Review Problems 3 Solution
Review Problems#3
Question-1
Mark Goldsmith 's broker has shown him two bonds. Each has a maturity of 5 years, a par value of $1,000, and a yield to maturity of 12%. Bond A has a coupon interest rate of 6% paid annually. Bond B has a coupon interest rate of 14% paid annually.
a. Calculate the selling price for each of the bonds.
ANSWER:
b. Mark has $20,000 to invest. Judging on the basis of the price of the bonds, how many of either one could Mark purchase if he were to choose it over the other? (Mark cannot really purchase a fraction of a bond, but for purposes of this question, pretend that he can.)
ANSWER:
Mark can buy 20,000/783.71=25.52 Bond A and 20,000/1072.10=18.66 Bond B
c. Calculate the yearly interest income of each bond on the basis of its coupon rate and the number of bonds that Mark could buy with his $20,000.
ANSWER:
Annul Interest Income from Investment in Bond A: 25.52 x 60 =$1,531.17
Annul Interest Income from Investment in Bond B: 18.66 x 140 =$2,611.71
d. Assume that Mark will reinvest the interest payments as they are paid (at the end of each year) and that his rate of return on the reinvestment is only 10%. For each bond, calculate the value of the principal payment plus the value of Mark 's reinvestment account at the end of the 5 years.
T
Reinvestment Account
Bond-A
Reinvestment Account
1
60.00
87.85
2
60.00
79.86
3
60.00
72.60
4
60.00
66.00
5
60.00
60.00
FV
1000.00
1000.00
Total
1,366.31
T
Reinvestment Account
Bond-A
Reinvestment Account
1
140
204.97
2
140
186.34
3
140
169.4
4
140
154
5
140
140
FV
1000
1000
Total
1,854.71
Based on the final amounts accumulated, Compound Average Growth Rate for investments A and B are the following:
Investment A: Initial investment: $783.71 Accumulated future value as of year 5 =1,366.31
CAGR=(1366.21/783.71)(1/5)-1=11.77%
Investment A: Initial investment: $783.71 Accumulated future value
Question-1
Mark Goldsmith 's broker has shown him two bonds. Each has a maturity of 5 years, a par value of $1,000, and a yield to maturity of 12%. Bond A has a coupon interest rate of 6% paid annually. Bond B has a coupon interest rate of 14% paid annually.
a. Calculate the selling price for each of the bonds.
ANSWER:
b. Mark has $20,000 to invest. Judging on the basis of the price of the bonds, how many of either one could Mark purchase if he were to choose it over the other? (Mark cannot really purchase a fraction of a bond, but for purposes of this question, pretend that he can.)
ANSWER:
Mark can buy 20,000/783.71=25.52 Bond A and 20,000/1072.10=18.66 Bond B
c. Calculate the yearly interest income of each bond on the basis of its coupon rate and the number of bonds that Mark could buy with his $20,000.
ANSWER:
Annul Interest Income from Investment in Bond A: 25.52 x 60 =$1,531.17
Annul Interest Income from Investment in Bond B: 18.66 x 140 =$2,611.71
d. Assume that Mark will reinvest the interest payments as they are paid (at the end of each year) and that his rate of return on the reinvestment is only 10%. For each bond, calculate the value of the principal payment plus the value of Mark 's reinvestment account at the end of the 5 years.
T
Reinvestment Account
Bond-A
Reinvestment Account
1
60.00
87.85
2
60.00
79.86
3
60.00
72.60
4
60.00
66.00
5
60.00
60.00
FV
1000.00
1000.00
Total
1,366.31
T
Reinvestment Account
Bond-A
Reinvestment Account
1
140
204.97
2
140
186.34
3
140
169.4
4
140
154
5
140
140
FV
1000
1000
Total
1,854.71
Based on the final amounts accumulated, Compound Average Growth Rate for investments A and B are the following:
Investment A: Initial investment: $783.71 Accumulated future value as of year 5 =1,366.31
CAGR=(1366.21/783.71)(1/5)-1=11.77%
Investment A: Initial investment: $783.71 Accumulated future value