Question

Refer to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 12 percent to 11 percent.

a. What is the bond price at 12 percent?

b. What is the bond price at 11 percent?

c. What would be your percentage return on investment if you bought when rates were 12 percent and sold when rates were 11 percent?

Answer 1

Price of bond is equal to present value of coupon payment plus present value of par value to be paid on maturity
Assuming face value is $1,000
Coupon amount	$100	1000*10%
Yield to maturity	12%
a.
Following shows the calculation of price of bond at yield to maturity of 12%
Year	Cash flow	Discount factor@12%	Present Value
1	$100	0.89286	$89.29
2	$100	0.79719	$79.72
3	$100	0.71178	$71.18
4	$100	0.63552	$63.55
5	$100	0.56743	$56.74
6	$100	0.50663	$50.66
7	$100	0.45235	$45.23
8	$100	0.40388	$40.39
9	$100	0.36061	$36.06
10	$100	0.32197	$32.20
11	$100	0.28748	$28.75
12	$100	0.25668	$25.67
13	$100	0.22917	$22.92
14	$100	0.20462	$20.46
15	$100	0.18270	$18.27
16	$100	0.16312	$16.31
17	$100	0.14564	$14.56
18	$100	0.13004	$13.00
19	$100	0.11611	$11.61
20	$1,100	0.10367	$114.03
			850.61
Price of bond at yield to maturity of 12% is $850.61
b.
Following shows the calculation of price of bond at yield to maturity of 11%
Year	Cash flow	Discount factor@12%	Present Value
1	$100	0.90090	$90.09
2	$100	0.81162	$81.16
3	$100	0.73119	$73.12
4	$100	0.65873	$65.87
5	$100	0.59345	$59.35
6	$100	0.53464	$53.46
7	$100	0.48166	$48.17
8	$100	0.43393	$43.39
9	$100	0.39092	$39.09
10	$100	0.35218	$35.22
11	$100	0.31728	$31.73
12	$100	0.28584	$28.58
13	$100	0.25751	$25.75
14	$100	0.23199	$23.20
15	$100	0.20900	$20.90
16	$100	0.18829	$18.83
17	$100	0.16963	$16.96
18	$100	0.15282	$15.28
19	$100	0.13768	$13.77
20	$1,100	0.12403	$136.44
			920.37
Price of bond at yield to maturity of 11% is $920.37
c.
The percentage return on investment = (Sale Price - Purchase Price)/Purchase Price
The percentage return on investment = (920.37 - 850.61)/850.61
The percentage return on investment = 69.76/850.61
The percentage return on investment = 0.0820
The percentage return on investment is 8.20%