Question

For the bond problem, assume interest payments are on an annual basis.

Go 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 11 percent to 8 percent:

a. What is the bond price at 11 percent?

b. What is the bond price at 8 percent?

c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent?

Reference: Table 10-1:

Answer 1

Yield to Maturity (YTM) is the annual rate of return that is earned on the purchase of a bond at a current market price held by the investor till the maturity period.

It shows an effective annual return from a security expressed as a percentage of the current market price of the security. It measures the total income earned by an investor over the total security life. YTM is also known as market rate of return or market rate of interest.

Formula to calculate bond price is:

Here,

The annuity amount is ‘A’

The yield to maturity is ‘i’

The future value of annuity is ‘FV’

The number of years is ‘n’

a)

Calculate the current price of the bond, when yield to maturity (YTM) is 11%:

Consider the following:

The annuity amount, A is $100 (10% on $1,000)

The future value of annuity, FV is $1,000

The number of years, n is 20 years

Therefore, the price of the bond is $920.37.

b)

Calculate the current price of the bond, when yield to maturity (YTM) is 8%:

Therefore, the price of the bond is $1196.37.

c)

Calculate the percentage return on the investment, when bought at a rate 11% and sold at a rate 8%:

Therefore, the percentage return is 29.99%.