Finance

B16. (Interest-rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEls bonds have identical coupon rates of 9.125 but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday.
If the yield to maturity for all three bonds is 8, what is the fair price of each bond
PARVALUE1000INSTALLMENTS 1000x 0.0913 91.31 year7 years15 yearsINSTALLMENTS 91.391.391.3YTM 0.080.080.08PV84.46475.34781.48PV of 1000925.93583.49 315.24 PV OF BOND1,010.381,058.831,096.72
Suppose that the yield to maturity for all of these bonds changed instantaneously to 7. What is the fair price of each bond now

1 year7 years15 yearsinstallments91.391.391.3YTM0.070.070.07PV85.33492.04831.55PV 1000934.58622.70 362.40 Fair price1,019.911,114.741,193.9
Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9. Now what is the fair price of each bond
1 year7 years15 yearsinstallments91.391.391.3YTM0.090.090.09PV83.76459.51735.94PV 1000917.43547.03 274.53 Fair price1,001.191,006.541,010.47
d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer- versus shorter-maturity bonds

The risk of decline in the price of a bond due to an increase in interest rate is evident in the above calculations, with interest rates moving from 7 to 8 and finally to 9 the price of the bond decreased from 1019 to 1010 and 1001 respectively with maturity of 1 year. However, it has also been observed that the longer the maturity of the bond, the greater is the price change of the bond, in response to an interest rate change (Brigham 1994). For e.g. for 1 year bond the price change was within 19, however for 7 years bond the price of the bond changed from 1114 at 7 to 1058 at 8 and finally 1006 at 9. Thus, for longer maturity bonds, with change in interest rate the price change is higher as compared to shorter maturity bonds.

B18. (Default risk) You buy a very risky bond that promises a 9.5 coupon and return of the 1,000 principal in 10 years. You pay only 500 for the bond.

You receive the coupon payments for three years and the bond defaults. After liquidating the firm, the bondholders receive a distribution of 150 per bond at the end of 3.5 years. What is the realized return on your investment
at 10at373837.34PV of installments269.47171.45169.02170.62PV of 1000716.3332.259965323.9091329.3899538PV985.77503.71 492.93 500.01 NPV500-503.71 3.71 (7.07)
YTM is found by interpolation using the following formula
Interpolate
Lower rate                NPV with lower rate x difference in rates
                         NPV with lower rate  NPV with higher rate

 0.37 3.71(3.717.07)0.01) 37.34
YTM of 37.34 is equal to the realized rate of return.

The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment
10152522.412222.50PV of inst583.73476.78339.20367.80372.70366.74PV of 1000385.50 247.18 107.37132.28136.89131.41PV of bond969.23723.96446.57500.08509.59498.15NPV-9.591.85
The realized rate of return  22.41

B20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its common stock. James Weber, an analyst for A. G. Edwards, believes that Medtrans will begin paying a 1.00 per share dividend in two years and that the dividend will increase 6 annually thereafter. Bret Kimes, one of James colleagues at the same firm, is less optimistic. Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend will be 1.00, and that it will grow at 4 annually. James and Bret agree that the required return for Medtrans is 13.
a. What value would James estimate for this firm
b. What value would Bret assign to the Medtrans stock

Value of firm according to James
g 6PV at 13D310.69305 D41.06P315.1428610.49476PV of stock11.18781
The PV of stock  PV of dividends  PV of terminal Value
 The dividend in year 3 will be discounted at 13 for three years. 1(1.13)30.69305
PV of terminal value D4 (k-g)  1.06 (0.13-0.06)  10.49476
PV of stock  10.4976  0.69305 11.187
Value of stock according to Bret
g 4D410.613319D51.04P411.555567.087239PV7.700557
The PV of stock  PV of dividends  PV of terminal Value
 The dividend in year 4 will be discounted at 13 for four years. 1(1.13)40.613319
PV of terminal value D5 (k-g)  1.04 (0.13-0.04)  7.08723
PV of stock  0.61337.087  7.7005
C1. (Beta and required return) The riskless return is currently 6, and Chicago Gear has estimated the contingent returns given here.
a. Calculate the expected returns on the stock market and on Chicago Gear stock.
b. What is Chicago Gears beta
c. What is Chicago Gears required return according to the CAPM
123456789101112variancevariancemktmktgeargearCOVstatePR mktR gearER makretRmkt-ERMER gearRgear-ERgear(R-ERM)2P(R-ERM)2(R-ERG)2P(R-ERG)20.01185stagnant0.2-0.1-0.15-0.02-0.1975-0.0300-0.30000.03900.00780.09000.01800.0000slow growth0.350.10.150.0350.00250.05250.00000.00000.00000.00000.00000.0016average growth0.30.150.250.0450.05250.07500.10000.00280.00080.01000.00300.0046rapid growth0.150.250.350.03750.15250.05250.20000.02330.00350.04000.00600.000010.09750.15000.01210.02700.018(0.21STDdev0.1100851940.1643168

Explanation
Column 1 shows the probability
Column 2 shows the Probable Market rates of return
Column 3 shows the probable Chicago Gear s Rates of return
Column 4 shows Expected Market rates of return (Probability x Probable returns)
Column 5 shows Probable market rates of return -  Expected Market rates of return
Column 6 shows Expected Chicago Gear s rates of return (Probability x Probable returns)
Column 7 shows Probable Chicago Gear s rates of return -  Expected Chicago Gear s rates of return
Column 8 shows (Probable market rates of return -  Expected Market rates of return)
Column 9 shows (Probability x (Probable market rates of return -  Expected Market rates of return) )
Column 10 (Probable Chicago Gear s rates of return -  Expected Chicago Gear s rates of return)
Colum 11 shows (Probability x (Probable Chicago Gear s rates of return -  Expected Chicago Gear s rates of return) )
Column 12 shows (Probability x (Probable market rates of return -  Expected Market rates of return) ) x (Probability x (Probable Chicago Gear s rates of return -  Expected Chicago Gear s rates of return) )
Formulae used