Question

Patricia Johnson is looking to invest in a three-year bond that makes semi-annual coupon payments at a rate of 5.325 percent. If these bonds have a market price of $988.09, what yield to maturity can she expect to earn? (Round intermediate calculations to 5 decimal places, e.g. 1.25145 and final answer to 2 decimal places, e.g. 15.25%.)

Answer 1

We have following formula for calculation of bond’s yield to maturity (YTM) in the given situation

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $988.09

Face value or Par value of the bond = $1000

C = coupon payment = 5.325% of $1000 = $53.25 but semiannual coupon, therefore C = $53.25/2 = $26.625

n = number of payments (time remaining to maturity) = 3 years; therefore number of payments n = 3 *2 = 6

YTM = interest rate, or yield to maturity =?

Now we have,

$988.09 = $26.625 * [1 – 1 / (1+YTM) ^6] /YTM+ $1000/ (1+YTM) ^6

By trial and error method we can calculate the value of YTM = 2.88% semiannual

Or annual YMT = 2 *2.88% = 5.76% per year

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(6,-26.625,988.09,-1000)” = 2.88%]

Therefore yield to maturity of the bond is 5.76%