The Pennington Corporation issued a new series of bonds on January 1, 1985. The

Question

The Pennington Corporation issued a new series of bonds on January 1, 1985. The

bonds sold at par value, this is $1,000. The bonds have a 12% percent coupon rate, and

mature on December 31, 2014 (30 years after issue). Coupon payments are due semiannually,

on June 30 and December 31 respectively.

a. What was the Yield to Maturity (YTM) of the Pennington’s bonds on

January 1, 1985? Although you do not have to make any calculation to

answer this question, use the YTM Excel Function or the I.R.R. excel

function to demonstrate your answer.

b. What was the price of the bond on January 1, 1990, five years later,

assuming that the level of interest rates had fallen to 10%?

c. Find the current yield and capital gains yield on the bond on January 1,

1990, given the price as determined in part b.

d. On July 1, 2005, Pennington’s bonds sold for $891.64. What was the

YTM at that date?

e. What were the current yield and capital gains yield on July 1, 2005?

Explanation / Answer

a. whenever bonds are sold at par, the YTM equals the coupon rate and therefore YTM=12%.

b. The price of the bond on January 1, 1990 (i.e five years later), is the present value of future cashflows. The period from January 1, 1990 until December 31, 2014, (i.e. the date of maturity of the series of bonds) is 25 years. However, as coupon payments are made semi-annually, this will be 25*2=50 periods.

= 60* [{1 - 1/(1.05)^50}/0.05] +1000 {1/(1.05)^50}

= 60* 18.25593 + 1000 * 0.0872

= 1095.36 + 87.20

= 1182.56

c. The current yield is the annual coupon payment divided to the price and therefore:

Current yield = 120 / 1,182.56 = 0.101475 = 10.15%

The capital gains yield is the total yield minus the current yield,

i.e. 10% - 10.15% = -0.15%

d. The YTM on July 1, 2005 takes into account the period from July 1, 2005 until December 31, 2014, where the period is 9 and a half years. However, as coupon payments are made semi-annually, this will be 9.5*2=19 periods.     

YTM = {60 + (1000 -891.64) /19} / {2(891.64) + 1000} /3

   = (60 + 5.703158) / 927.76

   = 0.070819

   = 7.08%

e. The current yield and the capital gains yield are therefore:

Current yield = 120/891.64 = 13.46%

Capital gains yield = 14.1%-13.46%=0.64%

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