Question

An investor is considering the purchase of a 20-year 7% coupon bond selling for $816 and a par value of $1,000. The yield to maturity for this bond is 9%. Assume the investor’s horizon is 15 years. Market participants expect the yield rate for comparable issues to be 10% for the first 10 years and 6% for years 11 to 20.

1. What is the projected sale price at the end of 15 years?

2. What is total coupon payments plus the interest on interest at the end of 15 years? Note, there are two different yield rates for this period.

3. What is the ANNUALIZED total return in percentage?

Answer 1

1. The amortisation schedule of the bond from 16 years would be;

Time	Y16	Y17	Y18	Y19	Y20
Coupon	70	70	70	70	70
Principal redemption					1000

Hence, total future cashflows for the bonds after 15 years would be;

Time	Y16	Y17	Y18	Y19	Y20
Coupon	70	70	70	70	1070

Hence, the Price of bond at the end of 15 year is NPV of these cashflows discounted at expected yield, i.e. 6%

Hence we have

$Price = \frac{70}{1.06}+\frac{70}{1.06^{2}}+\frac{70}{1.06^{3}}+\frac{70}{1.06^{4}}+\frac{1070}{1.06^{5}}=$1042.12$

Hence, bond will sell at $1042.12 at the end of 15 years.

2. As the bond is yielding 7% coupon hence, the coupon payment every year would be 1000*7% = $70

Further, the sale of bond will fetch the investor a sum of $1042.12.

3. Let x be annualized return on the investment.

Hence, we have;

$816 = \sum_{i=1}^{15}(\frac{70}{(1+x)^{i}})+\frac{1042.12}{(1+x)^{15}}$

Solving for x, we get, Annualized return = 9.49%.