Question

On July 1, 2013 an investment manager purchased five-hundred $1,000 par value bonds with an 8.75% coupon rate for $467,000. The bonds mature on July 15, 2021.

a. According to this information, would you expect that the rates being offered by similar investments on the open market carry a rate that is higher, or lower, than the coupon rate? Explain.

b. Find the current yield AND the yield to maturity. Show your work.

Answer 1

a. According to this information, would you expect that the rates being offered by similar investments on the open market carry a rate that is higher, or lower, than the coupon rate? Explain.

We know that the par value of the bond is $ 1000

And total purchase price of 500 bonds are $467,000

Therefore, its current market price = total purchase price/ number of bonds = $467,000/500 = $934.00 per bond

As the current market price ($934) of the bond is less than its par value ($1,000), therefore we can expect that rates being offered by similar investments on the open market carry a rate that is higher than the coupon rate of this bond.

a. Find the current yield AND the yield to maturity.

Bond’s current yield = annual coupon payment / market price of bond

Where,

Annual coupon payment = 8.75% of $1000 = $87.50

Market price of the bond = $934

Therefore,

Current yield = $87.50 / $934 = 0.0937 or 9.37%

We can use following formula for calculation of bond’s yield to maturity (YTM)

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

Where,        

M = value at maturity, or par value = $ 1000

P0 = the current market price of bond = $934

C = coupon payment = 8.75% of $1000 = $87.50

n = number of payments (time remaining to maturity) = 8 years 15 days or 8+ (15/365) = 8.041 years (purchased on July 1, 2013 and mature on July 15, 2021)

YTM = interest rate, or yield to maturity =?

Now we have,

$934 = $87.50 * [1 – 1 / (1+YTM) ^8.041] /YTM+ 1000 / (1+YTM) ^8.041

By trial and error method we can calculate the value of YTM = 9.98%

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

“= Rate(N,PMT,PV,FV)”

“Rate(8.041,-87.50,934,-1000)” = 9.98%]

Therefore YTM of the bond is 9.98%