Question

Sam Strother and Shawna Tibbs are vice presidents of Mutual of Seattle Group Health Cooperative and codirectors of the organization's pension fund management division. The unions that represent the GHC hospital staff have requested an investment seminar so that they better understand the decisions being made on behalf of their members. Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions. a. What is the value of a ten-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent? b. What would be the value of the bond described in question a. if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Would we now have a discount or a premium bond? c. What would be the value of the bond described in question a. if, just after it had been issued, the expected inflation rate fell by 3 percentage points, causing investors to require a 7 percent return? Would we now have a discount or a premium bond? d. What would happen to the value of the ten-year bond over time if the required rate of return remained at 13 percent, remained at 7 percent, or remained at 10 percent? Graph your results using the table below: Value of Bond in Given Year: N 7% 10% 13% 0 1 2 3 4 5 6 7 8 9 10 e. What is the yield to maturity on a ten-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.00? f. What are the total return, the current yield, and the capital gains yield for the bond in question e.? (Assume the bond is held to maturity and the company does not default on the bond.)

Answer 1

a) The value of the bond is equal to par value if coupon rate and required rate of return is same. Hence, in this case, the value of the bond = $1,000.

b) Bond Value can be calculated using PV function on a financial calculator

N = 10, I/Y = 13%, PMT = 10% x 1000 = 100, FV = 1000

=> Compute PV = $837.21 is the value of bond.

As the bond value is lower than the par value, the bond is called a discount bond.

c) N = 10, I/Y = 7%, PMT = 100, FV = 1000

=> Compute PV = $1,210.71 is the value of bond.

As the bond value is higher than the par value, the bond is called a premium bond.

d) The value of bond at maturity would be equal to par value of $1,000.

The value of premium bond will decline over the years, while the value of discount bond will increase of the years and hit the par value at maturity.

N	7%	10%	13%
0	$1,210.71	$1,000.00	$837.21
1	$1,195.46	$1,000.00	$846.05
2	$1,179.14	$1,000.00	$856.04
3	$1,161.68	$1,000.00	$867.32
4	$1,143.00	$1,000.00	$880.07
5	$1,123.01	$1,000.00	$894.48
6	$1,101.62	$1,000.00	$910.77
7	$1,078.73	$1,000.00	$929.17
8	$1,054.24	$1,000.00	$949.96
9	$1,028.04	$1,000.00	$973.45
10	$1,000.00	$1,000.00	$1,000.00

e) YTM can be calculated using I/Y function on a calculator

N = 10, PMT = 9% x 1000 = 90, FV = 1000, PV = -887

=> Compute I/Y = 10.91%