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### Chapter 13

Cost of Capital

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 refers to money acquired for use over long periods
- Generally used to start businesses and acquire long-lived assets
- The cost of capital provides a benchmark against which to evaluate investment returns
- 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

Capital Components

- A firm’s Capital Components are
- Debt
- Borrowed money, either loans or bonds
- Common equity
- Ownership interest
- Preferred stock
- A hybrid security, a cross between debt and equity
- Capital structure is the mix of the three capital components - generally expressed in percentages

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
- In cost of capital calculations, we assume money is raised in a constant proportion of debt, preferred and common equity
- Usually either the current or a target structure
- Idea used despite being somewhat unrealistic

Returns on Investments and the Costs of Capital Components

- Investors provide capital by purchasing securities
- Returns paid to investors adjusted for taxes and administrative expenses are the firm’s costs
- The risk levels of Capital Component securities differ
- Leads to different investor returns for each component
- And different costs to the issuing firm for each component
- Equity is the riskiest investment, earns the highest return, and has the highest cost
- Debt is the safest investment, earns the lowest return, and costs the firm least
- Preferred Stock offers investors intermediate risk and return levels and has a cost between that of equity and debt

The Weighted Average Calculation—The 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

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

A: 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 Component

Value

Cost

Debt

$60,000

9%

Preferred Stock

50,000

11

Common stock

90,000

14

$200,000

Example

Capital Component

Value

Weight

Cost

Debt

$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%

The Weighted Average CalculationExample 13.1Capital Structure and Cost—Book Versus Market Value

- We can think of the WACC in terms of either book or market values of capital components
- For both structure and component costs
- Which is the correct focus?
- WACC used to evaluate next year’s capital projects
- Must be supported by capital raised next year
- Book values reflect capital raised and spent years ago
- Current market values represent our best estimate of next year’s capital market conditions
- Market values are the appropriate basis for WACC
- For capital structure
- For component costs

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.

Calculating the WACC

- Step 1: Develop a market-based capital structure
- Step 2: Adjust market returns on the underlying securities to reflect the costs of the three capital component
- Step 3: Combine in calculating the WACC

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.

Example

Developing Market-Value-Based Capital StructuresExample 13.2A: The market value of each capital component is the current price of each security multiplied by the number outstanding.

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

Example

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

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

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

= $1,182.55

Developing Market-Value-Based Capital StructuresExample 13.2The 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

$7.50 / .13 = $57.69

And the total market value of Wachusett's preferred stock is

$57.69 x 4,000 = $230,760

Each share of Wachusett's common stock is trading at $15, thus the total market value of the firm's equity is

$15 x 200,000 shares = $3,000,000

Next summarize and calculate the component weights:

Example

Debt

$2,365,100

42.3%

Preferred

230,760

4.1

Equity

3,000,000

53.6

$5,595,860

100.0%

Developing Market-Value-Based Capital StructuresExample 13.2Calculating 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
- 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, the cheapest source, made even cheaper by tax adjustment
- Flotation costs are a percentage of a security’s price (f)
- Apply to preferred and new sales of common equity
- Increases effective cost
- Cost of component = kp / (1 – f) or ke / (1 – f)

Cost of Debt Example 13.3

Q. Blackstone Inc. has 12% coupon rate bonds outstanding that yield 8% to investors buying them now. Blackstone’s marginal tax rate including federal and state taxes is 37%. What is Blackstone’s cost of debt?

A. First notice that kd is the current market yield of 8%, not the coupon rate. To calculate the cost of debt we simply write equation 13.1 and substitute from the information given.

cost of debt = kd(1 - T)

= .08(1 - .37)

= 5.04%

Example

The Cost of Preferred StockExample 13.4

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 the cost of preferred if the return on similar issues is now 9%?

(b) Calculate the cost of preferred if shares are selling at $75.

A: (a) and (b) ask the same question in different situations and with different given information. In (a) we have the market return, and in (b) we have the information needed to calculate it .

(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%

Example

The Cost of Common Equity

- Unlike debt and preferred, the cost of common stock is not precise due to the uncertainty of future equity cash flows
- The market return on common equity is estimated
- CAPM
- Gordon model
- Risk premium
- The sources of new common equity include
- Retained earnings
- Newly sold stock
- Costs are different

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
- Stockholders are entitled to a return on these funds
- So there’s a cost to RE capital
- No adjustments to the return on RE necessary to calculate component cost of equity from RE
- Payments to stockholders not tax deductible to firm
- No new securities issued so no flotation costs
- Investor return on RE = Component cost of RE

The CAPM Approach

- The market return on a stock can be approximated by estimating the required or expected return using the CAPM’s SML

kx = kRF + (kM - kRF) bX

where:

kX is the required return on stock X

kRF is the risk-free rate (return on three-month T bills)

kM is the return on the market or on an “average” stock (usually

estimated through a market index like the S&P 500)

bX is stock X’s beta, the measure of its market risk

The CAPM ApproachExample 13.5

Q. The return on the Strand Corporation’s stock is relatively volatile as reflected by the company’s beta of 1.8. The return on the S&P 500 is currently 12% and is expected to remain at that level. Treasury bills are yielding 6.5%. Estimate Strand’s cost of retained earnings.

A. Write equation 13.5 and substitute directly, using the return on the S&P 500 as kM and the treasury bill yield as kRF.

cost of RE = kX kRF (kM kRF)bX

= 6.5% (12% 6.5%)1.8

= 16.4%

Example

Solve for ke, which represents expected return.

The Dividend Growth Approach- The Dividend Growth Approach (the Gordon Model)

The Gordon model is 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

Use actual price

The Dividend Growth ApproachExample 13.6

Q. Periwinkle Inc. paid a dividend of $1.65 last year and its stock is currently selling for $33.60 a share. The company is expected to grow at 7.5% indefinitely. Estimate the firm’s cost of retained earnings.

A. Write equation 13.7 and substitute for Periwinkle’s expected return and the cost of RE.

cost of RE = ke

Example

The Risk Premium Approach

- The relationship between the risks of debt and equity is fairly constant among firms.
- The incremental risk premium between debt and equity returns is similar for high-risk and low-risk firms.
- The return on a firm's equity can be estimated by adding 3 to 5 percentage points to the market return on its debt, if rpe is the additional risk premium on equity:

ke = kd + rpe

The Risk Premium ApproachExample 13.7

Q. The Carter Company’s long-term bonds are currently yielding 12%. Estimate Carter’s cost of retained earnings.

A. Simply write equation 13.8 and substitute, using 4% for the incremental risk premium.

cost of RE = ke kd rPe

= 12% + 4%

= 16%

Example

The Cost of New Common Stock

- Firms 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 (receive less than P0 for new stock

The Cost of New Common Stock Example 13.8

Q. Suppose Periwinkle Inc. of Example 13.6 had to raise capital beyond that available from retained earnings. What would be its cost of equity from new stock if flotation costs were 12% of money raised?

A. Write equation 13.9 and substitute from Example 13.6, including a 12% flotation cost.

cost of new equity = ke

Example

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 a graph of the WACC showing abrupt increases as larger amounts of capital are raised in a planning period

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
- The first breakpoint is always found by dividing the amount of RE expected to be available by the fractional proportion of equity in the capital structure

Locating the Break In Brighton’s MCC Schedule

- Assume the business plan projects RE of $3,000,000
- Note that capital structure is 60% equity
- Since capital is raised in the proportions of the capital structure we ask
- $3M is 60% of what number?
- $3M / .6 = $5M

Other Breaks in the MCC Schedule

- Other Breaks in the MCC Schedule occur when the cost of borrowing increases
- As debt increases the firm becomes riskier so lenders require higher interest rates
- Causes further upward breaks in the MCC

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 the intersection of the MCC and the IOS

MCC Schedule and IOSFigure 13.2

Projects A, B and C should be undertaken because their expected returns exceed the expected costs.

Comprehensive Example Baxter Metalworks Inc Example 13.9

Baxter Metalworks Inc. has the following elements of capital.

Debt: Baxter issued $1,000, thirty year bonds ten years

ago at a coupon rate of 9%. Five thousand (5,000) bonds were sold at par. Similar bonds are now selling to yield 12%.

Preferred Stock: Twenty thousand (20,000) shares of 10% preferred stock were sold five years ago at their $100 par value. Similar securities now yield 13%.

Equity: The company was originally financed with the sale of one million shares of common stock at $10. Accumulated retained earnings are currently $3 million. The stock is now selling at $12.50.

Comprehensive Example Baxter Metalworks Inc Example 13.9

Target Capital Structure:

Debt 20%

Preferred Stock 10%

Equity 70%

Other information:

Baxter's marginal income tax rate is 40%.

Flotation costs average 10% for stocks.

Short term treasury bills currently yield 7%.

An average stock currently yields a return of 13.5%

Baxter's beta is 1.4.

The firm is expected to grow at 6.5% indefinitely.

The annual dividend paid last year was $1.10 per share.

Next year's business plan includes earnings of $2 million

of which $1.4 million will be retained.

Baxter Metalworks Inc.

Problem:

Calculate Baxter's capital component weights and its WACC before and after the retained earnings break.

Sketch the firm's MCC.

Baxter Metalworks

MARKET VALUES AND WEIGHTS

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

= $45[PVFA6,40] + $1,000[PVF6,40]

= $45(15.0463) + $1,000(.0972)

= $774.28

Market Value = $774.28 x 5,000 = $3,871,400

Preferred Stock: Dp = $10 kp = .13

Pp = Dp / kp = $10 / .13 = $76.92

Market Value = $76.92 x 20,000 = $1,538,400

Common Equity:

Market Value =$12.50 x 1,000,000 = $12,500,000

Market Value Based Weights:

$ %

Debt $ 3,871,400 21.6%

Preferred $ 1,538,400 8.6%

Equity $12,500,00069.8%

$17,909,800 100.0%

Baxter Metalworks Inc

CAPITAL COMPONENT COSTS

Debt: Cost of debt = kd (1 - T) = .12 (1-.40) = 7.2%

Preferred Stock:

Cost of kp 13%

Preferred = ———— = ———— = 14.4%

Stock (1-f) 1-.10

Equity - Retained Earnings:

CAPM: Cost of RE = kB = kRF + (kM - kRF)bB

= 7.0% + (13.5% - 7.0%) 1.8 = 16.1%

Dividend Growth: D0(1+g)

Cost of RE = ke = ———— + g.

P0

$1.10 (1.065)

= —————— + .065 = 15.9%

$12.50

Baxter Metalworks Inc

Risk Premium: Cost of RE = ke = kd + rpe

= 12% + 4% = 16%

Reconciliation - Cost of RE

CAPM 16.1%

Dividend Growth 15.9%

Risk Premium 16.0%

Use 16.0%

Equity - New Stock:

D0(1+g)

Cost of RE = ke = ———— + g.

(1-f)P0

$1.10 (1.065)

= —————— + .065 = 16.9%

(.90)$12.50

Baxter Metalworks Inc.

Computation of WACCs

Baxter Metalworks Inc.

- Break in the MCC
- $1,400,000 / .698 = $2,005,731

A Potential Mistake—Handling Separately Funded Projects

- A project can be 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

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