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Cost of Capital: Concept Cost of capital, required return, discount rate We need to earn at least the required return to compensate our investors for the financing they have provided. From an investor’s point of view, it is the required return. The return to investors is a cost to the firm. So, from the firm’s point of view, it is the cost of capital. The required return is the rate of return we use to discount cash flows, which presents the opportunity cost of capital.
Cost of Capital & Capital Structure 1
Cost of Capital: Concept The company’s assets (left-hand side of BS) as a portfolio of, typically, equity and debt (right-hand side): Assets (A) = Debt (D) + Equity (E) The overall cost of capital depends on the average riskiness of the firm’s total assets.
Calculate the cost of capital Determine the cost of equity capital, ke Determine the cost of debt capital, kd Determine the overall cost of capital, as a weighted average of ke and kd, or the weighted average cost of capital (WACC)
Cost of Capital & Capital Structure 2
Estimating the Cost of Equity, ke Estimating ke using CAPM k e = R F + βE R M − R F Equityholders’ expected return is the cost of equity capital.
Estimating the (default) risk-free rate, RF It is the expected rate of return obtained by investing in a defaultfree security, e.g., T-bills, T-notes and T-bonds in US. Matching duration: the maturity of the risk-free rate is matched for investment horizon (and hence cash flows). Using current-time return rates.
Cost of Capital & Capital Structure 3
Estimating the Cost of Equity, ke Estimating the market risk (MRP), RM – RF Estimating MRP by looking at the historical earned by stocks over default-free securities over long time periods. Time period: sufficiently long The longer the period, the more accurate the estimate, because: Standard error SE = Standard deviation
Sample size
But the shorter the period, the more updated the estimate.
It is matched for investment horizon.
10 year project: use 10 year Tbill
Arithmetic vs. geometric average
Cost of Capital & Capital Structure 4
Estimating the Cost of Equity, ke Potential danger with less mature markets: higher SE
1970-2010
The country approach: RP = Base RP + Country Use mature market as base
Cost of Capital & Capital Structure 5
Estimating the Cost of Equity, ke Estimating equity beta,
E
For a publicly listed company, one can determine its historical beta using financial information resources such as Bloomberg (one can estimate it by running a regression). For a non-listed firm (or a listed firm’s division), it needs to be derived from peer companies (to be discussed). Important determinants of betas Type of business, including the degree of operating leverage (i.e., the relationship between fixed costs and total costs) Degree of financial leverage
Business risk!!
Cost of Capital & Capital Structure 6
Estimating the Cost of Equity, ke Advantages of the CAPM approach
Backward thinking and need a lot estimate!!! But it adjusts for risk!!
Explicitly adjusting for systematic risk Applicable to all projects as long as we can estimate the beta
Disadvantages of the CAPM approach We have to estimate the expected market risk and the beta, of which both do vary over time. By using historical return data, we use the past to predict the future, which is not always reliable.
How useful is this approach in practices? About 80% of firms use CAPM to estimate the cost of equity. Less than 10% use a modified CAPM. Others are uncertain about how to estimate the cost of equity. Cost of Capital & Capital Structure 7
Estimating the Cost of Equity, ke Estimate RE using the dividend growth model Dividend growth model D1 P0 = RE − g
→
D1 ke = RE = +g P0
Hence ke can be estimated from the following variables: P0: current share price of common stock (publicly observed) D1: expected dividend payment next period (when dividends do not change greatly from year to year, historical average dividend yield over a few previous years can be used to determine the expected dividend yield D1/P0) g: the constant growth rate (which is often difficult to determine) Cost of Capital & Capital Structure 8
Estimating the Cost of Equity, ke Advantages of the DGM approach
Forward thinking but require companies pay dividend and have stable dividend growth rate!
Market-driven and using current data (no need for historical data) Easy to use and understand
Disadvantages of the DGM approach Only applicable to companies that currently pay dividends Dividends are assumed to grow at a reasonably constant rate. The estimate is very sensitive to the growth rate – an increase in g of 1% increases the cost of equity by 1%. Does not explicitly quantify risk.
Cost of Capital & Capital Structure 9
Estimating the Cost of Debt, kd The cost of debt, kd, is the required return by creditors. Three factors determining kd The risk-free rate (as for cost of equity) The default risk (i.e. default spread) The tax advantage associated with debt
Can we use CAPM to estimate kd?
Cost of Capital & Capital Structure 10
Estimating the Cost of Debt, kd For firms with publicly traded bonds Obtain the yield-to-maturity (YTM) and use it as kd . The required return on a bond is the YTM, determined as below:
Bond price =
Coupon Coupon + (1+YTM) 1+YTM 2
Coupon + Face value 1+YTM T
+…
Bond issues information available from Internet You can obtain bond issues information for companies listed in US from the Financial Industry Regulatory Authority (FINRA) site: http://finra-markets.morningstar.com/MarketData/Default.jsp Go to the bond section and search the company name or ticker symbol.
Cost of Capital & Capital Structure 11
Estimating the Cost of Debt, kd For firms without bond information (or with private debt) kd = Risk-free rate + Spread Estimate the risk-free rate as we do for cost of equity. Estimate the default-risk spread (i.e., default risk ) from its bond rating (when its bonds are rated but not traded), or from a related financial ratio such as interest coverage ratio (when bond rating information is unavailable). See next slide.
Current borrowing rates information is also useful.
Cost of Capital & Capital Structure 12
Estimating the Cost of Debt, kd
Cost of Capital & Capital Structure 13
Estimating the Cost of Debt, kd The after-tax cost of debt Because interest expenses are tax deductible, we have After-tax cost of debt = kd × (1 − Tax rate) Using the marginal tax rate In contrast to the effective tax rate (i.e., the average rate at which the firm’s pre-tax profits are taxed), the marginal tax rate is the rate at which the firm’s last dollar of income is taxed. Interest expenses save the firm taxes at the margin, so the marginal tax rate should be used.
Cost of Capital & Capital Structure 14
The Cost of Preferred Stock, kps Estimating the cost of preferred stock, kps Preferred stock shares some of the characteristics of debt (prespecified dividend, before common dividend) and some of the characteristics of equity (no tax advantage and pay not guaranteed).
With perpetual preferred dividend, 𝐷𝑝𝑠 :
Pps,0 =
Dps Rps
→
k ps = R ps =
Dps Pps,0
where Pps,0 is the current market price per preferred share.
The formula applies to preferred stocks with no special features (e.g., convertibility, callability, etc.)
Cost of Capital & Capital Structure 15
Weighted Average Cost of Capital (WACC) Capital structure weights Determine the market value based weights Value of debt, D Use total debt rather than total liabilities (for operating leases, treat them as debt). Use the market value of total debt; use the book value as an approximation when market value is difficult to obtain. If you need to estimate the market value of a bond portfolio, treat the entire debt on the books as one coupon debt, with a coupon set equal to the interest expenses on all debt and the maturity set equal to the face-value weighted average maturity of all debt, using current interest rates.
Cost of Capital & Capital Structure 16
Weighted Average Cost of Capital (WACC) Value of equity, E It is the market cap: Number of stock shares × Price per share Add the market value of other equity claims such as convertible preferred stock and management stock options, if you can.
Weights with E and D: wE = E/ (E+D), wD = D/ (E+D) The firm’s target capital structure A firm’s target capital structure is long-run oriented. A firm’s current capital structure may be unstable. When a firm is acquired, its capital structure is often changed through the process of acquisition.
Use the firm’s target capital structure when it is known. Cost of Capital & Capital Structure 17
Weighted Average Cost of Capital (WACC) Example Charlie Co. has 15,000 shares of common stock outstanding at a market price of $21 a share. The firm has a bond issue outstanding with a face value of $200,000 which is selling at 98 percent of face value. What weights should be given to the common stock when computing the WACC for this company? E = $21(15,000) = $315,000; D=$200,000(98%) = $196,000;
wE =315,000/511,000 = 61.64%; wD=196,000/511,000=38.36% Determine capital structure weights using the D/E ratio. For example, if D/E = 1.5 is given, then: wE = E/(E+D) = 1/(1+D/E) = 1/(1 + 1.5) = 40% wD = D/(E+D) = (D/E) / (1+D/E) = 1.5/(1 + 1.5) = 60%
Cost of Capital & Capital Structure 18
Weighted Average Cost of Capital (WACC) Determining WACC WACC is the firm’s overall cost of capital, which is the required return on the firm’s total assets. WACC depends on the after-tax expenses. The after-tax cost of debt: kd (1-TC) Dividends are not tax deductible, and hence: ke , kps E
D
With E and D: WACC = E+D k e + E+D k d 1 − TC With E, D and PS: WACC =
E k E+D+PS e
+
D k E+D+PS d
1 − TC +
PS k E+D+PS PS
Cost of Capital & Capital Structure 19
Capital Structure Capital restructuring Capital restructuring involves changing the amount of leverage a firm has without changing the firm’s long-term assets. A firm can increase its financial leverage by issuing debt and buying back outstanding shares. A firm can decrease its financial leverage by retiring outstanding debt and issuing new shares.
How does a firm’s capital restructure affect its risk and value?
Cost of Capital & Capital Structure 20
Capital Structure Modigliani and Miller theory of capital structure Three cases of capital structure with respect to assumptions regarding corporate taxes and bankruptcy costs: Case 1: No corporate taxes; no bankruptcy costs
Case 2: With corporate taxes; no bankruptcy costs Case 3: With both corporate taxes & bankruptcy costs
Cost of Capital & Capital Structure 21
Capital Structure Case 1: No corporate taxes; no bankruptcy costs M&M Proposition I (firm value): The value of the firm is not affected by changes in the capital structure. M&M Proposition II (cost of capital): The WACC of the firm is not affected by capital structure. Intuition: In the absence of market frictions, the firm’s cash flows do not change when its capital structure changes. Therefore, the firm’s value doesn’t change (two pie models of capital structure) and its overall cost of capital (that depends on the riskiness of the cash flows) does not change.
Cost of Capital & Capital Structure 22
Capital Structure Equations for the cost of capital E D WACC = R A = R + R D+E E D+E D D RE = RA + RA − RD E RA: the “cost” of the firm’s business risk (i.e., the risk of its assets). (RA – RD)(D/E): the “cost” of the firm’s financial risk - the additional return required by stockholders for taking the risk of leverage.
Intuition: when we increase the amount of debt financing, we increase the fixed interest expenses and, consequently, the residual cash flow to equityholders becomes riskier. The cost of equity is a positive linear function of the capital structure. Cost of Capital & Capital Structure 23
Capital Structure
Cost of Capital & Capital Structure 24
Capital Structure Case 2: With corporate taxes, but no bankruptcy costs The tax effect on cash flows Interest expenses are tax deductible, so when a firm adds debt, it reduces its income taxes, all else being equal.
The reduction in taxes increases the cash flow of the firm.
The value of interest tax shield In general: Value = PV(all interest expense savings) Special case of constant debt amount: Value = D × Tax rate
Cost of Capital & Capital Structure 25
Capital Structure M&M Proposition I (firm value): The value of the firm increases by the present value of the annual interest tax shield. Value of levered firm = Value of unlevered firm + Value of interest tax shield M&M Proposition II (cost of capital): WACC decreases as D/E increases (due to government subsidy on interest payments.)
E D RE + R D 1 − TC D+E D+E D RE = R0 + R0 − RD 1 − TC E
WACC =
Now, the cost of equity increases as debt financing increases based on R0 (instead of RA), where R0 is the unlevered cost of capital (which is the cost of capital when the firm is fully equity financed). Cost of Capital & Capital Structure 26
Capital Structure
R0
R0
R0 Cost of Capital & Capital Structure 27
Capital Structure Example East Asia, Inc. has constant operating earnings of $550,000 every year forever, and hence its fixed assets and working capital will remain unchanged in the future. The company can borrow at 12%. With no debt, East Asia’s cost of equity is 20%. The tax rate is 16%. East Asia plans to borrow $400,000 and use the proceeds to repurchase shares. Determine the WACC after recapitalization. Unlevered firm value = 550,000(1 - 0.16)/0.20 = $2,310,000 Levered firm value = 2,310,000 + (400,000)(16%) = $2,374,000 D/V = 400,000/2,374,000 = 0.1685 D/E = 400,000/(2,374,000 - $400,000) = 0.2026 RE = 0.20 + (0.20 – 0.12)(0.2026)(1 - 0.16) = 21.36% WACC = 0.2136(1 – 0.1685) + 0.12(0.1685) (1 - 0.16) = 19.46% DCF and Bond and Stock Valuation 28
Capital Structure Case 3: With both corporate taxes & bankruptcy costs Financial distress & financial distress costs When a firm is having significant problems in meeting its debt obligations, we say that it is experiencing financial distress (though such firms do not necessarily file for bankruptcy). Financial distress costs include direct bankruptcy costs (legal and istrative costs) and indirect bankruptcy costs associated with going bankrupt or experiencing financial distress.
Financial leverage and bankruptcy costs As debt increases, the probability of financial distress/bankruptcy increases, which increases the expected bankruptcy costs.
Cost of Capital & Capital Structure 29
Capital Structure The static theory of capital structure At some point, the additional value of the interest tax shield will be offset by the increase in expected bankruptcy cost. At this point, the value of the firm will start to decrease, and the WACC will start to increase as more debt is added.
A firm borrows up to the point where the tax benefit from an extra dollar in debt is exactly equal to the cost that comes from the increased probability of financial distress.
Cost of Capital & Capital Structure 30
Capital Structure
R0
R0
C
Cost of Capital & Capital Structure 31
Capital Structure VLevered = VUnlevered + ITS ̶ BFDC ITS: value of interest tax shield BFDC: expected bankruptcy and financial-distress costs EV
Optimal D/(D+E)
0%
D/(D+E)
Cost of Capital & Capital Structure 32
Capital Structure Summary Case 1: no taxes or bankruptcy costs There is no optimal capital structure.
Case 2: corporate taxes but no bankruptcy costs Optimal capital structure is almost 100% debt, because each additional dollar of debt increases the cash flow of the firm.
Case 3: corporate taxes and bankruptcy costs Optimal capital structure is part debt and part equity, which occurs where the benefit from an additional dollar of debt is just offset by the increase in expected bankruptcy costs.
Cost of Capital & Capital Structure 33
Further Issues about Cost of Capital The cost of capital for a division or project A firm makes investment decisions on various projects and might have multiple business divisions. Can we use the firm’s overall WACC for all its divisions or projects? Using the WACC as the discount rate is only appropriate for projects that have the same risk as the firm’s current operations. For a project that does not have the same risk as the firm, we need to estimate the appropriate discount rate for that project. For firms of multiple business divisions, a separate discount rate is often required for each division.
Cost of Capital & Capital Structure 34
Further Issues about Cost of Capital Estimating WACC from comparable firms When there is no public information on a project, we can estimate the cost of capital for the project from the information of comparable firms Comparable firms are such companies that are in the same business as our project, and publicly listed (so that there is public information on their risk and return) Comparable firms are useful in situations such as: Valuation of a project IPO valuation Valuation of a private company in an acquisition
Cost of Capital & Capital Structure 35
Further Issues about Cost of Capital Estimating equity beta from comparable firms The effect of financial leverage on equity beta Viewing assets as a portfolio of debt and equity, then
βA =
E D βE + βD E+D E+D
→
βE = βA +
D β A − βD E
Even if comparable firms’ asset betas are similar, their equity betas can vary significantly because of their different leverages.
Hence, unless your investment has the same leverage as a comparable firm, the equity beta of your investment can be very different from that of the comparable firm.
Cost of Capital & Capital Structure 36
Further Issues about Cost of Capital We deal with this problem by utilizing a special equity beta: the unlevered beta – the beta when the firm was fully equity financed. The relation between a levered beta (with leverage effect) and its corresponding unlevered beta (without leverage effect) is: D E
βLevered = βUnlevered 1 + × 1 − TC We do the following two-step adjustment: Step 1. Apply the formula to the comparable firm to obtain the unlevered beta, which is the same for all firms of the same business. Step 2. With the unlevered beta, apply the formula again (but to our investment) to obtain the relevered beta for our investment.
Cost of Capital & Capital Structure 37
Further Issues about Cost of Capital Example: Sun Hung Kai Properties Ltd wants to sell its fast-food division in Los Angeles, which is non-listed. To evaluate the market value of this division, Sun Hung Kai needs to determine the cost of capital. Three fastfood companies are identified as comparable firms. The following information is given on these firms:
E
D ($bill)
E ($bill)
D/(D+E)
Church’s Chicken
0.75
0.004
0.096
0.04
McDonald’s
1.00
2.300
7.700
0.23
Wendy’s
1.08
0.210
0.790
0.21
We also have TC = 34%, RD = Rf = 4% and RM – Rf = 8.4%. Sun Hung Kai’s fast-food division has a target debt-to-equity ratio of 40%. Determine the cost of capital of this division using the comparable firms. Cost of Capital & Capital Structure 38
Further Issues about Cost of Capital Step 1. Estimate the unlevered beta from comparable firms D E
βUnlevered = βLevered 1 + × 1 − TC
−1
Church’s Chicken:
0.75 [1+(0.004/0.096)(0.66) ]-1 = 0.73
McDonald’s:
1.00 [1+(2.3/7.7)(0.66) ]-1 = 0.84
Wendy’s:
1.08 [1+(0.21/0.79)(0.66) ]-1 = 0.92
Taking average gives our estimated unlevered beta: (0.73+0.84+0.92)/3 = 0.83
Cost of Capital & Capital Structure 39
Further Issues about Cost of Capital Step 2. Relever beta using the target leverage of the fast-food division.
βE = βRelevered D E
= βUnLevered 1 + × 1 − TC = 0.83 1 + 0.4 1 − 0.34
= 1.049
Step 3. Determine WACC for the fast-food division. ke = Rf + βE (RM – Rf) = 4% + 1.049(8.4%) = 12.81% WACC = (1/(1+0.4)×0.1281 + (0.4/(1+0.4)×0.04(1 - 0.34) = 9.9%
Cost of Capital & Capital Structure 40
Cost of Capital & Capital Structure 1
Cost of Capital: Concept The company’s assets (left-hand side of BS) as a portfolio of, typically, equity and debt (right-hand side): Assets (A) = Debt (D) + Equity (E) The overall cost of capital depends on the average riskiness of the firm’s total assets.
Calculate the cost of capital Determine the cost of equity capital, ke Determine the cost of debt capital, kd Determine the overall cost of capital, as a weighted average of ke and kd, or the weighted average cost of capital (WACC)
Cost of Capital & Capital Structure 2
Estimating the Cost of Equity, ke Estimating ke using CAPM k e = R F + βE R M − R F Equityholders’ expected return is the cost of equity capital.
Estimating the (default) risk-free rate, RF It is the expected rate of return obtained by investing in a defaultfree security, e.g., T-bills, T-notes and T-bonds in US. Matching duration: the maturity of the risk-free rate is matched for investment horizon (and hence cash flows). Using current-time return rates.
Cost of Capital & Capital Structure 3
Estimating the Cost of Equity, ke Estimating the market risk (MRP), RM – RF Estimating MRP by looking at the historical earned by stocks over default-free securities over long time periods. Time period: sufficiently long The longer the period, the more accurate the estimate, because: Standard error SE = Standard deviation
Sample size
But the shorter the period, the more updated the estimate.
It is matched for investment horizon.
10 year project: use 10 year Tbill
Arithmetic vs. geometric average
Cost of Capital & Capital Structure 4
Estimating the Cost of Equity, ke Potential danger with less mature markets: higher SE
1970-2010
The country approach: RP = Base RP + Country Use mature market as base
Cost of Capital & Capital Structure 5
Estimating the Cost of Equity, ke Estimating equity beta,
E
For a publicly listed company, one can determine its historical beta using financial information resources such as Bloomberg (one can estimate it by running a regression). For a non-listed firm (or a listed firm’s division), it needs to be derived from peer companies (to be discussed). Important determinants of betas Type of business, including the degree of operating leverage (i.e., the relationship between fixed costs and total costs) Degree of financial leverage
Business risk!!
Cost of Capital & Capital Structure 6
Estimating the Cost of Equity, ke Advantages of the CAPM approach
Backward thinking and need a lot estimate!!! But it adjusts for risk!!
Explicitly adjusting for systematic risk Applicable to all projects as long as we can estimate the beta
Disadvantages of the CAPM approach We have to estimate the expected market risk and the beta, of which both do vary over time. By using historical return data, we use the past to predict the future, which is not always reliable.
How useful is this approach in practices? About 80% of firms use CAPM to estimate the cost of equity. Less than 10% use a modified CAPM. Others are uncertain about how to estimate the cost of equity. Cost of Capital & Capital Structure 7
Estimating the Cost of Equity, ke Estimate RE using the dividend growth model Dividend growth model D1 P0 = RE − g
→
D1 ke = RE = +g P0
Hence ke can be estimated from the following variables: P0: current share price of common stock (publicly observed) D1: expected dividend payment next period (when dividends do not change greatly from year to year, historical average dividend yield over a few previous years can be used to determine the expected dividend yield D1/P0) g: the constant growth rate (which is often difficult to determine) Cost of Capital & Capital Structure 8
Estimating the Cost of Equity, ke Advantages of the DGM approach
Forward thinking but require companies pay dividend and have stable dividend growth rate!
Market-driven and using current data (no need for historical data) Easy to use and understand
Disadvantages of the DGM approach Only applicable to companies that currently pay dividends Dividends are assumed to grow at a reasonably constant rate. The estimate is very sensitive to the growth rate – an increase in g of 1% increases the cost of equity by 1%. Does not explicitly quantify risk.
Cost of Capital & Capital Structure 9
Estimating the Cost of Debt, kd The cost of debt, kd, is the required return by creditors. Three factors determining kd The risk-free rate (as for cost of equity) The default risk (i.e. default spread) The tax advantage associated with debt
Can we use CAPM to estimate kd?
Cost of Capital & Capital Structure 10
Estimating the Cost of Debt, kd For firms with publicly traded bonds Obtain the yield-to-maturity (YTM) and use it as kd . The required return on a bond is the YTM, determined as below:
Bond price =
Coupon Coupon + (1+YTM) 1+YTM 2
Coupon + Face value 1+YTM T
+…
Bond issues information available from Internet You can obtain bond issues information for companies listed in US from the Financial Industry Regulatory Authority (FINRA) site: http://finra-markets.morningstar.com/MarketData/Default.jsp Go to the bond section and search the company name or ticker symbol.
Cost of Capital & Capital Structure 11
Estimating the Cost of Debt, kd For firms without bond information (or with private debt) kd = Risk-free rate + Spread Estimate the risk-free rate as we do for cost of equity. Estimate the default-risk spread (i.e., default risk ) from its bond rating (when its bonds are rated but not traded), or from a related financial ratio such as interest coverage ratio (when bond rating information is unavailable). See next slide.
Current borrowing rates information is also useful.
Cost of Capital & Capital Structure 12
Estimating the Cost of Debt, kd
Cost of Capital & Capital Structure 13
Estimating the Cost of Debt, kd The after-tax cost of debt Because interest expenses are tax deductible, we have After-tax cost of debt = kd × (1 − Tax rate) Using the marginal tax rate In contrast to the effective tax rate (i.e., the average rate at which the firm’s pre-tax profits are taxed), the marginal tax rate is the rate at which the firm’s last dollar of income is taxed. Interest expenses save the firm taxes at the margin, so the marginal tax rate should be used.
Cost of Capital & Capital Structure 14
The Cost of Preferred Stock, kps Estimating the cost of preferred stock, kps Preferred stock shares some of the characteristics of debt (prespecified dividend, before common dividend) and some of the characteristics of equity (no tax advantage and pay not guaranteed).
With perpetual preferred dividend, 𝐷𝑝𝑠 :
Pps,0 =
Dps Rps
→
k ps = R ps =
Dps Pps,0
where Pps,0 is the current market price per preferred share.
The formula applies to preferred stocks with no special features (e.g., convertibility, callability, etc.)
Cost of Capital & Capital Structure 15
Weighted Average Cost of Capital (WACC) Capital structure weights Determine the market value based weights Value of debt, D Use total debt rather than total liabilities (for operating leases, treat them as debt). Use the market value of total debt; use the book value as an approximation when market value is difficult to obtain. If you need to estimate the market value of a bond portfolio, treat the entire debt on the books as one coupon debt, with a coupon set equal to the interest expenses on all debt and the maturity set equal to the face-value weighted average maturity of all debt, using current interest rates.
Cost of Capital & Capital Structure 16
Weighted Average Cost of Capital (WACC) Value of equity, E It is the market cap: Number of stock shares × Price per share Add the market value of other equity claims such as convertible preferred stock and management stock options, if you can.
Weights with E and D: wE = E/ (E+D), wD = D/ (E+D) The firm’s target capital structure A firm’s target capital structure is long-run oriented. A firm’s current capital structure may be unstable. When a firm is acquired, its capital structure is often changed through the process of acquisition.
Use the firm’s target capital structure when it is known. Cost of Capital & Capital Structure 17
Weighted Average Cost of Capital (WACC) Example Charlie Co. has 15,000 shares of common stock outstanding at a market price of $21 a share. The firm has a bond issue outstanding with a face value of $200,000 which is selling at 98 percent of face value. What weights should be given to the common stock when computing the WACC for this company? E = $21(15,000) = $315,000; D=$200,000(98%) = $196,000;
wE =315,000/511,000 = 61.64%; wD=196,000/511,000=38.36% Determine capital structure weights using the D/E ratio. For example, if D/E = 1.5 is given, then: wE = E/(E+D) = 1/(1+D/E) = 1/(1 + 1.5) = 40% wD = D/(E+D) = (D/E) / (1+D/E) = 1.5/(1 + 1.5) = 60%
Cost of Capital & Capital Structure 18
Weighted Average Cost of Capital (WACC) Determining WACC WACC is the firm’s overall cost of capital, which is the required return on the firm’s total assets. WACC depends on the after-tax expenses. The after-tax cost of debt: kd (1-TC) Dividends are not tax deductible, and hence: ke , kps E
D
With E and D: WACC = E+D k e + E+D k d 1 − TC With E, D and PS: WACC =
E k E+D+PS e
+
D k E+D+PS d
1 − TC +
PS k E+D+PS PS
Cost of Capital & Capital Structure 19
Capital Structure Capital restructuring Capital restructuring involves changing the amount of leverage a firm has without changing the firm’s long-term assets. A firm can increase its financial leverage by issuing debt and buying back outstanding shares. A firm can decrease its financial leverage by retiring outstanding debt and issuing new shares.
How does a firm’s capital restructure affect its risk and value?
Cost of Capital & Capital Structure 20
Capital Structure Modigliani and Miller theory of capital structure Three cases of capital structure with respect to assumptions regarding corporate taxes and bankruptcy costs: Case 1: No corporate taxes; no bankruptcy costs
Case 2: With corporate taxes; no bankruptcy costs Case 3: With both corporate taxes & bankruptcy costs
Cost of Capital & Capital Structure 21
Capital Structure Case 1: No corporate taxes; no bankruptcy costs M&M Proposition I (firm value): The value of the firm is not affected by changes in the capital structure. M&M Proposition II (cost of capital): The WACC of the firm is not affected by capital structure. Intuition: In the absence of market frictions, the firm’s cash flows do not change when its capital structure changes. Therefore, the firm’s value doesn’t change (two pie models of capital structure) and its overall cost of capital (that depends on the riskiness of the cash flows) does not change.
Cost of Capital & Capital Structure 22
Capital Structure Equations for the cost of capital E D WACC = R A = R + R D+E E D+E D D RE = RA + RA − RD E RA: the “cost” of the firm’s business risk (i.e., the risk of its assets). (RA – RD)(D/E): the “cost” of the firm’s financial risk - the additional return required by stockholders for taking the risk of leverage.
Intuition: when we increase the amount of debt financing, we increase the fixed interest expenses and, consequently, the residual cash flow to equityholders becomes riskier. The cost of equity is a positive linear function of the capital structure. Cost of Capital & Capital Structure 23
Capital Structure
Cost of Capital & Capital Structure 24
Capital Structure Case 2: With corporate taxes, but no bankruptcy costs The tax effect on cash flows Interest expenses are tax deductible, so when a firm adds debt, it reduces its income taxes, all else being equal.
The reduction in taxes increases the cash flow of the firm.
The value of interest tax shield In general: Value = PV(all interest expense savings) Special case of constant debt amount: Value = D × Tax rate
Cost of Capital & Capital Structure 25
Capital Structure M&M Proposition I (firm value): The value of the firm increases by the present value of the annual interest tax shield. Value of levered firm = Value of unlevered firm + Value of interest tax shield M&M Proposition II (cost of capital): WACC decreases as D/E increases (due to government subsidy on interest payments.)
E D RE + R D 1 − TC D+E D+E D RE = R0 + R0 − RD 1 − TC E
WACC =
Now, the cost of equity increases as debt financing increases based on R0 (instead of RA), where R0 is the unlevered cost of capital (which is the cost of capital when the firm is fully equity financed). Cost of Capital & Capital Structure 26
Capital Structure
R0
R0
R0 Cost of Capital & Capital Structure 27
Capital Structure Example East Asia, Inc. has constant operating earnings of $550,000 every year forever, and hence its fixed assets and working capital will remain unchanged in the future. The company can borrow at 12%. With no debt, East Asia’s cost of equity is 20%. The tax rate is 16%. East Asia plans to borrow $400,000 and use the proceeds to repurchase shares. Determine the WACC after recapitalization. Unlevered firm value = 550,000(1 - 0.16)/0.20 = $2,310,000 Levered firm value = 2,310,000 + (400,000)(16%) = $2,374,000 D/V = 400,000/2,374,000 = 0.1685 D/E = 400,000/(2,374,000 - $400,000) = 0.2026 RE = 0.20 + (0.20 – 0.12)(0.2026)(1 - 0.16) = 21.36% WACC = 0.2136(1 – 0.1685) + 0.12(0.1685) (1 - 0.16) = 19.46% DCF and Bond and Stock Valuation 28
Capital Structure Case 3: With both corporate taxes & bankruptcy costs Financial distress & financial distress costs When a firm is having significant problems in meeting its debt obligations, we say that it is experiencing financial distress (though such firms do not necessarily file for bankruptcy). Financial distress costs include direct bankruptcy costs (legal and istrative costs) and indirect bankruptcy costs associated with going bankrupt or experiencing financial distress.
Financial leverage and bankruptcy costs As debt increases, the probability of financial distress/bankruptcy increases, which increases the expected bankruptcy costs.
Cost of Capital & Capital Structure 29
Capital Structure The static theory of capital structure At some point, the additional value of the interest tax shield will be offset by the increase in expected bankruptcy cost. At this point, the value of the firm will start to decrease, and the WACC will start to increase as more debt is added.
A firm borrows up to the point where the tax benefit from an extra dollar in debt is exactly equal to the cost that comes from the increased probability of financial distress.
Cost of Capital & Capital Structure 30
Capital Structure
R0
R0
C
Cost of Capital & Capital Structure 31
Capital Structure VLevered = VUnlevered + ITS ̶ BFDC ITS: value of interest tax shield BFDC: expected bankruptcy and financial-distress costs EV
Optimal D/(D+E)
0%
D/(D+E)
Cost of Capital & Capital Structure 32
Capital Structure Summary Case 1: no taxes or bankruptcy costs There is no optimal capital structure.
Case 2: corporate taxes but no bankruptcy costs Optimal capital structure is almost 100% debt, because each additional dollar of debt increases the cash flow of the firm.
Case 3: corporate taxes and bankruptcy costs Optimal capital structure is part debt and part equity, which occurs where the benefit from an additional dollar of debt is just offset by the increase in expected bankruptcy costs.
Cost of Capital & Capital Structure 33
Further Issues about Cost of Capital The cost of capital for a division or project A firm makes investment decisions on various projects and might have multiple business divisions. Can we use the firm’s overall WACC for all its divisions or projects? Using the WACC as the discount rate is only appropriate for projects that have the same risk as the firm’s current operations. For a project that does not have the same risk as the firm, we need to estimate the appropriate discount rate for that project. For firms of multiple business divisions, a separate discount rate is often required for each division.
Cost of Capital & Capital Structure 34
Further Issues about Cost of Capital Estimating WACC from comparable firms When there is no public information on a project, we can estimate the cost of capital for the project from the information of comparable firms Comparable firms are such companies that are in the same business as our project, and publicly listed (so that there is public information on their risk and return) Comparable firms are useful in situations such as: Valuation of a project IPO valuation Valuation of a private company in an acquisition
Cost of Capital & Capital Structure 35
Further Issues about Cost of Capital Estimating equity beta from comparable firms The effect of financial leverage on equity beta Viewing assets as a portfolio of debt and equity, then
βA =
E D βE + βD E+D E+D
→
βE = βA +
D β A − βD E
Even if comparable firms’ asset betas are similar, their equity betas can vary significantly because of their different leverages.
Hence, unless your investment has the same leverage as a comparable firm, the equity beta of your investment can be very different from that of the comparable firm.
Cost of Capital & Capital Structure 36
Further Issues about Cost of Capital We deal with this problem by utilizing a special equity beta: the unlevered beta – the beta when the firm was fully equity financed. The relation between a levered beta (with leverage effect) and its corresponding unlevered beta (without leverage effect) is: D E
βLevered = βUnlevered 1 + × 1 − TC We do the following two-step adjustment: Step 1. Apply the formula to the comparable firm to obtain the unlevered beta, which is the same for all firms of the same business. Step 2. With the unlevered beta, apply the formula again (but to our investment) to obtain the relevered beta for our investment.
Cost of Capital & Capital Structure 37
Further Issues about Cost of Capital Example: Sun Hung Kai Properties Ltd wants to sell its fast-food division in Los Angeles, which is non-listed. To evaluate the market value of this division, Sun Hung Kai needs to determine the cost of capital. Three fastfood companies are identified as comparable firms. The following information is given on these firms:
E
D ($bill)
E ($bill)
D/(D+E)
Church’s Chicken
0.75
0.004
0.096
0.04
McDonald’s
1.00
2.300
7.700
0.23
Wendy’s
1.08
0.210
0.790
0.21
We also have TC = 34%, RD = Rf = 4% and RM – Rf = 8.4%. Sun Hung Kai’s fast-food division has a target debt-to-equity ratio of 40%. Determine the cost of capital of this division using the comparable firms. Cost of Capital & Capital Structure 38
Further Issues about Cost of Capital Step 1. Estimate the unlevered beta from comparable firms D E
βUnlevered = βLevered 1 + × 1 − TC
−1
Church’s Chicken:
0.75 [1+(0.004/0.096)(0.66) ]-1 = 0.73
McDonald’s:
1.00 [1+(2.3/7.7)(0.66) ]-1 = 0.84
Wendy’s:
1.08 [1+(0.21/0.79)(0.66) ]-1 = 0.92
Taking average gives our estimated unlevered beta: (0.73+0.84+0.92)/3 = 0.83
Cost of Capital & Capital Structure 39
Further Issues about Cost of Capital Step 2. Relever beta using the target leverage of the fast-food division.
βE = βRelevered D E
= βUnLevered 1 + × 1 − TC = 0.83 1 + 0.4 1 − 0.34
= 1.049
Step 3. Determine WACC for the fast-food division. ke = Rf + βE (RM – Rf) = 4% + 1.049(8.4%) = 12.81% WACC = (1/(1+0.4)×0.1281 + (0.4/(1+0.4)×0.04(1 - 0.34) = 9.9%
Cost of Capital & Capital Structure 40
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