BEATRICE PEABODY - Questions
1. According to ValueLine estimates in Figure 1, James River's expected annual dividend growth rate from the 91-93 to 97-99 period is 5.50%, and the next dividend (1995) is expected to be $0.60. Assume that the required return for James River was 8.36% on January 1 1995 and that the 5.50% growth rate was expected to continue indefinitely.
a. Based on the Constant Growth Rate or Gordon Model, what was James River's price at the beginning of 1995?
D1/r-g=.60/.0836-.0550=$20.98
b. What conditions must hold to use the constant growth model? Do many "real world" stocks satisfy the constant growth assumptions?
Dividends per share and the company's payout should remain constant to use the constant growth rate. Since their incomes change from year to year, no real world stock isn't satisfied by a constant growth.
2. The Wall Street Journal (WSJ) lists the current price of James River common stock at $27.00.
a. Based on this information, the ValueLine 1995 expected dividend, and the annual rate of dividend change for the growth estimate, what is the company's return on common stock using the constant growth model? What is the expected dividend yield and expected capital gains yield? Explain the difference in the required return estimates from the ValueLine (see question 1a) to the WSJ price data.
Expected capital gain= expected growth rate =5.50%
Expected dividend yield= d1/p0=.60/$27=2.22%
Expected return=d1/p0+g=.60/27 +5.50%=7.72%
In regards to the expected return on the stock, it has decreased from 8.36% to 7.72%. This shows a less risky return, especially that we know this is a constant growth model.
b. What is the relationship between dividend yield and capital gains yield over time under constant growth assumptions?
Since both dividends and price growth remain the same or constant, the dividend yield and the capital gains yields remain constant as well. This are provisions under the constant growth model.
3. A successful joint venture is expected to result in the 4.0% growth rate until 2000 but would increase the company's normal growth rate to a constant 8.00% after that time. The joint venture also is expected to increase investors' required return to 9.50%.
a. Based on this information, what is the value of the company's stock?
PV of the price=$32.11
PV of expected CFs= 34.58
b. What is the value of the stock at the end of the first year assuming that the stock is in equilibrium?
$37.27
c. What is the dividend yield, capital gains yield, and total yield of the stock for the year? If you are using the spreadsheet model for this case, discuss the changes in dividend yields and capital gains yields over time.
For year 1996, dividend yield = .60/34.58=1.74%
Capital Gain yield= (37.27-34.58)/34.58=7.78%
Total return=1.74%+7.78%=9.52%
The dividend yield decreases each year while the capital gains yield increases each year of the non-constant growth period.
4. One method of determining the company's growth rate is from the fundamentals of the retention ratio and return on retained earnings. How does the growth rate-based on ValueLine's 1997-1999 estimated retention ratio (Hint: use 1 - % all dividends to net profit) and expected return on retained earnings of 10.5%-affect the return on the stock as compared to the initial return found in question 2?
g=bxr
g=.51(10.50%)=5.36%
expected return= d1/p0 +g=.60/27 +5.36%= 7.58%
5. Using the yields for the 10 year T-bond from The Wall Street Journal, an annual average risk premium of stock over risk free treasuries of 6.20%, and the beta from ValueLine, what is the required return on the stock based on the CAPM? How does this return compare to the return found in question 2?
CAPM = Rrf + (Rm-Rf) *b= 6.40% + (6.2%)(1.2)= 13.84%
This return is greater than the return in question 2. Therefore, the growth is expected to increase in the future.
6. Answer the following questions on preferred stock using The Wall Street Journal stock information.
a. What is the nominal expected rate of return for James River series K preferred stock? (Hint: Preferred stock pays a quarterly dividend) What is the effective annual rate?
Wall Street Journal series K preferred annual dividend= $3.38
Price=$43.50
Nominal rate= D/P= 3.38/43.50=7.77%
Effective rate= quarterly dividend=$3.38/4= $0.845
Quarterly return= 0.845/43.50=1.94%
EAR= (1.0194)^4-1=8%
b. What is the value of the preferred stock if it has a sinking fund in which 20% of the initial issue of stock was redeemed annually at par ($100) and the required nominal return is 9.76%?
years= 1(.20)+2(.20)+3(.20)+4(.20)+5(.20)=3 years
N=3*4=12
PMT=.845
FV=100
I/Y= 9.76/4=2.44
CPT PV=$83.58
7. Answer the following questions concerning James River debt using the S&P Bond Guide Information.
a. Why do the coupon rates of James River debt vary so widely?
When the bonds are issued, James River sells bond at par and set the coupon rate at the market rate. Since interest rates declined over time, coupons declined as well.
b. Based on the required returns of 8.5% and 9% for similar short term and long term bonds respectively, what are the values of the semiannual coupon bonds and notes held in Ms. Peabody's portfolio? Are the bonds and notes selling at a discount or a premium?
For 8 years:
N=8*2=16
I/Y=8.50/2=4.25
PMT=6.75%(1000)/2=33.75
FV=1000
CPT PV=899.90
For 26 years:
N=26*2=52
I/Y=9/2=4.50
PMT=9.25(1000)/2=46.25
FV=1000
CPT PV=1024.96 Selling at premium
For 28 years:
N=28*2=56
I/Y=9/2=4.50
PMT=7.75(1000)/2=38.75
FV=1000
CPT PV=872.92 selling at discount
8. Based on the bond analysts current expected prices of the company's debt, what is the nominal yield to maturity of each issue in the portfolio? What is the effective annual rate? Would you expect a semiannual payment bond to sell at a higher or lower price than an otherwise equivalent annual payment bond? Explain why.
For 8 years: N=8*2=16 PV=$910.20 PMT=6.75(1000)/2=33.75 FV=1000 CPT I/Y=4.15 Nominal rate of return=4.15(2)=8.30% EAR= (1.0415)^2-1=8.47%
For 26 years: N=26*2=52 PV=1090.50 FV=1000 PMT=9.25(1000)/2=46.25 CPT I/Y=4.19 Nominal rate of return=4.19(2)=8.38% EAR= (1.0419)^2-1=8.56%
For 28 years: N=28*2=56 PV=920.34 FV=1000 PMT=7.75(1000)/2=38.75 CPT I/Y= 4.25 Nominal rate of return=4.25(2)=8.50 EAR= (1.0425)^2-1=8.68%
The bond should sell at a higher price than an otherwise equivalent annual coupon payment bond. Some coupons are received early but this makes semiannual coupon bonds more valuable because it can invested longer.
9. Assume that James River Corporation's anticipated new 28 year 12% bond is not callable and sells for $1,371.73.
a. What is the nominal and effective annual YTM on this bond?
N=28*2=56 PMT=12%(1000)/2=60 PV=1371.73 FV=1000 CPT I/Y=4.25 Nominal rate=4.25(2)=8.50 EAR= (1.0425)^2-1=8.68%
b. What is the current yield on this and the original 28 year bond selling for $920.34?
Discount bond current yield=$77.50/920.34=8.42%
Premium bond current yield=$120/1371.73=8.75%
c. What is each bond's expected price after one year, assuming they both have a YTM of 8.50%? What is the capital gains yields for the year for each bond assuming no change in interest rates?
Price after one year
Discount Bond
N=27(2)=54 PMT=7.75(1000)/2=38.75 FV=1000 I/Y=8.50/2=4.25 CPT PV=921.09
Premium Bond
N=27*2=54 PMT=12(1000)/2=60 FV=1000 I/Y=8.50/2=4.25 CPT PV=1368.26
Capital Gains Yield for Discount Bond= (921.09-92.34)/920.34= .08%
Capital Gains Yield for Premium Bond=(1368.26-1371.73)/1371.73= -.25%
d. What is the expected total (percentage) return on each bond during the next year?
Discount bond total yield=8.42%+.08%=8.50%
Premium bond total yield=8.75% - .25%=8.50%
e. What would happen to the price, current yield, and total return of each bond over time assuming constant future interest rates?
The price of premium bond would decrease, and price of discount bond would increase until both reach par at maturity. For premium, the current yield would increase as the prices decreases. And for discount, it would decrease as the price increases. The total yield for both would remain the same.
f. If you were a tax-paying investor, which bond would you prefer? Why? What impact would this preference have on the prices, hence YTM, of the tow bonds?
Tax paying investors would prefer a discount bond because they're paying a lower coupon bond and lower taxes with a result in higher capital gains. For premium bond, the lower the price would get the investor a higher return, therefore, a higher before tax yield to maturity than the discount.
10. Assuming the proposed 28 year bond is callable and sells for $1,225, what is the yield to first call? Do you think it is likely that the bond will be called? Explain how the probability of call affects the required yield on a bond.
Bond held for 5 years and will receive a call premium for one years interest, which is $120
N=5*2=10 PMT=12(1000)/2=60 PV=1225 FV at call=1000+120=1120 CPT I/Y=4.19% Nominal yield=4.19(2)=8.38%
The company may call the bond because the probability that investors will request a higher rate of return to make up the risk of not being able to hold the bond to maturity.
11. Consider the risk of the bonds.
a. Explain the difference between interest rate price risk and coupon reinvestment rate risk.
Interest rate risk is the risk that arises for bond owners from fluctuating interest rates. How much interest rate risk a bond has depends on how sensitive its price is to interest rate changes in the market. Reinvestment risk is the risk that proceeds from the payment of principal and interest, which have to be reinvested at a lower rate than the original investment.
b. Which of the two long term bonds in Ms. Peabody's portfolio have the greatest price risk? Why? If you are using the case spreadsheet model, illustrate your answer by calculating the change in value of each bond assuming the interest rates rose from the initial 9% to 12% and dropped from 9% to 6%.
|
Required nominal
|
Price goes up
|
% change
|
Price goes down
|
% change
|
|
9%
|
1024.96
|
-
|
872.92
|
-
|
|
12%
|
789.91
|
-22.93%
|
659.39
|
24.46%
|
|
6%
|
1425.20
|
39.05%
|
1235.95
|
+41.59
|
c. Assume that you have money to invest in a bond but need the proceeds of the investment in 10 years. Which type of bonds could you purchase to eliminate interest rate risk?
A bond that you can purchase that eliminates interest rate risk is a bond with a 10 year investment horizon or a zero coupon bond with a 10 year maturity.
12. Assume Ms. Peabody sold some of her James River bonds and bought a 5 year 9% coupon bond selling at par.
a. Immediately after the bond was purchased, market rates fell to 6%. Given she can only invest her coupons at 6%, what is the actual realized return on her investment? Hint: Find the terminal (future) value of her coupons and the par value at maturity. Then find the rate of return that equates the price with the terminal value. How does the actual realized return compare with the expected rate of return?
N=5*2=10 PMT=9%(1000)/2=45 I/Y=6/2=3 CPT FV=$515.87 FV+PAR VALUE= 515.87+1000=$1515.87
Compute semiannual rate= 4.25%
Effective actual realized annual rate=8.60%
The actual realized rate is lower than the initial YTM b/c the coupons would be invested at a lower rate.
b. What would happen if the interest rates increased rather than decreased? The coupons could be invested at a higher rate because the actual realized rate would be higher.
c. How would the results differ if she would have bought a longer term bond? It would be a larger difference because for a long period of time more coupons would be invested at the new market rates.
13. Many bond market participants are speculators as opposed to long-term investors. If you thought interest rates were going to fall from current levels, what type of bonds would you advise Ms. Peabody to purchase in order to maximize short-term capital gains?
She would purchase long term bonds rather than short term bonds because the lower coupon bonds are more sensitive to interest rate changes. If interest rates decrease these bonds would have greater price increases.