Question

The Pennington Corporation issued a new series of bonds on January 1, 1987. The bonds were sold at par ($1,000); had a 12% coupon; and mature in 30 years, on December 31, 2016. Coupon payments are made semiannually (on June 30 and December 31). a. What was the YTM on January 1, 1987? b. What was the price of the bonds on January 1, 1992, 5 years later, assuming that interest rates had fallen to 10%? c. Find the current yield, capital gains yield, and total return on January 1, 1992, given the price as determined in part b.

Answer 1

Par Value of Bond = $1000

Semi-annual coupon payment = $1000*12%*1/2

= $60

a). On January 1, 1987 the bond was sold at par value which is $1000

When bond is sold at par value its Coupon rate is equal to the Yield to Maturity(YTM). Thus, YTM on Jan 1,1987 is 12%

b). 5 years later on 1 jan, 1992 the interest rate(or YTM) falls to 10%

No of coupon paymnets left from today(n) = (No of years to maturity-5)*2

= (30-5)*2 = 50

Semi-annual YTM = 10%/2

= 5%

Calculating the Price of Bond on January 1, 1992:-

Price = $1095.354 + $87.20

Price of bond on January 1, 1992= $1182.55

c). Current yield = Annual Copon Payment/Current Price

Current yield on January 1, 1992 = ($60*2)/$1182.55

= 10.15%

- Capital gains yield = (Current price - Buy Price)/Buy Price

Capital gains yield on January 1, 1992 = ($1182.55 - $1000)/$1000

= 18.255%

- Total Return on Bond = (Current price - Buy Price) + total Coupon Payment received in 5 years

= ($1182.55 - $1000) + ($60*2*5)

= $782.55

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