10.12: Problem
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Assume our company has a bond outstanding with 20-years remaining until maturity. This bond has a 7.5% coupon rate. Our marginal tax rate is 35%. Find our after-tax cost of debt if the bond price is:
- $1135
- $875
- Answer
-
First we must find the YTM and then plug it into the formula:
ki = YTM(1 – T)
Remember that bonds pay interest semi-annually so that we must set our calculators to 2 Periods per Year and adjust the N and PMT to reflect the semi-annual framework.
Part a
40 N
-1135 PV
37.50 PMT
1000 FV
I/Y ⇒ 6.30%ki = 6.30%(1 – 0.35) = 4.10%
Part b
40 N
-875 PV
37.50 PMT
1000 FV
I/Y ⇒ 8.84%ki = 8.86%(1 – 0.35) = 5.75%
If the par value of our preferred stock is $30 and the dividend rate is 5% of par while the current price is $16.50, what is the cost of preferred stock?
- Answer
-
kp = D/P = (0.05)(30)/16.50 = 1.50/16.50 = 9.09%
The price of our common stock is $25. The constant growth rate in dividends is 8% and our current dividend (D0) is $0.75. Also, the risk-free rate of interest is 5% and the expected return on the market is 12%. Beta for this stock is 0.8. Finally, we estimate a risk premium of 5% for stocks relative to bonds and the current YTM on our long-term debt is 9%. Find the estimated cost of capital for common stock under each of the 3 methods.
- Answer
-
Dividend Valuation Approach
ks = (D1/P) + g = [(0.75)×(1.08)/25] + 0.08 = 11.24%Security Market Line Approach
ks = krf + β(km – krf) = 5% + 0.8(12% – 5%) = 5% + 5.6% = 10.60%Bond Yield plus Risk Premium Approach
ks = YTM + RP = 9% + 5% = 14.00%Average ks = (11.24% + 10.60% + 14.00%)/3 = 11.95%
You have the following information about XYZ Corp:
Asset | Book Value | Market Value |
Bonds | $20,000,000 | $24,000,000 |
Preferred Stock | $4,000,000 | $5,000,000 |
Common Stock | $10,000,000 | $35,000,000 |
Constant growth on common | 6.5% |
YTM on bonds | 11% |
Beta | 1.35 |
Treasury bond yield | 5% |
Price of common stock | $34 |
Tax rate | 40% |
Coupon rate on bonds | 10% |
Risk prem. stocks over bonds | 5% |
Expected market return (km) | 12% |
Expected Common Dividend (D1) | 2.75 |
Number of pref. shares | 100,000 |
Per share dividend on preferred | $6.50 |
- What is the marginal cost of capital for this firm?
- If you have a capital budgeting project that will generate after tax cash flows of $25,000 per year for the next four years and costs $75,000, should you take it?
- Answer
-
Part a
Step 1 ⇒ Solve for Market Value Weights
MVdebt = 24,000,000
MVpref = 5,000,000
MVcom = 35,000,000
MVtotal = 64,000,000Wdebt = 24,000,000/64,000,000 = 0.38
Wpref = 5,000,000/64,000,000 = 0.08
Wcom = 35,000,000/64,000,000 = 0.55Step 2 ⇒ Solve for After-tax Cost of Debt
ki = YTM(1 – T) = 11%(1 – 0.40) = 6.60%
Step 3 ⇒ Solve for Cost of Preferred Stock
kp = D/P = 6.50/50 = 13%
Note that the price per share for preferred stock is found by taking the total market value of preferred stock divided by the number of shares ⇒ $5,000,000/100,000 = $50
Step 4 ⇒ Solve for Cost of Common Stock
Dividend Valuation Approach
ks = (D1/P) + g = (2.75/34) + 0.065 = 14.59%Security Market Line Approach
ks = krf + β(km – krf) = 5% + 1.35(12% – 5%) = 14.45%Bond Yield Plus Risk Premium Approach
ks = YTM + RP = 11% + 5% = 16.00%Cost of Common Stock Financing
(14.59% + 14.45% + 16.00%)/3 = 15.01%Step 5 ⇒ Solve for Marginal Cost of Capital (MCC)
MCC = Wdebt(ki) + Wpref(kp) + Wcom(ks)
= (0.38)(6.60%) + (0.08)(13.00%) + (0.55)(15.01%)
= 11.80%Part b
Solve for IRR ⇒ IRR = 12.59% > 11.80% ⇒ Accept Project
Solve for NPV@11.80% ⇒ $1254.70 > $0 ⇒ Accept ProjectNote – Since there is no crossover problem and it is a single project instead of mutually exclusive, we can use either IRR or NPV to make our decision.
The following information is available about ACME Inc.
Balance Sheet:
LT 10% Coupon Bonds (10,000 bonds) | $10,000,000 |
Preferred Stock (40,000 shares) ($50 par with a 10% dividend) |
2,000,000 |
Common Stock (1,000,000 shares) | 20,000,000 |
The market values are $1060 for each $1000 par value bond, $53 for each share of preferred, and $41.25 for each share of common. The bonds are recorded on the balance sheet at their par value and mature in 10 years.
Beta | 1.3 |
Current Treasury bond rate | 6% |
Risk Premium for stocks over bonds | 5% |
Tax Rate | 40% |
Growth rate in dividends | 10% |
Expected market return | 13% |
Dividend (D0) | 2.25 |
- What are the appropriate weights for the opportunity cost of capital?
- What are the appropriate costs of debt, preferred, and common (use an average of the 3 methods for common)?
- What is the marginal cost of capital?
- Answer
-
Part a
MVdebt = 10,000*1060 = $10,600,000
MVpref = 40,000*53 = $ 2,120,000
MVcom = 1,000,000*41.25 = $41,250,000
MVtotal = $53,970,000Wdebt = 0.20
Wpref = 0.04
Wcom = 0.76Part b
ki = YTM(1 – T) = 9.07%(1 – 0.40) = 5.44%
Find YTM
20 N
-1060 PV
50 PMT
1000 FV
I/Y ⇒ 9.07%kp = D/P = $5/$53 = 9.43%
Div Val Approach ⇒ ks = (D1/P) + g = [(2.25)(1.10)/41.25] + 0.10 = 16.00%
SML Approach ⇒ ks = krf + β(km – krf) = 6% + 1.3(13% – 6%) = 15.10%
BY + RP Approach ⇒ ks = YTM + RP = 9.06% + 5% = 14.06%
Average of Three Approaches ⇒ (16.00% + 15.10% + 14.06%)/3 = 15.05%Part c
MCC = Wdebt(ki) + Wpref(kp) + Wcom(ks)
= (0.20)(5.44%) + (0.04)(9.43%) + 0.76(15.05%)
= 12.90%