Question

Cricket Systems Co. plans to issue bonds with a par value of $1,000 and 30 years to maturity. These bonds will pay $25 interest every 6 months. Current market conditions are such that the bonds will be sold to net $1,205.62. What is the yield to maturity (YTM) on an annual basis that a broker would quote to an investor.

Please answer without using a financial calculator and without using excel. The final answer is 3.84%.

Answer 1

Here the no. of paying period = 30 years * 2 periods of 6 months in a year = 60 periods. Let the annual YTM be 2x and so YTM for 6 month period will be 2x/2 = x

The $25 periodic coupon payment will be in the form of an annuity and so its present value = 25*PVIFA (x, 60)

= 25 * [1 - 1/(1+x)^60]/x

Also maturity amount = 1000 and its present value = 1000*PVIF (x, 60) = 1000/(1+x)^60

Thus 25 * [1 - 1/(1+x)^60]/x + 1000/(1+x)^60 = 1,205.62

let 1+x = y and so we can rewrite the equation as:

25 * [1 - 1/y^60]/(y-1) + 1000/y^60 = 1205.62

or (25*y^60 - 25)/(y-1) + 1000/y^60 = 1205.62

Or solving the above algebrically we get y = 1.01919900

Thus x = 0.01919900

YTM = 2x = 2*0.01919900

= 3.8398%.

This amount gets rounded to 3.84%