Chapter # 06 - Cost Of Capital 5lk1c
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The Cost of Capital
Learning Goals
Understanding cost of capital Significance of cost of capital Cost of each source of capital funding Approaches used to estimate the cost of common equity? Optimal Capital Structure Optimal Capital Structure Calculation of the weighted average cost of capital (WACC), (which is the firm’s Required Rate of Return = K) Marginal Cost of Capital (MCC) and its application in decision making Exercises
Understanding Cost of Capital The term ‘capital’ is used by the firms for funds needed for investment purposes, its cost is the key input to calculate a firm’s or division’s economic value added (EVA).
The required return necessary to make a capital budgeting project, such as building a new factory, worthwhile. Cost of capital includes the cost of debt and the cost of equity capital.
Significance of Cost of Capital
Managers estimate and use the cost of capital when deciding if they should lease or purchase assets. It is the key input used to calculate a firm’s or division’s economic value added. To properly evaluate investment decisions, the firm must know how much it will cost them to raise capital funds. This capital carries a cost because the investors want a return on their investment (fixed assets, technology, etc.)
Sources / Components of Capital
Debt capital / Borrowing, such as Bonds, bank loans, etc. Issuing Preferred stock Issuing Common stock Net Income (retained earnings) Each of these sources carries a different cost based on the required rate of return of each provider (source) of these funds.
Optimal Capital Structure The capital structure of a firm is, how the firm has selected / decided to finance its assets. Firm must decide the level or percentage of total assets financed by debt, preferred stock and common equity (common stock and retained earnings) to minimizing the costs and increasing the value of the firm.
Each firm has an optimal level of debt and equity at which it can operate most efficiently and profitability.
Stages of Weighted Cost of Capital
Compute the cost of each source of capital; debt, preferred stock, common stock, and earnings. Determine percentage to total assets of each source of capital in the optimal capital structure Multiply each components weight or ratio with its cost and adding the costs the find Weighted Average Cost of Capital (WACC).
Approaches used to estimate the cost of common equity?
o
1. The CAPM Approach Ks = KRF +(KM - KRF ) 2. Dividend growth model Ks= D1/ Po +g Po= D1/ (Ks- g)
o
Here,
D1= Do* (1+g)
3. Bond Yield Plus Risk approach Ks = Bond yield + Risk
1. Compute Cost of Debt
Required rate of return for creditors e.g. Suppose that a company issues bonds with a before tax cost (interest) of 10%. Since interest payments are tax deductible, the true cost of the debt to the company is the after tax cost. AT kd = K(1-T), where T = tax rate, K= interest rate If the company’s tax rate (state and federal combined) is, say, 40%, the after tax cost of debt AT kd = 10%(1-.40) = 6%.
Flotation Costs – cost of issuing securities
ing Legal Printing (prospectus) Underwriting (investment banker) Filing Fees (SEC)
2. Compute
Cost Preferred Stock
Cost to raise a dollar of preferred stock; derived from same formula as a perpetuity. Required rate kp =
Dividend (Dp) Net Price (MP – F)
Example: You can issue preferred stock for $45 (Market Price). However, if Flotation costs are $3, then the firm only gets $42 and if the preferred stock pays a $5 dividend, then The cost of preferred stock: $5.00 kp = = $45.00 – 3.00
11.90%
3. Compute
Cost of Common Equity
Two Types of sources of Common Equity Financing
Retained Earnings (internal common equity) ; symbol is Ks Issuing new shares of common stock (external common equity) ; symbol is Ke
3. Compute Cost of Common Equity
3.1 Cost of Internal Common Equity Management should retain earnings only if they can earn as much as stockholder’s next best investment opportunity at the same level of risk. Method to determine stockholder’s next best investment opportunity:
Dividend Growth Model
Internal – retained earnings External – new common stock
3. Compute
Cost of Common
Equity
Cost of Internal Common Equity Dividend Growth Model kS =
D1 P0
+ g
Ks = cost of internal common equity D1 = the next dividend to be paid Po = the current market price of the stock g = the projected rate of growth of the company
3. Compute Cost of Common Equity
Cost of Internal Common Equity Dividend Growth Model
kS = D1 + g P0 Example: The market price (Po) of a share of common stock is $60. The prior dividend paid (D0) was $3, and the expected growth rate (g) is 10%. (Discuss D0 vs D1 )
3. Compute Cost of Common Equity
Cost of Internal Common Equity Dividend Growth Model
kS =
D1 P0
+ g
Example: The market price of a share of common stock is $60. The prior dividend is $3, and the expected growth rate is 10%. Use the growth rate to calculate D1. D1 = Do (1 + g) kS =
3.00(1.10) + .10 60
=.155
15.5%
3. Compute Cost of Common Equity 3.2 Cost of External Equity - New Common
Stock Must adjust the Dividend Growth Model equation for Floatation costs of the new common shares.
kn =
D1 P0 - F
+ g
Example: If additional shares are issued floatation costs will be 12% of the Market Price. D0 = $3.00 and estimated growth is 10%, Price is $60 as before.
3. Compute Cost of Common Equity
Cost of External Equity - New Common Stock Must adjust the Dividend Growth Model equation for floatation costs of the new common shares.
D1 kn = + g P0 - F
Example: If additional shares are issued floatation costs will be 12%. D0 = $3.00 and estimated growth is 10%, Price is $60 as before. (Flotation =12% x $60 = $7.20) kn = 3.00(1.10) + .10 = .1625 = 16.25% 60.00 – 7.20
Weighted Average Cost of Capital Gallagher Corporation estimates the following costs for each component in its capital structure: Source of Capital Bonds (After-tax) Preferred Stock Common Stock Retained Earnings New Shares
Cost kd = 6.0% kp = 11.9% ks = 15.5% kn = 16.25%
Weighted Average Cost of Capital If using retained earnings (Internal Equity) to finance the equity portion: WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
WACC = weighted average cost of capital WT = the weight, or percentage of each element of capital (% of debt, preferred and common stock to total assets) ATkd = after tax cost of debt Kp = Cost of preferred stock Ks = Cost of equity (Internal – retained earnings)
Weighted Average Cost of Capital If using retained earnings (Internal Equity) to finance the equity portion: WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
Assume that Gallagher’s desired capital structure is 40% debt, 10% preferred and 50% common equity. WACC = Cost of Debt .40 x 6% = 2.40% + Cost of Preferred .10 x 11.9% = 1.19% + Cost of Common .50 x 15.5% = 7.75% = 11.34%
Weighted Average Cost of Capital If using new common stock (External Equity) to finance the common stock portion: WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
Then we must use the cost of stock adjusted for the Flotation costs WACC = Cost of Debt + Cost of Pref + Cost of common
.40 x 6.0% .10 x 11.9% .50 x 16.25%
= 2.40% = 1.19% = 8.13% = 11.72%
Marginal Cost of Capital
The WACC of the next dollar of capital raised is called the marginal cost of capital (MCC). Gallagher’s weighted average cost will change if any component (debt, preferred or common equity) cost of capital changes. This may occur when a firm raises a particularly large amount of capital such that investors think that the firm is riskier.
Raising/Spending Capital
The assumption is that the capital money is spent or raised in direct proportion to the optimal capital structure. If we raise or spend $100,000, it would be in the following proportions:
Capital Structure Raise Spend Debt 40% 40,000 Preferred 10% 10,000 Common 50% 50,000
40,000 10,000 50,000
Calculating the Breakpoint
Assume now that Gallagher Corporation has $100,000 in retained earnings with which to finance its capital budget. We can calculate the point at which they will need to issue new equity (common stock) since we know that Gallagher’s desired capital structure calls for 50% common equity. Breakpoint =
Available Retained Earnings (RE) Percentage of RE to Total Capital
the Calculating Breakpoint Breakpoint = ($100,000)/.5 = $200,000 •What this means is that once we spend $200,000 total on capital projects, we will have used up our retained earnings of $100,000 (internal equity). •Therefore, if we spend over $200,000, we will need additional financing from the issue of new shares of stock since 50% of our spending must come from Equity. •The cost of new shares is greater than internal equity due to flotation costs.
Making Decisions Using MCC
Weighted Cost of Capital
Marginal weighted cost of capital curve: 12%
11.72%
11%
11.34% 10%
Using internal common equity
9% 0
100,000
200,000
Total Financing
Using external (new) common equity 300,000
400,000
Making Decisions Using MCC
Graph IRRs of potential projects
Weighted Cost of Capital
Marginal weighted cost of capital curve: 12% 11%
Project 1 $100,000 IRR = 12.4%
10%
9% 0
Project 2 $150,000 IRR = 12.1%
100,000
200,000
Total Financing
Project 3 $100,000 IRR = 11.5% 300,000
400,000
Making Decisions Using MCC
Graph IRRs of potential projects
Graph MCC Curve
Weighted Cost of Capital
Marginal weighted cost of capital curve: 12%
11.72%
11.34%
11%
Project 1 $100,000 IRR = 12.4%
10%
9% 0
Project 2 $150,000 IRR = 12.1%
100,000
200,000
Total Financing
Project 3 $100,000 IRR = 11.5% 300,000
400,000
Making Decisions Using MCC
Graph IRRs of potential projects Graph MCC Curve
Weighted Cost of Capital
Choose projects whose IRR is above the weighted marginal cost of capital Marginal weighted cost of capital curve: 12%
11.34%
11%
Project 1 $100,000 IRR = 12.4%
10%
9% 0
Accept Projects #1 & #2 11.72%
Project 2 $150,000 IRR = 12.1%
100,000
200,000
Total Financing
Project 3 $100,000 IRR = 11.5% 300,000
400,000
WACC A calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC calculation. All else equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk.
Review Questions
What is cost of capital ? Discuss the significance as well as objectives of cost of capital. What are the approaches used to estimate the cost of common equity? What is Optimal Capital Structure? How are weight determined? What factors influence a company’s composite weighted Average cost of Capital? Why is a cost for retained earnings? Is preferred stock more or less risky to investors? How many ways cost of common equity is determined?
Problems for Practice
Contd.
Contd.
Solution -10.1 We are given, debt = 40% (Wd) Equity = 60% (We) kd= 9%. Tax rate 40%, WACC = 9.965 Ke= ? We know, WACC = {wd*kd(1-T)+ (We*Ke)} Or 0.996= 0.40*0.09(1-0.40+ 0.60*Ke) Or 0.0996= 0.0216+ 0.60Ke Or 0.078= 0.6Ke Or Ke= 13%
Learning Goals
Understanding cost of capital Significance of cost of capital Cost of each source of capital funding Approaches used to estimate the cost of common equity? Optimal Capital Structure Optimal Capital Structure Calculation of the weighted average cost of capital (WACC), (which is the firm’s Required Rate of Return = K) Marginal Cost of Capital (MCC) and its application in decision making Exercises
Understanding Cost of Capital The term ‘capital’ is used by the firms for funds needed for investment purposes, its cost is the key input to calculate a firm’s or division’s economic value added (EVA).
The required return necessary to make a capital budgeting project, such as building a new factory, worthwhile. Cost of capital includes the cost of debt and the cost of equity capital.
Significance of Cost of Capital
Managers estimate and use the cost of capital when deciding if they should lease or purchase assets. It is the key input used to calculate a firm’s or division’s economic value added. To properly evaluate investment decisions, the firm must know how much it will cost them to raise capital funds. This capital carries a cost because the investors want a return on their investment (fixed assets, technology, etc.)
Sources / Components of Capital
Debt capital / Borrowing, such as Bonds, bank loans, etc. Issuing Preferred stock Issuing Common stock Net Income (retained earnings) Each of these sources carries a different cost based on the required rate of return of each provider (source) of these funds.
Optimal Capital Structure The capital structure of a firm is, how the firm has selected / decided to finance its assets. Firm must decide the level or percentage of total assets financed by debt, preferred stock and common equity (common stock and retained earnings) to minimizing the costs and increasing the value of the firm.
Each firm has an optimal level of debt and equity at which it can operate most efficiently and profitability.
Stages of Weighted Cost of Capital
Compute the cost of each source of capital; debt, preferred stock, common stock, and earnings. Determine percentage to total assets of each source of capital in the optimal capital structure Multiply each components weight or ratio with its cost and adding the costs the find Weighted Average Cost of Capital (WACC).
Approaches used to estimate the cost of common equity?
o
1. The CAPM Approach Ks = KRF +(KM - KRF ) 2. Dividend growth model Ks= D1/ Po +g Po= D1/ (Ks- g)
o
Here,
D1= Do* (1+g)
3. Bond Yield Plus Risk approach Ks = Bond yield + Risk
1. Compute Cost of Debt
Required rate of return for creditors e.g. Suppose that a company issues bonds with a before tax cost (interest) of 10%. Since interest payments are tax deductible, the true cost of the debt to the company is the after tax cost. AT kd = K(1-T), where T = tax rate, K= interest rate If the company’s tax rate (state and federal combined) is, say, 40%, the after tax cost of debt AT kd = 10%(1-.40) = 6%.
Flotation Costs – cost of issuing securities
ing Legal Printing (prospectus) Underwriting (investment banker) Filing Fees (SEC)
2. Compute
Cost Preferred Stock
Cost to raise a dollar of preferred stock; derived from same formula as a perpetuity. Required rate kp =
Dividend (Dp) Net Price (MP – F)
Example: You can issue preferred stock for $45 (Market Price). However, if Flotation costs are $3, then the firm only gets $42 and if the preferred stock pays a $5 dividend, then The cost of preferred stock: $5.00 kp = = $45.00 – 3.00
11.90%
3. Compute
Cost of Common Equity
Two Types of sources of Common Equity Financing
Retained Earnings (internal common equity) ; symbol is Ks Issuing new shares of common stock (external common equity) ; symbol is Ke
3. Compute Cost of Common Equity
3.1 Cost of Internal Common Equity Management should retain earnings only if they can earn as much as stockholder’s next best investment opportunity at the same level of risk. Method to determine stockholder’s next best investment opportunity:
Dividend Growth Model
Internal – retained earnings External – new common stock
3. Compute
Cost of Common
Equity
Cost of Internal Common Equity Dividend Growth Model kS =
D1 P0
+ g
Ks = cost of internal common equity D1 = the next dividend to be paid Po = the current market price of the stock g = the projected rate of growth of the company
3. Compute Cost of Common Equity
Cost of Internal Common Equity Dividend Growth Model
kS = D1 + g P0 Example: The market price (Po) of a share of common stock is $60. The prior dividend paid (D0) was $3, and the expected growth rate (g) is 10%. (Discuss D0 vs D1 )
3. Compute Cost of Common Equity
Cost of Internal Common Equity Dividend Growth Model
kS =
D1 P0
+ g
Example: The market price of a share of common stock is $60. The prior dividend is $3, and the expected growth rate is 10%. Use the growth rate to calculate D1. D1 = Do (1 + g) kS =
3.00(1.10) + .10 60
=.155
15.5%
3. Compute Cost of Common Equity 3.2 Cost of External Equity - New Common
Stock Must adjust the Dividend Growth Model equation for Floatation costs of the new common shares.
kn =
D1 P0 - F
+ g
Example: If additional shares are issued floatation costs will be 12% of the Market Price. D0 = $3.00 and estimated growth is 10%, Price is $60 as before.
3. Compute Cost of Common Equity
Cost of External Equity - New Common Stock Must adjust the Dividend Growth Model equation for floatation costs of the new common shares.
D1 kn = + g P0 - F
Example: If additional shares are issued floatation costs will be 12%. D0 = $3.00 and estimated growth is 10%, Price is $60 as before. (Flotation =12% x $60 = $7.20) kn = 3.00(1.10) + .10 = .1625 = 16.25% 60.00 – 7.20
Weighted Average Cost of Capital Gallagher Corporation estimates the following costs for each component in its capital structure: Source of Capital Bonds (After-tax) Preferred Stock Common Stock Retained Earnings New Shares
Cost kd = 6.0% kp = 11.9% ks = 15.5% kn = 16.25%
Weighted Average Cost of Capital If using retained earnings (Internal Equity) to finance the equity portion: WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
WACC = weighted average cost of capital WT = the weight, or percentage of each element of capital (% of debt, preferred and common stock to total assets) ATkd = after tax cost of debt Kp = Cost of preferred stock Ks = Cost of equity (Internal – retained earnings)
Weighted Average Cost of Capital If using retained earnings (Internal Equity) to finance the equity portion: WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
Assume that Gallagher’s desired capital structure is 40% debt, 10% preferred and 50% common equity. WACC = Cost of Debt .40 x 6% = 2.40% + Cost of Preferred .10 x 11.9% = 1.19% + Cost of Common .50 x 15.5% = 7.75% = 11.34%
Weighted Average Cost of Capital If using new common stock (External Equity) to finance the common stock portion: WACC = (WTd x AT kd ) + (WTp x kp ) + (WTs x ks)
Then we must use the cost of stock adjusted for the Flotation costs WACC = Cost of Debt + Cost of Pref + Cost of common
.40 x 6.0% .10 x 11.9% .50 x 16.25%
= 2.40% = 1.19% = 8.13% = 11.72%
Marginal Cost of Capital
The WACC of the next dollar of capital raised is called the marginal cost of capital (MCC). Gallagher’s weighted average cost will change if any component (debt, preferred or common equity) cost of capital changes. This may occur when a firm raises a particularly large amount of capital such that investors think that the firm is riskier.
Raising/Spending Capital
The assumption is that the capital money is spent or raised in direct proportion to the optimal capital structure. If we raise or spend $100,000, it would be in the following proportions:
Capital Structure Raise Spend Debt 40% 40,000 Preferred 10% 10,000 Common 50% 50,000
40,000 10,000 50,000
Calculating the Breakpoint
Assume now that Gallagher Corporation has $100,000 in retained earnings with which to finance its capital budget. We can calculate the point at which they will need to issue new equity (common stock) since we know that Gallagher’s desired capital structure calls for 50% common equity. Breakpoint =
Available Retained Earnings (RE) Percentage of RE to Total Capital
the Calculating Breakpoint Breakpoint = ($100,000)/.5 = $200,000 •What this means is that once we spend $200,000 total on capital projects, we will have used up our retained earnings of $100,000 (internal equity). •Therefore, if we spend over $200,000, we will need additional financing from the issue of new shares of stock since 50% of our spending must come from Equity. •The cost of new shares is greater than internal equity due to flotation costs.
Making Decisions Using MCC
Weighted Cost of Capital
Marginal weighted cost of capital curve: 12%
11.72%
11%
11.34% 10%
Using internal common equity
9% 0
100,000
200,000
Total Financing
Using external (new) common equity 300,000
400,000
Making Decisions Using MCC
Graph IRRs of potential projects
Weighted Cost of Capital
Marginal weighted cost of capital curve: 12% 11%
Project 1 $100,000 IRR = 12.4%
10%
9% 0
Project 2 $150,000 IRR = 12.1%
100,000
200,000
Total Financing
Project 3 $100,000 IRR = 11.5% 300,000
400,000
Making Decisions Using MCC
Graph IRRs of potential projects
Graph MCC Curve
Weighted Cost of Capital
Marginal weighted cost of capital curve: 12%
11.72%
11.34%
11%
Project 1 $100,000 IRR = 12.4%
10%
9% 0
Project 2 $150,000 IRR = 12.1%
100,000
200,000
Total Financing
Project 3 $100,000 IRR = 11.5% 300,000
400,000
Making Decisions Using MCC
Graph IRRs of potential projects Graph MCC Curve
Weighted Cost of Capital
Choose projects whose IRR is above the weighted marginal cost of capital Marginal weighted cost of capital curve: 12%
11.34%
11%
Project 1 $100,000 IRR = 12.4%
10%
9% 0
Accept Projects #1 & #2 11.72%
Project 2 $150,000 IRR = 12.1%
100,000
200,000
Total Financing
Project 3 $100,000 IRR = 11.5% 300,000
400,000
WACC A calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC calculation. All else equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk.
Review Questions
What is cost of capital ? Discuss the significance as well as objectives of cost of capital. What are the approaches used to estimate the cost of common equity? What is Optimal Capital Structure? How are weight determined? What factors influence a company’s composite weighted Average cost of Capital? Why is a cost for retained earnings? Is preferred stock more or less risky to investors? How many ways cost of common equity is determined?
Problems for Practice
Contd.
Contd.
Solution -10.1 We are given, debt = 40% (Wd) Equity = 60% (We) kd= 9%. Tax rate 40%, WACC = 9.965 Ke= ? We know, WACC = {wd*kd(1-T)+ (We*Ke)} Or 0.996= 0.40*0.09(1-0.40+ 0.60*Ke) Or 0.0996= 0.0216+ 0.60Ke Or 0.078= 0.6Ke Or Ke= 13%
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