Mini Case
Situation
During the last few years, Harry Davis Industries has been too constrained by the high cost of capital to make many capital investments. Recently, though, capital costs have been declining, and the company has decided to look seriously at a major expansion program that has been proposed by the marketing department. Assume that you are an assistant to Leigh Jones, the financial vice president. Your first task is to estimate Harry Davis’s cost of capital. Jones has provided you with the following data, which she believes may be relevant to your task:
(1) The firm’s tax rate is 40%.
(2) The current price of Harry Davis’s 12% coupon, semiannual payment, noncallable bonds with 15 years remaining to maturity is $1,153.72. Harry Davis does not use short-term interest-bearing debt on a permanent basis. New bonds would be privately placed with no flotation cost.
(3) The current price of the firm’s 10%, $100 par value, quarterly dividend, perpetual preferred stock is $116.95. Harry Davis would incur flotation costs equal to 5% of the proceeds on a new issue.
(4) Harry Davis’s common stock is currently selling at $50 per share. Its last dividend (D0) was $3.12, and dividends are expected to grow at a constant rate of 5.8% in the foreseeable future. Harry Davis’s beta is 1.2, the yield on T-bonds is 5.6%, and the market risk premium is estimated to be 6%. For the own-bond-yield-plus-judgmental-risk-premium approach, the firm uses a 3.2% judgmental risk premium.
(5) Harry Davis’s target capital structure is 30% long-term debt, 10% preferred stock, and 60% common equity.
To help you structure the task, Leigh Jones has asked you to answer the following questions.
a. (1.) What sources of capital should be included when you estimate Harry Davis’s weighted average cost of capital (WACC)? Answer: See Chapter 10 PowerPoint file.
(2.) Should the component costs be figured on a before-tax or an after-tax basis? Answer: See Chapter 10 PowerPoint file.
(3.) Should the costs be historical (embedded) costs or new (marginal) costs? Answer: See Chapter 10 PowerPoint file.
b. What is the market interest rate on Harry Davis’s debt and what is the component cost of this debt for WACC purposes?
COST OF DEBT, rd
N 30
PV 1,153.72
PMT 60
FV 1000 rd = 10%
The relevant cost of debt is the after-tax cost of new debt, taking account of the tax deductibility of interest. The after-tax rate is calculated by multiplying the interest rate (or the before-tax cost of debt) times one minus the tax rate.
B-T rd 10%
Tax rate 40%
A-T rd = (1 – Tax rate) x (B-T rd)
A-T rd = 60% x 10%
A-T rd = 6.0%
COST OF PREFERRED STOCK, rps
c. (1.) What is the firm’s cost of preferred stock?
The cost of preferred stock is simply the preferred dividend divided by the price the company will receive if it issues new preferred stock. No tax adjustment is necessary, as preferred dividends are not tax deductible.
Pref. Dividend $10.00
Pref. Price $116.95
Flotation costs 5%
rps = Pref. Dividend ÷ Pps(1 – F)
rps = $10.00 ÷ $111.10
rps = 9.0%
” (2.) Harry Davis’s preferred stock is riskier to investors than its debt, yet the preferred’s yield to investors is lower than the
yield to maturity on the debt. Does this suggest that you have made a mistake? (Hint: Think about taxes.) ”
Preferred stock carries a higher risk to investors than debt. Companies are not required to pay preferred dividends although, firms typically want to pay preferred dividends. Otherwise, they cannot pay common dividends, so there will be difficulty raising additional funds, and preferred stockholders may gain control of the firm.
Corporations own most preferred stock, because 70% of preferred dividends are non-taxable to corporations. Therefore, preferred stock often has a lower before-tax yield than the before-tax yield on debt. But, the after-tax costs to the issuer are higher on preferred stock than debt. This is consistent with the higher risks of preferred stock.
Example:
rps 9%
rd 10%
T 40%
A-T rps = rps – rps × (1 – 0.7) × T
A-T rps = 9% – 9% × 0.12
A-T rps = 7.92%
A-T rd = (1 – Tax rate) × (B-T rd)
A-T rd = 60% × 10%
A-T rd = 6.0%
A-T Risk Premium on Preferred 1.92%
COST OF EQUITY (INTERNAL), rs
d. (1.) What are the two primary ways companies raise common equity? Answer: See Chapter 10 PowerPoint file.
(2.) Why is there a cost associated with reinvested earnings? Answer: See Chapter 10 PowerPoint file.
(3.) Harry Davis doesn’t plan to issue new shares of common stock. Using the CAPM approach, what is Harry Davis’s estimated cost of equity?
The CAPM Approach
rs = Risk-free rate + (Market risk premium) (Beta)
rs = rRF + (RPM) bi (Note: RPM is the expected return on the market minus the risk-free rate.)
PROBLEM
Assuming the risk-free rate (i.e., the current yield on a long-term Treasury bond) equals 5.6%, the expected market risk premium is 6%, and the firm’s beta is 1.2, what is the company’s cost of equity from internal funds?
Risk-free rate 5.6%
Expected market risk premium 6%
Beta 1.2
rs = rRF + (RPM) (bi)
rs = 5.6% + 6.0% 1.2
rs = 5.6% + 7.2%
rs = 12.80%
THE DISCOUNTED CASH FLOW APPROACH
e. (1.) What is the estimated cost of equity using the discounted cash flow (DCF) approach?
The simplest DCF model assumes that growth is expected to remain constant, and in this case: rs = D1/P0 + g.
The next expected dividend is easy to estimate, and the stock price can be determined readily. However, it is not easy to determine the marginal investor’s expected future growth rate. Three approaches are commonly used: (1) historical growth rates, (2) retention growth model, and (3) analysts’ forecasts.
Suppose a firm’s stock trades at $50 and its most recent dividend was $3.12. If the expected constant growth rate is 5.8%, what is the firm’s cost of equity?
P0 = $50.00
D0 = $3.12
g = 5.8%
D1 = $3.30
rs = D1 ÷ P0 + g
rs = $3.30 ÷ $50.00 + 5.80%
rs = 6.60%
rs = 12.40%
2. Retention Growth Model
e. (2.) Suppose the firm has historically earned 15% on equity (ROE) and retained 35% of earnings, and investors expect this situation to continue in the future. How could you use this information to estimate the future dividend growth rate, and what growth rate would you get? Is this consistent with the 5% growth rate given earlier?
Find g:
Payout rate = 62%
ROE = 15%
g = (1 – Payout rate) (ROE)
g = 38% 15.00%
g = 5.70%
(3.) Could the DCF method be applied if the growth rate was not constant? How?
BONUS: APPLICATION OF THE DISCOUNTED CASH FLOW APPROACH WHEN GROWTH IS NOT CONSTANT
As we noted earlier, analysts often provide non-constant estimates of future growth. We can use a modification of the discounted cash flow valuation procedure for non-constant growth from Chapter 5 to estimate the cost of equity.
Suppose the current dividend is $2.16 per share and the current actual price that we observe is $32.00 per share. Analysts forecast growth of 11% the first year, 10% the second year, 9% the third year, 8% the fourth year, and 7% thereafter. Estimate the cost of equity.
Step 1:
Create a time line showing the expected future dividend payments. These are based on the current dividend and the estimated growth rates.
Year 0 1 2 3 4 5
Growth 11% 10% 9% 8% 7%
Dividend $2.16 $2.40 $2.64 $2.87 $3.10 $3.32
Step 2:
Using the constant growth formula from Chapter 5 to estimate the price at Year 4: P4 = D5 / (rs – g). Notice that D5 and g are given in the time line above, but the estimate for rs is shown below.
Price at Year 4 = $42.20
Step 3:
Calculate the current price of the stock, based on the estimate of rs below. To do this, find the present value of the price at Year 4, P4, and then find the present value of the dividends from Year 1 through Year 4. Use the cost of equity, rs, shown below, as the discount rate.
Calculated Current Price = $32.00
Step 4:
Use Goal Seek to determine the cost of equity, rs, shown below. Click Tools (What-If Analysis), Goal Seek and set the value of the Calculated Current Price, cell C186, equal to the actual current stock price of $32 by changing the cost of equity, rs, in cell B194. Note: You must begin with a value in cell B194 that is greater than the long-term growth rate of 7%, or the constant growth formula will not be valid.
rs= 14.87% Note: you must begin with a value that is greater than the long-term constant growth rate.
Note that if rs is not equal to 14.87%, then the Calculated Current Price will not be equal to the actual current price of $32. In other words, 14.87% is the only correct value for rs, given the current stock price, the expected future dividends, and the long-term constant growth rate of 7%.
f. What is the cost of equity based on the over-own-bond-yield-plus-judgmental-risk-premium method?
THE BOND-YIELD-PLUS-JUDGMENTAL-RISK-PREMIUM APPROACH
This approach consists of adding a judgmental risk premium to the yield on the firm’s own long-term debt. It is logical that a firm with risky, low-rated debt would also have risky, high-cost equity. Historically, we have observed that the risk premium for equity is in the range of 3 to 5 percentage points. This method provides a ballpark estimate, and it is generally used as a check on the CAPM and DCF estimates. This method is used primarily in utility rate case hearings.
Over-own-bond-judgmental risk premium = 3.2%
Bond yield = 10.0%
rs = Judgmental premium + Own bond yield
rs = 3.2% + 10.0%
rs = 13.2%
g. What is your final estimate for the cost of equity, rs?
THE COST OF EQUITY ESTIMATE
It is common to use several methods to estimate the cost of equity, and then find the average of these methods.
Method Cost of Equity
CAPM rs = 12.8%
Constant growth DCF rs = 12.4%
Bond-yield-plus-judgmental-risk-premium rs = 13.2%
Average rs= 12.8%
THE WEIGHTED AVERAGE COST OF CAPITAL
The weighted average cost of capital (WACC) is calculated using the firm’s target capital structure together with its after-tax cost of debt, cost of preferred stock, and cost of common equity.
h. What is Harry Davis’s weighted average cost of capital (WACC)?
T = 40%
wd = 30% rd = 10.0%
wps = 10% rps = 9.0% WACC = 10.38%
ws = 60% rs = 12.8%
i. What factors influence a company’s WACC? Answer: See Chapter 10 PowerPoint file.
j. Should the company use the overall, or composite, WACC as the hurdle rate for each of its division’s? Answer: See Chapter 10 PowerPoint file.
k. What procedures are used to determine the risk-adjusted cost of capital for a particular division? What approaches are used to measure a division’s beta? Answer: See Chapter 10 PowerPoint file.
l. Harry Davis is interested in establishing a new division that will focus primarily on developing new Internet-based projects. In trying to determine the cost of capital for this new division, you discover that specialized firms involved in similar projects have on average the following characteristics:
-Their capital structure is 10% debt and 90% common equity.
-Their cost of debt is typically 12%.
-The beta is 1.7.
Given this information, what would your estimate be for the new division’s cost of capital?
Risk-free rate 5.6%
Market risk premium 6.0% rs = 15.8%
Beta 1.7
Target Debt Ratio 10%
rd 12%
Tax Rate 40%
WACC = (wd × rd) × (1 – T) + (ws × rs)
WACC = 1.2% x 60% + 14.2%
WACC = 14.9%
Division WACC 14.94%
Company WACC 10.38%
This indicates that the division’s market risk is greater than the firm’s average division. Typical projects within this new division would be accepted if their returns are above the divisional WACC.
m. What are three types of project risk? How is each type of risk used? Answer: See Chapter 10 PowerPoint file.
n. Explain in words why new common stock that is raised externally has a higher percentage cost than equity that is raised internally as retained earnings. Answer: See Chapter 10 PowerPoint file.
o. (1.) Harry Davis estimates that if it issues new common stock, the flotation cost will be 15%. Harry Davis incorporates the flotation costs into the DCF approach. What is the estimated cost of newly issued stock, taking into account the flotation cost?
ADJUSTING THE COST OF CAPITAL FOR FLOTATION COSTS
Flotation costs are the fees charged by investment bankers plus the accounting and legal expenses associated with the issuance of new securities. A company cannot use the entire proceeds of a new security issuance, because it must use some of the proceeds to pay the flotation costs.
P0 = $50.00
D0 = $3.12
g = 5.8%
D1 = $3.30
rs = D1 ÷ P0 + g
rs = $3.30 ÷ $50.00 + 5.8%
rs = 12.4%
Flotation percentage cost (F) = 15%
Stock price = $50.00
Net proceeds after flotation costs = (Stock Price) (1 – F)
Net proceeds after flotation costs = $50.00 85%
Net proceeds after flotation costs = $42.50
Net proceeds after flotation costs = $42.50
D1 = $3.30
g = 5.8%
rs = D1 ÷ Net Proceeds + g
rs = $3.30 ÷ $42.50 + 5.8%
rs = 13.6%
Notice that this cost of stock is quite different than the cost of stock without flotation costs. To find the cost of perpetual preferred stock, simply use the procedure above with g = 0. If the preferred stock has a fixed maturity, then use the same procedure as for debt, except that the preferred dividend is not tax deductible.
o. (2.) Suppose Harry Davis issues 30-year debt with a par value of $1,000 and a coupon rate of 10%, paid annually. If flotation costs are 2%, what is the after-tax cost of debt for the new bond issue?
PROBLEM: Flotation Costs and the Cost of Debt
Tax rate = 40%
Flotation percentage cost (F) = 2%
Par value = $1,000
Maturity payment = $1,000
Pre-tax coupon payment = $100
First, calculate the after-tax coupon payments and the net proceeds after the flotation costs.
After-tax coupon payment = (Coupon pmt.) (1 – Tax rate)
After-tax coupon payment = $100 60%
After-tax coupon payment = $60
Net proceeds after flotation costs = (Par value) (1 – F)
Net proceeds after flotation costs = $1,000 98%
Net proceeds after flotation costs = $980
Now find the rate that the company pays, based on its net proceeds after flotation costs and its after-tax payments.
Number of coupon payments = N = 30
After-tax coupon payment = PMT = 60
Net proceeds after flotation costs = PV = 980
Payment of face value at maturity = FV = 1000
After tax cost of debt = Rate = 6.15% Note: use the Rate function.
Notice that this after-tax cost of debt is only slightly higher than the after-tax cost of debt for which flotation costs are ignored. Therefore, analysts often ignore the flotation costs of debt.
“p. What four common mistakes in estimating the WACC should Harry Davis avoid?
Answer: See Chapter 10 PowerPoint file.”
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