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10.12: Problem

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Problem 10.12.1

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:

  1. $1135
  2. $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%

Problem 10.12.2

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%

Problem 10.12.3

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%

Problem 10.12.4

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
  1. What is the marginal cost of capital for this firm?
  2. 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 = 64,000,000

Wdebt = 24,000,000/64,000,000 = 0.38
Wpref = 5,000,000/64,000,000 = 0.08
Wcom = 35,000,000/64,000,000 = 0.55

Step 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 Project

Note – 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.

Problem 10.12.5

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
  1. What are the appropriate weights for the opportunity cost of capital?
  2. What are the appropriate costs of debt, preferred, and common (use an average of the 3 methods for common)?
  3. 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 = $53,970,000

Wdebt = 0.20
Wpref = 0.04
Wcom = 0.76

Part 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%


10.12: Problem is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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