o
If a firm's after-tax cost of equity exceeds its after-tax cost of debt, it can always reduce its WACC by increasing its use of debt.
o
Suppose a firm has less than its optimal amount of debt. Increasing its use of debt to the point where it is at its optimal capital structure will decrease the costs of both debt and equity.
ANSWER: a
o
Companies HD and LD have identical amounts of assets, investorsupplied capital, operating income (EBIT), tax rates, and business risk. Company HD, however, has a higher debt ratio than LD. Company HD's return on investors' capital (ROIC) exceeds its after-tax cost of debt, rd(1 − T). Which of the following statements is CORRECT? o
Company HD has a higher return on assets (ROA) than Company LD.
o
Company HD has a higher times interest earned (TIE) ratio than Company LD.
o
Company HD has a higher return on equity (ROE) than Company LD, and its risk as measured by the standard deviation of ROE is also higher than LD's.
o
The two companies have the same ROE.
o
Company HD's ROE would be higher if it had no debt.
ANSWER: c
o
Companies HD and LD have the same total assets, total investor-supplied capital, operating income (EBIT), tax rate, and business risk. Company HD, however, has a much higher debt ratio than LD. Also, both companies' returns on investors' capital (ROIC) exceed their after-tax costs of debt, rd(1 − T). Which of the following statements is CORRECT? o
HD should have a higher return on assets (ROA) than LD.
o
HD should have a higher times interest earned (TIE) ratio than LD.
o
HD should have a higher return on equity (ROE) than LD, but its risk, as measured by the standard deviation of ROE, should also be higher than LD's.
o
Given that ROIC > rd(1 − T), HD's stock price must exceed that of LD.
o
Given that ROIC > rd(1 − T), LD's stock price must exceed that of HD.
ANSWER: c
o
Which of the following statements is CORRECT? o
If Congress lowered corporate tax rates while other things were held constant, and if the Modigliani-Miller tax-adjusted theory of capital structure were correct, this would tend to cause corporations to decrease their use of debt.
o
A change in the personal tax rate should not affect firms' capital structure decisions.
o
"Business risk" is differentiated from "financial risk" by the fact that financial risk reflects only the use of debt, while business risk reflects both the use of debt and such factors as sales variability, cost variability, and operating leverage.
o
The optimal capital structure is the one that simultaneously (1) maximizes the price of the firm's stock, (2) minimizes its WACC, and (3) maximizes its EPS.
o
If changes in the bankruptcy code made bankruptcy less costly to corporations, this would likely reduce the average corporation's debt ratio.
ANSWER: a
o
Which of the following statements is CORRECT? o
When a company increases its debt ratio, the costs of equity and debt both increase. Therefore, the WACC must also increase.
o
The capital structure that maximizes the stock price is generally the capital structure that also maximizes earnings per share.
o
All else equal, an increase in the corporate tax rate would tend to encourage companies to increase their debt ratios.
o
Since debt financing raises the firm's financial risk, increasing a company's debt ratio will always increase its WACC.
o
Since the cost of debt is generally fixed, increasing the debt ratio tends to stabilize net income.
ANSWER: c
o
Which of the following statements is CORRECT? o
Generally, debt ratios do not vary much among different industries, although they do vary among firms within a given industry.
o
Electric utilities generally have very high common equity ratios because their revenues are more volatile than those of firms in most other industries.
o
Airline companies tend to have very volatile earnings, and as a result they generally have high target debt-to- equity ratios.
o
Wide variations in capital structures exist both between industries and among individual firms within given industries. These differences are caused by differing business risks and also managerial attitudes.
o
Since most stocks sell at or very close to their book values, book value capital structures are typically adequate for use in estimating firms' weighted average costs of capital.
ANSWER: d
o
Longstreet Inc. has fixed operating costs of $470,000, variable costs of $2.80 per unit produced, and its product sells for $4.00 per unit. What is the company's break-even point, i.e., at what unit sales volume would income equal costs?
o
391,667
o
411,250
o
431,813
o
453,403
o
476,073
ANSWER:
a
RATIONALE: Fixed operating costs (F)
$470,000
Variable costs per unit (V)
$2.80
Sales price per unit (P)
$4.00
QBE = F/(P − V) = 391,667
o
Your uncle is considering investing in a new company that will produce high quality stereo speakers. The sales price would be set at 1.5 times the variable cost per unit; the variable cost per unit is estimated to be $75.00; and fixed costs are estimated at $1,200,000. What sales volume would be required to break even, i.e., to have EBIT = zero?
o
28,880
o
30,400
o
32,000
o
33,600
o
35,280
ANSWER:
c
RATIONALE: Variable costs per unit (V)
$75.00
Price multiple over VC
1.50
Sales price per unit (P)
$112.50
Fixed costs (F) $1,200,000 QBE = F/(P − V) = 32,000
o
Southwest U's campus book store sells course packs for $15 each, the variable cost per pack is $9, fixed costs to produce the packs are $200,000, and expected annual sales are 50,000 What are the pre-tax profits from sales of course packs?
o
$ 72,900
o
$ 81,000
o
$ 90,000
o
$100,000
o
e. $110,000
ANSWER:
d
RATIONALE: Sales price per unit (P)
$15.00
Variable costs per unit (V) Annual sales (Q) Fixed costs (F)
$9.00 50,000 $200,000
Profit = PQ − VQ − F = EBIT = $750,000 − $450,000 − $200,000 = $100,000
o
Southwest U's campus book store sells course packs for $16 The variable cost per pack is $10, and at current annual sales of 50,000 packs, the store earns $75,000 before taxes on course packs. How much are the fixed costs of producing the course packs?
o
a. $164,025
o
$182,250
o
c. $202,500
o
$225,000
o
e. $247,500
ANSWER:
d
RATIONALE: Sales price per unit (P) Variable costs per unit (V) Annual sales (Q) Profit = PQ − VQ − F
$16.00 $10.00 50,000 $75,000
F = PQ − VQ − EBIT = $800,000 − $500,000 − 75000 = $225,000
o
Assume that you and your brother plan to open a business that will make and sell a newly designed type of Two robotic machines are available to make the sandals, Machine A and Machine B. The price per pair will be $20.00 regardless of which machine is used. The fixed and variable costs associated with the two machines are shown below. What is the difference between the break-even points for Machines A and B? (Hint: Find BEB− BEA)
Machine A
Machine B
Price per pair (P)
$20.00
$20.00
Fixed costs (F)
$25,000
$100,000
Variable cost/unit (V)
$7.00
$4.00
o
3,154
o
3,505
o
3,894
o
4,327
o
4,760
ANSWER:
d
RATIONALE:
MachineA Machine B
Sales price per pair (P)
$20.00
$20.00
Fixed costs (F)
$25,000
$100,000
Variable costs per unit (V)
$7.00
$4.00
QBE = F/(P − V)
1,923
6,250
Difference = BEB − BEA = 4,327
o
Your company plans to produce a new product, a wireless computer mouse. Two machines can be used to make the mouse, Machines A and B. The price per mouse will be $25.00 regardless of which machine is used. The fixed and variable costs associated with the two machines are shown below. At the expected sales level of 75,000 units, how much higher or lower will the firm's expected EBIT be if it uses Machine B with high fixed costs rather than Machine A with low fixed costs, i.e., what is EBITB− EBITA?
Machine A
Machine B
Price per mouse (P)
$25.00
$25.00
Fixed costs (F)
$100,000
$400,000
Variable cost/unit (V)
$15.25
$9.00
Exp. unit sales (Q)
75,000
75,000
o
a. $123,019
o
$136,688
o
c. $151,875
o
$168,750
o
e. $185,625
ANSWER:
d
RATIONALE:
MachineA Machine B
Sale price per mouse (P)
$25.00
$25.00
Fixed costs (F)
$100,000
$400,000
Variable costs per unit (V)
$15.25
$9.00
Expected unit sales (Q)
75,000
75,000
Expected EBIT = (P − V)Q − F
$631,250
$800,000
Difference = EBITB − EBITA = $168,750
o
Your company, which is financed entirely with common equity, plans to manufacture a new product, a cell phone that can be worn like a Two robotic machines are available to make the phone, Machine A and Machine B. The price per phone will be $250.00 regardless of which machine is used to make it. The fixed and variable costs associated with the two machines are shown below, along with the capital (all equity) that must be invested to purchase each machine. The expected sales level is 25,000 units. Your company has tax loss carry-forwards that will cause its tax rate to be zero for the life of the project, so T = 0. How much higher or lower will the project's ROE be if you select the machine that produces the higher ROE, i.e., what is ROEB− ROEA? (Hint: Since the firm uses no debt and its tax rate is zero, ROE = EBIT/Required investment.)
Machine A
Machine B
Price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$2,000,000
Variable cost/unit (V)
$200.00
$150.00
Expected unit sales (Q)
25,000
25,000
Required equity investment
$2,500,000
$3,000,000
o
6.00%
o
6.67%
o
7.00%
o
7.35%
o
7.72%
ANSWER:
b
RATIONALE:
MachineA Machine B
Sales price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$2,000,000
Variable costs per unit (V)
$200.00
$150.00
Expected unit sales (Q)
25,000
25,000
Required equity investment
$2,500,000
$3,000,000
Exp. profit = EBIT = (P − V)Q − F $250,000
$500,000
Return on investment = ROE
16.67%
10.00%
Difference = ROEB − ROEA = 6.67%
o
You work for the CEO of a new company that plans to manufacture and sell a new product, a watch that has an embedded TV set and a magnifying glass The issue now is how to finance the company, with only equity or with a mix of debt and equity. Expected operating income is $400,000. Other data for the firm are shown below. How much higher or lower will the firm's expected ROE be if it uses some debt rather than all equity, i.e., what is ROEL − ROEU? 0% Debt, U
60% Debt, L
Oper. income (EBIT)
$400,000
$400,000
Required investment
$2,500,000
$2,500,000
% Debt
0.0%
60.0%
$ of Debt
$0.00
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35%
35%
o
5.85%
o
6.14%
o
6.45%
o
6.77%
o
7.11%
ANSWER:
a
RATIONALE: 0% Debt, U
60% Debt, L
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
$ of Debt
$0
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
Operating income (EBIT)
$400,000
$400,000
Interest Taxable income
0
150,000
$400,000
$250,000
140,000
87,500
Net Income
$260,000
$162,500
ROE
10.40%
16.25%
Taxes
Difference in ROEs = 5.85%
o
You work for the CEO of a new company that plans to manufacture and sell a new type of laptop The issue now is how to finance the company, with only equity or with a mix of debt and equity. Expected operating income is $600,000. Other data for the firm are shown below. How much higher or lower will the firm's expected EPS be if it uses some debt rather than only equity, i.e., what is EPSL− EPSU?
0% Debt, U
60% Debt, L
Oper. income (EBIT)
$600,000
$600,000
Required investment
$2,500,000
$2,500,000
% Debt
0.0%
60.0%
$ of Debt
$0.00
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Shares issued, $10/share
250,000
100,000
Interest rate
NA
10.00%
Tax rate
35%
35%
o
$1.00
o
$1.11
o
$1.23
o
$1.37
o
$1.50
ANSWER: d RATIONALE: 0% Debt, U
60% Debt, L
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
$ of Debt
$0
$1,500,000
$ of Common equity
$2,500,000
$1,000,000
Shares issued at $10/share
250,000
100,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
Operating income (EBIT)
$600,000
$600,000
Interest
0
Taxable income Taxes Net income
150,000
$600,000
$450,000
210,000
157,500
$390,000
$292,500
Earnings per share (EPS)
$1.56
$2.93
Difference in EPS = $1.37
o
Confu expects to have the following data during the coming year. What is the firm's expected ROE?
Capital
$200,000
Debt/Capital, book value 65% EBIT
o
$25,000
12.51%
Interest rate
8%
Tax rate
40%
o
13.14%
o
13.80%
o
14.49%
o
15.21%
ANSWER:
a
RATIONALE: Capital
$200,000
Debt/Capital =
EBIT
$25,000
− Interest = rate × debt
65% 10,400
EBIT taxes
$25,000 Earnings before $14,600
Interest rate
− Taxes
8%
Tax rate
40%
Debt = (Debt/Capital)) × Capital =
$130,000
5,840
Net Income $ 8,760 NI/Equity = ROE =
12.51%
Equity = Assets − Debt = $70,000
o
Senate Inc. is considering two alternative methods for producing playing cards. Method 1 involves using a machine with a fixed cost (mainly depreciation) of $12,000 and variable costs of $1.00 per deck of cards. Method 2 would use a less expensive machine with a fixed cost of only $5,000, but it would require a variable cost of $1.50 per deck. The sales price per deck would be the same under each method. At what unit output level would the two methods provide the same operating income (EBIT)?
o
12,600
o
14,000
o
c. 15,400
o
16,940
o
e. 18,634 b Method 1
Method 2
Price/unit (P)
$2.00
$2.00
V
$1.00
$1.50
F
$12,000
$5,000
ANSWER: RATIONALE:
EBIT = PQ − VQ − F Insert data for Methods 1 and 2, then set the 2 equations equal to one another, and then solve for Q. EBIT1 = PQ − Q(V1) − F1 EBIT2 = PQ − Q(V2) − F2
The PQs cancel, divide by −1, and we are left with: Q(V1) + F1 = Q(V2) + F2 This reduces to: Q(V2 − V1) = F1 − F2 Q = (F1 − F2)/(V2 − V1) = 14,000 o
A group of venture investors is considering putting money into Lemma Books, which wants to produce a new reader for electronic books. The variable cost per unit is estimated at $250, the sales price would be set at twice the VC/unit, or $500, and fixed costs are estimated at $750,000. The investors will put up the funds if the project is likely to have an operating income of $500,000 or more. What sales volume would be required in order to meet the minimum profit goal? (Hint: Use the break-even formula, but include the required profit in the numerator.)
o
4,513
o
4,750
o
5,000
o
5,250
o
5,513
ANSWER:
c
RATIONALE: Variable costs per unit (V)
$250
Sale price per unit (P) Fixed costs (F) Required minimum profit
$500 $750,000 $500,000
Volume (units) required to meet profit goal = (F + Profit)/(P − V) = 5,000
Check: Op profit = (P − V) × Units − F = $500,000
o
El Capitan Foods has a capital structure of 40% debt and 60% equity, its tax rate is 35%, and its beta (leveraged) is 25. Based on the Hamada equation, what would the firm's beta be if it used no debt, i.e., what is its unlevered beta, bU?
o
0.71
o
0.75
o
0.79
o
0.83
o
0.87
ANSWER:
e
RATIONALE: bL wd
1.25 0.40
Tax rate
35%
D/E = wd/(1 − wd)
0.67
bU = bL/(1 + (D/E) ×(1 − T))
0.87
o
Gator Fabrics Inc. currently has zero debt (i.e., wd = 0). It is a zero growth company, and additional firm data are shown below. Now the company is considering using some debt, moving to the new capital structure indicated The money raised would be used to repurchase stock at the current price. It is estimated that the increase in risk resulting
from the additional leverage would cause the required rate of return on equity to rise somewhat, as indicated below. If this plan were carried out, by how much would the WACC change, i.e., what is WACCOld − WACCNew?
wd %
55%
Orig. cost of equity, rs
wc rs
45%
New cost of equity =
10.0
11.0%
Interest rate new = rd rate
o
2.74%
o
3.01%
o
3.32%
o
3.65%
o
4.01%
ANSWER:
7.0%
Tax
40%
a
RATIONALE: wd
55%
Interest rate = rd
wc
45%
New cost of equity =
rs 11.0%
equity
Tax rate 10.0%
40%
Old cost of
7.0%
WACCOLD = wd(1 − T)rd + wcrs = 0.00% + 10.00% = 10.00% WACCNEW = wd(1 − T)rd + wcrs = 2.31% + 4.95% = 7.26% Change in WACC = WACC Old − WACC New = 2.74%
o
As a consultant to First Responder Inc., you have obtained the following data (dollars in millions). The company plans to pay out all of its earnings as dividends, hence g = 0. Also, no net new investment in operating capital is needed because growth is zero. The CFO believes that a move from zero debt to 20.0% debt would cause the cost of equity to increase from 10.0% to 12.0%, and the interest rate on the new debt would be 8.0%. What would the firm's total market value be if it makes this change? Hints: Find the FCF, which is equal to NOPAT = EBIT(1 − T) because no new operating capital is needed, and then divide by (WACC − g).
Oper. income (EBIT)
$800
New cost of equity (rs)
12.00%
Interest rate (rd)
8.00%
o
a. $2,982
o
$3,314
o
c. $3,682
o
$4,091
o
e. $4,545
Tax rate New wd
40.0% 20.0%
ANSWER:
e
RATIONALE: Operating income (EBIT)
$800
Tax rate
40.0%
New cost of equity (rs)
12.00%
New wd
20.0%
Interest rate (rd)
8.00%
New WACC
= wd × rd(1 − T) + wc × rs = 0.96% + 9.60% = 10.56%
FCF = EBIT(1 − T) because there is no investment in new operating capital. FCF = EBIT(1 − T) = $800 × 0.6 = $480.0 Firm value = FCF/(WACC − g) = $480.0/10.56% = $4,545.45
o
You plan to invest in one of two home delivery pizza companies, High and Low, that were recently founded and are about to commence operations. They are identical except for their use of debt (wd) and the interest rates on their debt—High uses more debt and thus must pay a higher interest rate. Based on the data given below, how much higher or lower will High's expected EPS be versus that of Low, i.e., what is EPSHigh − EPSLow?
Applicable to Both Firms
Firm High's Data
Firm Low's Data
Capital
$3,000,000 wd
70%
wd
20%
EBIT
$500,000
90,000
Shares
240,000
Shares
Tax rate 35%
Int. rate
12%
Int. rate
10%
a. $0.49 b. $0.54 c. $0.60 d. $0.66 e. $0.73
ANSWER: c RATIONALE: Applicable to Both Firms Data Firm Low's Data
Firm High's
Capital
$3,000,000 wd
70%
wd
20%
EBIT
$500,000
90,000
Shares
240,000
Tax rate 35%
Shares
Int. rate 12% Debt
Int. rate 10%
$2,100,000 Debt
$600,000
EBIT
$500,000
$500,000
Interest = I = Debt × rate
252,000
60,000
Taxable income = EBIT − I
$248,000
$440,000
86,800
154,000
$161,200
$286,000
Taxes NI
EPS = NI/Shares outstanding
$1.79
$1.19
Difference in EPS = $0.60
o
Firms HD and LD are identical except for their use of debt and the interest rates they pay HD has more debt and thus must pay a higher interest Based on the data given below, how much higher or lower will HD's ROE be versus that of LD, i.e., what is ROEHD − ROELD?
Applicable to Both Firms
Firm HD's Data
Firm LD's Data
Capital
$3,000,000 wd
70%
wd
20%
EBIT
$500,000
12%
Int. rate
10%
Tax rate
35%
Int. rate
a. 5.41% b. 5.69% c. 5.99% d. 6.29% e. 6.61% ANSWER: c RATIONALE: Applicable to Both Firms D's Data
Firm HD's Data
Capital
wd
$3,000,000 wd 70%
20%
Firm L
EBIT rate
$500,000 Int.
Tax rate
35% Debt
12%
Int. rate
10%
$2,100,000 Debt
$600,000
EBIT
$500,000
$500,000
Interest = I = Debt × Rate
252,000
60,000
Taxable income = EBIT − I
$248,000
$440,000
86,800
154,000
NI
$161,200
$286,000
Equity = (1 − wd)(Capital)
$900,000
$400,000
ROE = NI/Equity
17.91%
11.92%
Taxes
Difference in ROEs = 5.99%
o
Firm A is very aggressive in its use of debt to leverage up its earnings for common stockholders, whereas Firm NA is not aggressive and uses no debt. The two firms' operations are identical they have the same total investor-supplied capital, sales, operating costs, and EBIT. Thus, they differ only in their use of financial leverage (wd). Based on the following data, how much higher or lower is A's ROE than that of NA, i.e., what is ROEA − ROENA?
Applicable to Both Firms Capital
$150,000
wd
Firm A's Data 50%
wd
Firm NA's Data 0%
EBIT
$40,000
Int. rate
12%
Int. rate
10%
Tax rate 35%
o
8.60%
o
9.06%
o
9.53%
o
10.01%
o
10.51%
ANSWER: RATIONALE: NA's Data
c Applicable to Both Firms
Capital EBIT Tax rate
$150,000 $40,000 35%
wd
Int. rate Debt
EBIT
Firm A's Data
50% 12% $75,000 $40,000
Interest = I = Debt × Rate
9,000
Taxable income = EBIT − I
$31,000
Taxes NI = (Taxable Income)(1 − T) Equity = (1 − wd)(Capital) ROE = NI/Equity
10,850 $20,150 $75,000 26.87%
Firm
wd
0%
Int. rate
10%
Debt
$0
$40,000 0 $40,000 14,000 $26,000 $150,000 17.33%
Difference in ROEs = 9.53%
o
Your firm's debt ratio is only 5.00%, but the new CFO thinks that more debt should be employed. She wants to sell bonds and use the proceeds to buy back and retire common shares so the percentage of common equity in the capital structure (wc) = 1 − wd. Other things held constant, and based on the data below, if the firm increases the percentage of debt in its capital structure (wd) to 60.0%, by how much would the ROE change, i.e., what is ROENew − ROEOld?
Operating Data Capital
$150,000
ROIC = EBIT(1 − T)/Capital rate
Other Data
13.00%
Old wd
5%
Old interest
10%
Tax rate
35%
New wd New interest rate
o
6.73%
o
7.09%
o
7.46%
o
7.83%
o
8.22%
ANSWER:
c
60% 12%
RATIONALE:
Operating Data
Capital wd
$150,000 60%
ROIC = EBIT(1 − T)/Capital Tax rate rate
Other Data
New
13.00% 35% 12%
Old wd
5%
New interest
Old interest rate
10%
New wd wd Debt
$90,000
EBIT = (ROIC × Capital)/(1 – T)
$30,000
Interest = Rate × Debt
10,800
Taxable income = EBIT – I
$19,200
$7,500 $30,000 750 $29,250
Taxes
6,720
NI
$12,480
$19,013
Equity = (1 − wd)(Capital)
$60,000
$142,500
ROE = NI/Equity
Difference in ROEs = 7.46%
20.80%
10,238
13.34%
Old
o
You have been hired by a new firm that is just being The CFO wants to finance with 60% debt, but the president thinks it would be better to hold the percentage of debt in the capital structure (wd) to only 10%. Other things held constant, and based on the data below, if the firm uses more debt, by how much would the ROE change, i.e., what is ROENew − ROEOld?
Operating Data
Other Data
Capital
$4,000
ROIC = EBIT(1 − T)/Capital
13.00%
rate
Higher wd
60%
Higher interest
13%
Tax rate
35%
Lower wd
10%
Lower interest rate
o
5.44%
o
5.73%
o
6.03%
o
6.33%
o
6.65%
ANSWER: RATIONALE:
9%
c Operating Data
Capital
$4,000
ROIC = EBIT(1 − T)/Capital
13.00%
Other Data
Higher wd New interest rate
60% 13%
Tax rate
35%
Lower wd
10%
Old interest rate
Lower wd Debt
9%
Higher wd
$400
$2,400
EBIT = (ROIC × Capital)/(1 − T)
$800.00
$800.00
Interest = Rate × Debt
36.00
312.00
Taxable income = EBIT − I
$764.00
Taxes
$488.00
267.40 170.80
NI
$496.60
$317.20
Equity = (1 − wd)(Capital) ROE = NI/Equity %
$3,600.00
13.79%
$1,600.00
19.83
Difference in ROEs = 6.03%
o
Your girlfriend plans to start a new company to make a new type of cat Her father will finance the operation, but she will have to pay him back. You are helping her, and the issue now is how to finance the company,
with equity only or with a mix of debt and equity. The price per unit will be $10.00 regardless of how the firm is financed. The expected fixed and variable operating costs, along with other information, are shown below. How much higher or lower will the firm's expected EPS be if it uses some debt rather than only equity, i.e., what is EPSL− EPSU?
0% Debt, U
60% Debt, L
Expected unit sales
225,000
225,000
Price per unit
$10.00
$10.00
Fixed costs
$1,000,000
$1,000,000
Variable cost/unit
$3.50
$3.50
Required investment
$2,500,000
$2,500,000
Shares issued at $10/share
250,000
100,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
o
$0.54
o
$0.60
o
$0.67
o
$0.75
o
$0.83
ANSWER:
e
RATIONALE:
sales
0% Debt, U Expected unit 225,000
60% Debt, L
225,000
Price per unit
$10.00
$10.00
costs
Fixed operating $1,000,000
$1,000,000
cost/unit
Variable operating $3.50
$3.50
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
equity
$ of common $2,500,000
$10/share
Shares of stock issued at 250,000 100,000 Interest rate Tax rate
$1,000,000
NA
10.00%
35.00%
35.00%
Sales revenues
$2,250,000
$2,250,000
1,000,000
1,000,000
Fixed costs Variable costs
787,500
787,500
Operating income
$ 462,500
$ 462,500
Interest
0
150,000
Taxable income
$ 462,500
$ 312,500
Taxes
161,875
109,375
Net income
$ 300,625 Earnings per share $1.20
(EPS)
$ 203,125
$2.03
Difference in EPS = $0.83 o
Southeast U's campus book store sells course packs for $15.00 each, the variable cost per pack is $11.00, fixed costs for this operation are $300,000, and annual sales are 100,000 The unit variable cost consists of a $4.00 royalty payment, VR, per pack to professors plus other variable costs of VO = $7.00. The royalty payment is negotiable. The book store's directors believe that the store should earn a profit margin of 10% on sales, and they want the store's managers to pay a royalty rate that will produce that profit margin. What royalty per pack would permit the store to earn a 10% profit margin on course packs, other things held constant?
o
$2.55
o
$2.84
o
$3.15
o
$3.50
o
$3.85
d Sales price (P) $15.00 Target profit margin
10%
Current royalty component of variable costs (VR)
$4.00
Other variable costs (VO)
7.00
Total variable costs (V)
$11.00
Annual sales (Q)
100,000
Fixed costs (F)
$300,000
ANSWER: RATIONALE:
Current profit = PQ − VRQ − VOQ − F = $1,500,000 − $400,000 − $700,000 − $300,000 = $100,000
Target profit (TP) = 0.10(PQ) = $150,000 Target profit (TP) = PQ − VR Q − VO Q − F = 0.10(PQ) = $150,000 Target VR = P − 0.1P − VO − F/Q = 0.9P − VO − F/Q = $3.50
Check: Profit with VR = P × Q − VR × Q − VO × Q − FC = 10% of Sales = $1,500,000 − $350,000 − $700,000 − $300,000 = $150,000
o
Dye Industries currently uses no debt, but its new CFO is considering changing the capital structure to 0% debt (wd) by issuing bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity in the capital structure (wc) = 1 − wd. Given the data shown below, by how much would this recapitalization change the firm's cost of equity, i.e., what is rL − rU?
Risk-free rate, rRF
6.00%
Market risk , RPM 4.00%
Tax rate, T
40%
Current wd
0%
Current beta, bU
1.15
Target wd
40%
a. 1.66% b. 1.84% c. 2.02% d. 2.23% e. 2.45% ANSWER:
b
RATIONALE: Risk-free rate, rRF T Market risk , RPM wd
6.00% Tax rate, 40% 4.00% Current 0%
Current beta, bU wd
1.15 Target 40%
Target D/E = wd/(1 − wd)
0.67
bL = bU[(1 + (D/E)(1 − T)]
1.61
rsU = rRF + bU(RPM )
10.60%
r sL = rRF + bL(RPM ) 12.44% Change in equity cost = 1.84%
o
Dyson currently finances with 20.0% debt (i.e., wd = 20%), but its new CFO is considering changing the capital structure so wd = 60.0% by issuing additional bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity in the capital structure (wc) = 1 − wd. Given the data shown below, by how much would this recapitalization change the firm's cost of equity? (Hint: You must unlever the current beta and then use the unlevered beta to solve the problem.)
Risk-free rate, rRF
5.00% Tax rate, T
40%
Market risk , RPM
6.00% Current wd
20%
Current beta, bL1
1.15
Target wd
60%
RATIONALE: Risk-free rate, rRF
5.00%
Tax rate, T
40%
Market risk , RPM
6.00%
Current wd
20%
Current beta, bL1
1.15
a. 4.05% b. 4.50% c. 4.95% d. 5.45% e. 5.99% ANSWER:
b
Current D/E = wd/(1 − wd)
Target wd
60%
0.25
Target D/E using target wd = wd/(1 − wd)
1.50
Unleveraged beta: Found with current data: bU = bL1/[1 + (1 − T)(D/E)]
1.00
Beta at new capital structure = bL2 = bU[(1 + (D/E)(1 − T)]
1.900
Original cost of equity = rsL1 = rRF + bL1(RPM ) 11.90% New cost of equity = rsL2 = rRF + bL2(RPM ) 16.40% Change in equity cost = 4.50%
o
Monroe Inc. is an all-equity firm with 500,000 shares outstanding. It has $2,000,000 of EBIT, and EBIT is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per shares (DPS), and its tax rate is 40%. The company is considering issuing $5,000,000 of 9.00% bonds and using the proceeds to repurchase stock. The risk-free rate is 4.5%, the market risk is 5.0%, and the firm's beta is currently 0.90. However, the CFO believes the beta would rise to 1.10 if the recapitalization occurs. Assuming the shares could be repurchased at the price that existed prior to the recapitalization, what would the price per share be following the recapitalization? (Hint: P0 = EPS/rs because EPS = DPS.)
o
$28.27
o
$29.76
o
$31.25
o
$32.81
o
$34.45
ANSWER: b
RATIONALE: Interest rate initially 500,000
rRF
9%
Risk-free rate, 4.5% EBIT
Shares outstanding
$2,000,000
Market risk , RPM
5.0%
Dividend payout ratio
Beta, before recap
0.90
Tax rate
Beta, after recap
1.10
Bonds issued = stock
40%
repurchased
$5,000,000
Before the recapitalization DPS = EPS = (EBIT)(1 − T)/Shares $2.40 rs = rRF + bold(RPM )
9.00%
P0 = DPS/rs
$26.67
Shares repurchased = Bonds issued/P0
187,500
After the recapitalization DPS = EPS = (EBIT − rd × Bonds)(1 − T)/Shares $2.98 rs = rRF + bNew(RPM )
100%
10.00%
P0 = DPS/rs
o
$29.76
You were hired as the CFO of a new company that was founded by three professors at your university. The company plans to manufacture and sell a new product, a cell phone that can be worn like a wrist watch. The issue now is how to finance the company, with equity only or with a mix of debt and equity. The price per phone will be $250.00 regardless of how the firm is financed. The expected fixed and variable operating costs, along with other data, are shown below. How much higher or lower will the firm's expected ROE be if it uses 60% debt rather than only equity, i.e., what is ROEL − ROEU?
0% Debt, U
60% Debt, L
Expected unit sales (Q)
28,500
28,500
Price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$1,000,000
Variable cost/unit (V)
$200.00
$200.00
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
o
5.68%
o
5.94%
o
6.22%
o
6.52%
o
6.83%
e 0% Debt, U
60% Debt, L
Expected unit sales
28,500
28,500
Price per phone
$250.00
$250.00
Fixed operating costs
$1,000,000
$1,000,000
Variable operating cost/unit
$200.00
$200.00
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
Sales revenues
$7,125,000
$7,125,000
Fixed costs
1,000,000
Variable costs
5,700,000
5,700,000
Operating income
$ 425,000
$ 425,000
Interest Taxable income Taxes
0 $ 425,000 148,750
1,000,000
150,000 $ 275,000 96,250
Net income
$ 276,250
$ 178,750
ROE
11.05%
17.88%
Difference in ROEs = 6.83%
ANSWER: RATIONALE:
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