Question

Wilson Oil Company issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 9 percent. This return was in line with the required returns by bondholders at that point in time as described below:

Real rate of return	3	%
Inflation premium	3
Risk premium	3
Total return	9	%

Assume that 10 years later, due to bad publicity, the risk premium is now 7 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity.

Compute the new price of the bond. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)

What is the new Price? __________

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:

where,

A is annuity amount

i is yield to maturity

FV is future value of annuity

n is number of years

Calculate the new yield to maturity(YTM):

Real rate of return	3%
Inflation premium	3
Risk premium	7
Total return	13%

Calculate the current price of the bond

Consider the following

The annuity amount, A = $90 (15% on $1000)

The future value of annuity, FV = $1000

The yield to maturity(YTM) = 13%

The maturity period , n = 15 years

Bond price = $581.61 + $159.89

Bond price = $741.53

Therefore, the current price of the bond is $741.53