Cost of Capital Chapter 13 (ch. 12 in 4 th ed.). Assignments Read chapter 13 There will not be homework per se on chapter 13 There will be problems in.

Cost of Capital

Chapter 13 (ch. 12 in 4th ed.)

Assignments

Read chapter 13 There will not be homework per se on chapter

13 There will be problems in lab on chapter 13

and there will likely be quizzes Monday, Wednesday and Friday of the next to last week of class to cover material past chapter 12.

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The Purpose of the Cost of Capital

The cost of capital is the average rate paid for the use of capital funds Primarily used in capital budgeting

Use as the ‘hurdle rate,’ or benchmark for projects Compare IRR to this rate Discount cash flows at this rate to find NPV

If a project cannot earn above this return, it is not worthwhile

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The Purpose of the Cost of Capital

A firm can only estimate what it will cost to raise future funds, so cost of capital will always be subject to uncertainty Important to estimate this cost as accurately

as possible in order to effectively manage the firm

The firm’s cost of capital can be viewed as the firm’s required rate of return on projects of average risk

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Capital Components

Components of a firm’s capital are Debt

Borrowed money, either loans or bonds Common equity

Ownership interest Preferred stock

Cross between debt and equity

Capital structure is the mix of the three capital components

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Capital Structure

Target Capital Structure A mix of components that management considers

optimal and strives to maintain Raising Money in the Proportions of the Capital

Structure An exact capital structure can’t be maintained

constantly Sometimes, if interest rates are low, a firm might issue

more debt (to take advantage of the low cost) Increases the weight of debt relative to equity Next time need more capital, issue equity to bring mix

back into balance

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Capital Structure

However, cost of capital calculations assume that capital is raised in the exact proportions of some capital structure Assumption is unrealistic but produces less

distortion than changing the proportions

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Returns on Investments and the Costs of Capital Components

Investors provide capital to companies by purchasing their securities The returns to investors represent the costs to the

firms in which investments are made Opposite sides of the same coin

Since equity is riskier than debt, generally the return on an equity investment is higher than that of debt (or preferred stock), thus the cost to the firm is higher Cost and return are not exactly equal, but are related

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The Weighted Average Calculation—The WACC

A firm’s WACC is the average of the costs of the separate sources weighted by the proportion of each source used

n

firm sourcesourcesource 1

WACC weight cost

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The Weighted Average Calculation—Example

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

A: First we need to calculate the capital structure weights based on the value given. For debt this weight is $60,000 $200,000 = 30%. Next, each component’s cost is multiplied by its weight and the results are summed as shown below:E

xam

ple

$200,000

1490,000Common stock

1150,000Preferred Stock

9%$60,000Debt

CostValueCapital Component

WACC =

14

11

9%

Cost

100%

45%

25%

30%

Weight

11.75%$200,000

6.30%90,000Common stock

2.75%50,000Preferred Stock

2.70%$60,000Debt

ValueCapital Component

Problem 56

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Capital Structure and Cost—Book Versus Market Value

Book values reflect the cost of capital already spent

Market value estimates the cost of capital to be raised in the near future Market values are appropriate because new

projects are generally funded with newly-raised equity

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Calculating the WACC

Step 1: Develop a market-based capital structure Step 2: Adjust the market returns on the securities underlying

the capital components to reflect the company's true component costs of capital

Step 3: Put the values obtained in Steps 1 and 2 together to determine the WACC

Developing Market-Value-Based Capital Structures Involves determining the percentage each source of capital

makes up of the firm's overall capital structure based on market values

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Developing Market-Value-Based Capital Structure—Example

Q: The Wachusett Corporation has the following capital situation.

Debt: Two thousand bonds were issued five years ago at a coupon rate of 12%. They had 30-year terms and $1,000 face values. They are now selling to yield 10%.

 Preferred stock: Four thousand shares of preferred are outstanding, each of which pays an annual dividend of $7.50. They originally sold to yield 15% of their $50 face value. They're now selling to yield 13%.

 Equity: Wachusett has 200,000 shares of common stock outstanding, currently selling at $15 per share.

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

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Developing Market-Value-Based Capital Structure—Example

A: To determine the market value of each source of capital, the market value (total) of each source must be calculated and then its percentage determined.

 The price of Wachusett's bonds in the market must be determined. We know the bonds have 25 years remaining until maturity, pay interest of $120 annually ($60 semi-annually) and are yielding 10% annually (5% semi-annually). Thus, each bond is selling for $1,182.55 in the market, calculated as shown below.

Because there are 2,000 bonds outstanding, the market value of the firm's debt is $2,365,100, or $1,182.55 x 2,000.

Exa

mpl

e

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

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

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

= $1,182.55

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Developing Market-Value-Based Capital Structure—Example

  The firm's preferred stock represents a perpetuity that pays $7.50 annually and is yielding 13%. Thus, the value of each share of preferred stock is $57.69, or $7.50 .13. Because there are 4,000 shares outstanding, the total market value of Wachusett's preferred stock is $230,760, or $57.69 x 4,000.

 Each share of Wachusett's common stock is trading for $15, thus the total market value of the firm's equity is $3,000,000, or $15 x 200,000 shares.

 Next, we calculate the portion of the the firm's total capital that each source represents:

Exa

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100.0%$5,595,860

53.63,000,000Equity

4.1230,760Preferred

42.3%$2,365,100Debt

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Calculating Component Costs of Capital We'll look at the market return received by new investors in

each component Then make adjustments to reflect practical reality Adjustments—The Effect of Financial Markets and Taxes

The amounts effectively paid to investors and received by a corporation when raising capital are impacted by income taxes and transaction costs

Taxes—interest expense on debt is tax deductible which makes the debt cheaper than it would be otherwise

Thus, a dollar paid in interest results in a lower taxable income and lower taxes

Therefore, the after-tax cost of debt is Interest (1 - tax rate)

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Calculating Component Costs of Capital Flotation costs—administrative fees and expenses

incurred in the process of issuing and selling securities Lower the amount received when a security is issued,

increasing the cost of the capital raised Thus, when a firm issues securities it will only net a

portion of the total amount issued, as the remainder must be paid as issuance costs

A firm's component cost of capital will be higher than the investor's return by the ratio of 1 (1 - flotation cost percentage)

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The Cost of Debt

The cost of debt is the investor's return adjusted for the tax deductibility of interest payments Most debt is placed privately (not initially sold

to the public) and flotation costs are minimal The cost of debt is the market return on debt

(kd) net of taxes or Kd × (1 - tax rate)

Problem 55 and 57

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The Cost of Preferred Stock

The cost of preferred stock is the investor's return adjusted for flotation costs A preferred stockholder's return is the dividend

received divided by the current price of the stock Adjusting this for the fact that a firm will only net the

portion of the issuing price after flotation costs (f) results in

Dp /(1 - f)Pp

or kp/(1 - f)

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The Cost of Preferred Stock—Example

Q: The preferred stock of the Francis Corporation was issued several years ago with each share paying 6% of a $100 par value. Flotation costs on new preferred are expected to average 11% of the funds raised. (a) What is Francis's cost of preferred capital if the interest rate on similar preferred stock is 9% today? (b) Calculate Francis's cost of preferred stock if the stock is selling at $75 per share today.

A: Questions (a) and (b) are both asking the same question; however with (a) we have the market return provided and with (b) we are given the information needed to calculate the market return.

(a) Using the formula kp/(1 - f) we simply adjust the market return by flotation costs: 9%/(1 - .11) = 10.1%.

(b) Using the formula Dp/(1 - f) Pp we calculate the cost using the dividend and current price of preferred stock: (6% × $100)/(1-.11)$75 = 9%.

Exa

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Problem 58

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The Cost of Common Equity

Debt and preferred stock offer investors known stream of payments so calculating returns are easy

The cost of equity is imprecise because of the uncertainty of future cash flows Thus, market return on an equity investment has to be

estimated We'll use the CAPM, the Gordon model and risk

premiums Equity sources include stock sales and retained

earnings, which have different costs

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The Cost of Retained Earnings

Retained earnings (RE) are not free to the company because they represent reinvested earnings for the stockholders Thus, retained earnings represent money stockholders

could have spent if it had been paid out as dividends Stockholders deserve a return on retained earnings The market return on new shares is an appropriate

starting point for estimating the cost of retained earnings

No adjustments are needed between the return earned by new buyers and the cost of RE because RE are generated internally—no need to adjust for flotation costs or taxes

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The Cost of Retained Earnings

The CAPM Approach—The Required Rate of Return The market return on a stock can be approximated by

estimating the required or expected return CAPM offers a method of estimating the required return using

beta as a measure of risk Kx = KRF + (Km - KRF) bX

The Dividend Growth Approach—The Expected Rate of Return The Gordon model is normally used to calculate the intrinsic

value of a stock However, we can use the Gordon model to solve for the

expected return by plugging in the current price of the stock P0 = D0(1 + g) / ( ke – g)

Use actual priceSolve for ke, which represents

expected return.

Problem 60

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The Cost of Retained Earnings

The Risk Premium Approach It's possible to estimate the return on a firm's equity by

adding 3 to 5 percentage points to the market return on its debt, or

Ke = kd + equity risk premium

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The Cost of New Common Stock

Firms often need to raise more equity than that generated by retained earnings Accomplish this by issuing new common stock

Equity from new stock is just like equity from RE, with the exception that raising it involves incurring flotation costs

Thus the market return estimates for RE must be adjusted for flotation costs to determine the cost of issuing new common stock Easiest to do with the Gordon model because the price

of the stock appears in that equation ke = [D0(1 + g) (1 – f)P0] + g

Problems 59, 65, 77

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Putting the Weights and Costs Together

Once the component costs are calculated and the target weights are determined, the calculation of the weighted average cost of capital is simple

Problem 85

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The Marginal Cost of Capital (MCC)

A firm's WACC is not independent of the amount of capital raised

WACC typically rises as the firm raises more capital

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

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The Break in MCC When Retained Earnings Run Out Breaks (jumps) in the MCC occur when a cheap

source 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 The first breakpoint is always found by dividing the

amount of RE available by the fractional proportion of equity in the capital structure

Problem 101

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The MCC Schedule

Other Breaks in the MCC Schedule For most companies the WACC is reasonably constant aside from the

break into external equity However, low-cost funds cannot be raised without limit For instance, as more debt is issued the firm becomes more risky and

the investors' required rates of return rise 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

Because it represents the cost of raising funds relative to the expected return of the projects

Interpreting the MCC The firm's WACC for the planning period is at the intersection of the

MCC and the IOS

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Figure 12.2: MCC Schedule and IOS

Projects A, B and C should be undertaken because their expected returns

exceed the expected costs.

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A Potential Mistake—Handling Separately Funded Projects Sometimes a project is funded entirely by a single

source of capital Should the cost of capital used to evaluate that

project be the cost of the single source, or the firm's overall WACC? It should be the firm's overall WACC because firms

cannot continue to raise a single source of capital indefinitely, such as cheap debt