Question

The Pennington Corporation issued a new series of bonds on January 1, 1993. The bonds were sold at par ($1,000), had a 12% coupon, and will mature in 30 years on December 31, 2022. Coupon payments are made semiannually (on June 30 and December 31).

a. What was the YTM on the date the bonds were issued?

b. What was the price of the bonds on January 1, 1998 (5 years later), assuming that interest rates had fallen to 10%?

c. Find the current yield, capital gains yield, and total yield on January 1, 1998, given the price as determined in Part b.

d. On July 1, 2016 (6.5 years before maturity), Pennington’s bonds sold for $916.42. What are the YTM, the current yield, and the capital gains yield for that date?

e. Now assume that you plan to purchase an outstanding Pennington bond on March 1,2016, when the going rate of interest given its risk is 15.5%. How large a check must you write to complete the transaction? (Hint: Don’t forget the accrued interest.)

Answer 1

a) YTM = Coupon = 12% when bonds are available at par.

b) Bond Price can be calculated using PV function

N = 25 x 2 = 50, PMT = 12% x 1000 / 2 = 60, FV = 1000, I/Y = 10%/2 = 5%

=> Compute PV = $1,182.56

c) Current Yield = Annual Coupon / Price = 60 x 2 / 1182.56 = 10.15%

Capital gains = 1,182.56 / 1,000 - 1 = 18.26%

Total Yield = (1,182.56 + 10 x 60) / 1000 - 1 = 78.26%

d) Yield to maturity (YTM) can be calculated using I/Y function

N = 6.5 x 2 = 13, PMT = 60, PV = -916.42, FV = 1000

=> Compute I/Y = 7.00% (semi-annual)

Annualized YTM = 2 x 7% = 14.00%

Current Yield = 120 / 916.42 = 13.09%

Capital Gains = 916.42 / 1000 - 1 = -8.36%