Question

The Change Corporation has two different bonds currently outstanding. Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $3,100 every six months over the subsequent eight years, and finally pays $3,400 every six months over the last six years. Bond N also has a face value of $30,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 12% compounded semi-annually. What is the current price of Bond M and Bond N?

Answer 1

Answer:

a. Current price of Bond M = $24,062.31

b. Current price of Bond N = $2,916.67

Explanation:

a. Calculation of current price of Bond M

Note: See the attached excel file for the calculation of current price of Bond M (in bold red color).

In the attached excel file, the following are used:

r = required return = 12%

s = number of semiannuals in a year = 2

From the attached excel file, we have:

Current price of Bond M = $24,062.31

b. Calculation of current price of Bond N

This can be calculated using the following formula:

Current price of Bond N = Face value of bond N / (100% + Semiannual required return)^n ............................ (1)

Where;

Face value of bond N = $30,000

Semiannual required return = Required return / Number of semiannual in a year = 12% / 2 = 6%

n = Number of semiannuals = Number of years of maturity * Number of semiannual in a year = 20 * 2 = 40

Substituting the above into equation (1), we have:

Current price of Bond N = $30,000 / (100% + 6%)^40 = $2,916.67