The Pennington Corporation issued a new series of bonds on January 1, 1987. The
ID: 2678256 • Letter: T
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.
d. On July 1, 2010, 6 1/2 years before maturity, Pennington's bonds sold for $916.42. What were the YTM, the current yield, the capital gains yield, and the total return at that time?
e. Now assume that you plan to purchase an outstanding Pennington bond on March 1, 2010, when the going rate of interest given its risk was 15.5%. How large a check must you write to complete the transaction?
Fundamentals of Financial Management by Brigham & Houston, concise 7th edition
Chapter 7, ST-2
Explanation / Answer
a) Par value = $1,000
Selling price = $1,000
Coupon interest = (1,000*0.12)/2 = $60
Number of periods = 2*30 = 60
N = 60
FV = 1000
PV = -1000
PMT=$60
Using calculator, rate = 6%
YTM/2 = 6%
YTM = 6% * 2 = 12%
b) N = 25*2 = 50
FV = 1000
PMT = 60
Rate = 10%/2 = 5%
Using calculator, PV = -1,182.56
Price of the bond = $1,182.56
c) Current yield = 120 / 1182.56 = 0.1015 or 10.15%
Capital gains yield = (1,182.56 – 1,000)/1,000 = 0.18256 or 18.26%
Total return = 10.15% + 18.26% = 28.41%
d) N = 13
FV = 1000
PV = -916.42
PMT=$60
Using calculator, rate = 7%
YTM/2 = 7%
YTM = 7% * 2 = 14%
Current yield = 120 / 916.42 = 0.131 or 13.1%
Capital gains yield = (916.42 – 1,000)/1,000 = -0.0836 or -8.36%
Total return = 13.1% + -8.36% = 4.74%
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