Chapter 13 Cost of Capital

Capital Structure

A firm’s Capital Structure its mix of the three components of long term funding– Debt– Preferred stock– Equity

Target Capital Structure

Raising Money in the Proportions of the Capital Structure

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The Purpose of the Cost of Capital

The cost of capital is the average rate paid for the use of the firm’s capital funds

Capital is money acquired for use over long periods

The cost of capital provides a benchmark against which to evaluate investments– Projects should not be undertaken unless they return

more than the cost of the funds invested in them => the cost of capital.

Rule is equivalent to – Project IRR exceeds the cost of capital – Project NPV > 0 when calculated at the cost of capital

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Capital Components and Structure

A firm’s Capital Components are– Debt– Preferred stock– Common equity

Capital structure is the mix of the three capital components - generally expressed in percentages

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Capital Structure Concepts

Target Capital Structure– A mix of components that management

considers optimal and strives to maintain

Raising Money in the Proportions of the Capital Structure– In cost of capital calculations, we

assume money is raised in a constant proportion of debt, preferred and common equity

Returns on Investments and the Costs of Capital Components

Investors provide capital by purchasing the firm’s securities– Returns paid to investors adjusted for taxes and

administrative expenses are the firm’s costs

The risk of securities to investors differ – Equity: riskiest investment, highest investor

return, highest cost to company– Debt: safest investment, earns lowest return,

costs firm least – Preferred stock: intermediate risk, return, and

cost

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The Weighted Average Calculation (WACC)

A firm’s cost of capital is a weighted average of the costs of the three capital components where the weights reflect the $ amounts of each component in use

Referred to in two ways– k, the cost of capital– WACC, for weighted average cost of capital

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Concept Connection Example 13-1 WACC Calculations

Capital Component Value Cost

Debt $60,000 9%

Preferred stock 50,000 11

Common stock 90,000 14

$200,000

Calculate the WACC for the Zodiac Company given the following information about its capital structure.

Concept Connection Example 13-1 WACC Calculations

Capital Component Value Weight CostDebt $60,000 30% 9% 2.70%

Preferred stock 50,000 25% 11 2.75%

Common stock 90,000 45% 14 6.30%

$200,000 100% WACC 11.75%

First calculate the capital structure weights based on the values given. For example the weight of debt is $60,000 $200,000 = 30%.

Next, each component’s cost is multiplied by its weight and the results are summed as shown:

Capital Structure and CostBook Versus Market Value

WACC can be calculated using either book or market values of capital componentsWACC used to evaluate next year’s projects – Supported by capital raised next year– Book values - capital raised and spent years

ago– Current market values are best estimate of next

year’s capital market conditions

Market values are the appropriate basis for WACC calculations

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Capital Structure Customary Approach

Structure: Assume the firm will either – Maintain present capital structure based

on the current market prices of its securities

– Or strive to achieve some target structure also based on current market prices.

Costs: Always use market-based component costs to develop the WACC.

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Calculating the WACC

Step 1: Develop a market-value-based capital structure

Step 2: Adjust market returns on the underlying securities to reflect the costs of the underlying capital components Step 3: Combine in calculating the WACC

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Concept Connection Example 13-2 Market-Value-Based Capital Structure

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The Wachusett Corporation has the following capital situation.

Debt: 2,000 30-year, $1,000 face value, 12% coupon bonds issued 5 years ago. Now selling to yield 10%.

  Preferred stock: 4,000 shares of preferred are outstanding, each share pays an annual dividend of $7.50. Originally sold to yield 15% of $50 face value. Now yielding 13%.

Equity: 200,000 shares of common stock are selling at $15. 

Develop Wachusett's market-value-based capital structure.

Concept Connection Example 13-2 Market-Value-Based Capital Structure

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The market value of each capital component is the current price of each security multiplied by the number outstanding.

 

Debt:

Multiply by 2,000 bonds outstanding for the the market value of debt

$1,182.55 x 2,000 = $2,365,100

Pb = PMT[PVFAk,n] + FV[PVFk,n]

= $60[PVFA5,50] + $1,000[PVF5,50]

= $60(18.2559) + $1,000(0.0872)

= $1,182.55

Concept Connection Example 13-2 Market Value-Based Capital Structure

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  Preferred stock PP = $7.50 / .13 = $57.69

Multiply by 4,000 for market value of preferred

$57.69 x 4,000 = $230,760

Equity At $15 the market value of equity is $15 x 200,000 shares = $3,000,000

 Summarize and calculate the component weights:

Calculating Component Costs of Capital

Begin with the market return received by new investors in each capital component, kd, kp, and ke

Make adjustments for the effects of taxes and transaction costs to arrive at cost to the issuing firm

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Calculating Component Costs of Capital

Tax adjustment applies only to debt (Tax rate is T)– Interest is tax deductible to the paying firm

– Cost of debt = kd (1 – T)

– Debt made even cheaper by tax adjustment

Flotation costs: percentage of security’s price (f)– Apply to preferred and new sales of common– Increases effective cost

– Cost of component = kp / (1 – f) or ke / (1 – f)

Concept Connection Example 13-3 Cost of Debt

Blackstone has 12% coupon bonds yielding 8% to investors buying them now. Blackstone’s marginal tax rate is 37%. What is Blackstone’s cost of debt?

Cost of debt = kd(1 - T)

= 8%(1 - .37)

= 5.04%

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Concept Connection Example 13-4 Cost of Preferred Stock

Francis issued preferred paying 6% of its $100 par value. Flotation costs are 11%.– a. What is Francis’s cost of preferred if

similar issues yield 9%– b. Calculate the cost of preferred if the

shares are selling for $75.

Concept Connection Example 13-4 Cost of Preferred Stock

Solution:– a. cost of preferred =

= kP / (1-f) = 9% / (1-.11) = 10.1%

– b. cost of preferred = = DP / (1-f)PP = $6 / (1-.11) $75 = 9.0%

The Cost of Common Equity

The cost of common equity is not precise due to the uncertainty of future equity cash flows– The market return on common equity is

estimatedCAPM

Constant Growth model

Risk premium

The sources of new common equity include – Retained earnings– Newly sold stock

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The Cost of Retained Earnings

Retained earnings (RE) are not free – Reinvested earnings that belong to

stockholders– Stockholders could have spent if paid as

dividends

No adjustments to return on RE necessary– Payments to stockholders not tax deductible– No new securities so no flotation costs

Investor return = Component cost of RE– Three ways to estimate

CAPM, Gordon Model, and Risk Premium

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The CAPM Approach

Estimate using using the CAPM’s SML:

kx = kRF + (kM - kRF) bX

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Concept Connection Example 13-5 Cost of Retained Earnings – SML

Strand Corp’s beta is 1.8. The return on the S&P 500 is 12%. Treasury bills are yielding 6.5%.

Estimate Strand’s cost of retained earnings using the CAPM’s SML:

cost of RE = kX = kRF + (kM - kRF)bX

= 6.5% (12% 6.5%)1.8

= 16.4%

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The Dividend Growth (Gordon Model) Approach

The Gordon model is usually used to estimate intrinsic value. However, it can also be solved for return by substituting the stock’s current price.

Use actual price Solve for ke, which represents expected

return.

gk

)g1(DP

e

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The Dividend Growth (Gordon Model) Approach Example 13-6

Periwinkle stock sells for $33.60, paid a

dividend of $1.65 and will grow at 7.5%.

Estimate its cost of retained earnings.

Solution:

The Risk Premium Approach

Difference between debt and equity risks is fairly constant. – Estimate return on equity by adding 3% to 5%

to the return on its debt: ke = kd + rpe

Example 13-7– Carter’s bonds yield 12%– ke = kd + rpe = 12% + 4% = 16%

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The Cost of New Common StockFirms often need to raise more equity than that generated by retained earnings

Equity from new stock is just like equity from RE, except it involves flotation costs

Market return estimates for RE must be adjusted for flotation costs to determine the cost of issuing new common stock– Use the Gordon model – Insert (1 ─ f) to recognize flotation cost

gP)f1(

)g1(Dk

0

0e

The Cost of New Common Stock Example 13-8

Periwinkle of Example 13-6 needs to raise money beyond RE. Estimate its cost of new equity from stock if floatation costs are 12%

Solution:

The Marginal Cost of Capital (MCC)

WACC not independent of amount of capital raised

WACC typically rises as more capital is raised

The Marginal Cost of Capital (MCC) is a graph of the WACC showing increases as larger amounts are raised during a planning period

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The Break in MCC When Retained Earnings Run Out

Breaks (jumps) in the MCC occur when cheap sources of financing are used up

First increase in MCC usually occurs when the firm runs out of RE and starts raising external equity by selling stock

Locating the Break is important

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Concept Connection Example 13-9 The MCC

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Concept Connection Example 13-9 The MCC

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Solution: Calculate the WACC using the cost of retained earnings and the cost of new equity.

Example 13-9 Locating the Break In Brighton’s MCC Schedule

Business plan projects RE of $3M

Capital structure is 60% equity

Capital is raised in the proportions of the capital structure we ask– $3M is 60% of what number?

$3M / .6 = $5M (WACC Break)

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Brighton’s MCC Schedule

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Other Breaks in the MCC Schedule

Other Breaks in the MCC Schedule occur when the cost of borrowing increases– As debt increases firm becomes riskier

so lenders require higher interest ratesCauses further upward breaks in the MCC

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Combining the MCC and IOS

The investment opportunity schedule (IOS) is a plot of the IRRs of available projects arranged in descending order

The MCC and IOS plotted together show which projects should be undertaken

Interpreting the MCC– The firm's WACC for the planning period

is at intersection of the MCC and the IOS

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Figure 13-2 MCC Schedule and IOS

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Projects A, B and C should be undertaken because their

expected returns exceed the expected costs.

A Potential Mistake—Handling Separately Funded Projects

If a project is funded entirely by a single capital source

Should the cost of capital used to evaluate that project be the cost of the single source, or the firm's WACC?– It should be the WACC because firms cannot

continue to raise capital at the single source rate indefinitely

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