Question

(Assume par value for all bonds to be $1,000 unless specified otherwise)

a. What is the YTM on a 15-year zero-coupon bond that currently sell for 65 percent of par value?
b. Megathon Inc has bonds which have 8 years remaining to maturity, a YTM of 5.1 percent, and a current price of $964. The bonds make semiannual payments. What must the coupon rate be on these bonds?
c. What is the price of a 25-year, 6% coupon bond, assuming semiannual interest payments, if the YTM is 6.3% ?

Answer 1

a. The YTM on a 15-year zero-coupon bond that currently sells for 65% of par value is approximately 53.85%. b. The coupon rate on Megathon Inc's bonds must be approximately 5.29% given a YTM of 5.1% and a current price of $964. c. The price of a 25-year, 6% coupon bond with a YTM of 6.3% is approximately $1,359.51.

Step-by-step explanation:

a. To calculate the yield to maturity (YTM) on a zero-coupon bond, we need to use the formula:

YTM = (Face Value - Purchase Price) / Purchase Price

Given that the bond currently sells for 65% of par value, or $650, the YTM can be calculated as:

YTM = (1000 - 650) / 650 = 0.5385, or 53.85%

b. To find the coupon rate on a bond, we can rearrange the formula for YTM and solve for the coupon rate:

Coupon Rate = YTM * (Face Value / Purchase Price)

Using the given values, we can calculate the coupon rate as:

Coupon Rate = 0.051 * (1000 / 964) = 0.0529, or 5.29%

c. To calculate the price of a coupon bond, we can use the formula:

Price = (Coupon Payment / YTM) * (1 - (1 / (1 + YTM)^n)) + (Face Value / (1 + YTM)^n)

Using the given values, we can calculate the price of the bond as:

Price = (30 / 0.063) * (1 - (1 / (1 + 0.063)^50)) + (1000 / (1 + 0.063)^50) = $1,359.51