SOLUTIONS TO
END-OF-CHAPTER STUDY PROBLEMS

7-1.

Value (Vb) =

Using a financial calculator, we find the value of the bond to be $1,105.94: 20 7 80 1,000  ANSWER -1,105.94

If you pay more for the bond, your required rate of return will not be satisfied. In other words, by paying an amount for the bond that exceeds $1,105.94, the expected rate of return for the bond is less than the required rate of return. If you have the opportunity to pay less for the bond, the expected rate of return exceeds the 7 percent required rate of return.

7-2
If interest is paid semiannually:

Value (Vb) =

The value of the bond would be $941.55:

14 2.5 20 1,000  ANSWER -941.55

If interest is paid annually:
Value (Vb) =

The value of the bond would be $942.14

7 5 40 1,000  ANSWER -942.14

7-3.
a. $875 =

20 875 70 1,000  ANSWER 8.30

b. Value (Vb) = = $744.59

20 10 70 1,000  ANSWER -744.59

c. You should sell the bond.

7.4.

The value of the bond is $825.09.

14 7 50 1,000  ANSWER -825.09

7-5. a. Value (Vb) =
The value of the bond was $865.80: 10 8 60 1,000  ANSWER -865.80

b. If the investor also receives $60 interest, then:

$865.80 = +

And the expected rate of return would be 22.43%

1 865.80 60 1,000  ANSWER 22.43

7-6. If the interest is paid semiannually:
Value (Vb) =
The value of the bond is $1,135.78 16 2 30 1,000  ANSWER -1,135.78

If interest is paid annually:
Value (Vb) =
The value of the bond is $1,134.65: 8 4 60 1,000  ANSWER -1,134.65

7-7.
a. Series A:
Value (Vb) =
Value (Vb) =
Value (Vb) =

12 = 4 7 10 55 1,000 ANSWER -1,140.78 -880.86 -693.38

Series B

Value (Vb) = +
Value (Vb) = +
Value (Vb) = +

1 = 4 7 10 55 1,000 ANSWER -1,014.42 -985.98 -959.09

b. Longer-term bondholders are locked into a particular interest rate for a longer period of time and are therefore exposed to more interest rate risk

7-8. $945 =

20 945 60 1,000  ANSWER 6.50 semiannual rate (1.0652 - 1) 13.42 annual rate

7-9. a. $1,085 =

15 1085 55 1,000  ANSWER 4.70

b. Vb =

15 7 55 1,000  ANSWER -863.38

c. Since the expected rate of return, 4.7 percent, is less than your required rate of return of 7 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,085, exceeds the value of the security to the investor of $863.38.

7-10. a. Value
Par Value $1,000.00
Coupon $70
Required Rate of Return 7%
Years to Maturity 15 Market Value $1,000

b. Value at Alternative Rates of Return
Required Rate of Return 9% Market Value $838.79

Required Rate of Return 5% Market Value $1,207.59

c. As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk" Thus, the greater the investor's required rate of return, the greater will be his/her discount on the bond. Conversely, the less his/her required rate of return below that of the coupon rate, the greater the premium will be.

d. Value at Alternative Maturity Dates
Years to Maturity 5
Required Rate of Return 7% Market Value $1,000.00
Required Rate of Return 9% Market Value $922.21
Required Rate of Return 5% Market Value $1086.59

e. The longer the maturity of the bond, the greater the interest rate risk the investor is exposed to, resulting in greater premiums and discounts.

7-11. a. Value
Par Value $1,000.00
Coupon $30
Required Rate of Return 4%
Years to Maturity 20
Market Value $864.10

b. Value at Alternative Rates of Return
Required Rate of Return 7%
Market Value $576.24

Required Rate of Return 2%
Market Value $1,163.51

c. As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk" Thus, the greater the investor's required rate of return, the greater