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?

A. What was the YTM on January 1, 1987?

since the bonds were sold at par, the YTM = coupon rate = 12%

B. What was the price of the bonds on January 1, 1992, 5 years later, assuming that interest rates had fallen to 10%?

0.5 = {60 + [(1,000 - m)/50]} / [(1,000 + m)/2]

25 + 0.025m = 60 + 20 - 0.02m

0.045m = 55

m = 55/0.045 = $1,222.22

C. Find the current yield, capital gains yield, and total return on January 1, 1992, given the price as determined in part b.

current yield = coupon / market price = $120 / $1,222.22 = 9.82%

capital gains yield = (P₁ - P₀)/P₀ = ($1,222.22 - $1,000)/$1,000 = 22.22%

total return = [(P₁ - P₀) + D]/P₀ = [($1,222.22 - $1,000) + $600] /$1,000 = 82.22%

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?

YTM = {60 + [(1,000 - 916.42)/13]} / [(1,000 + 916.42)/2] = 66.965 / 958.21 = 6.98856 x 2 (annual yield) = 13.98%

current yield = coupon / market price = $120 / $916.42 = 13.09%

capital gains yield = (P₁ - P₀)/P₀ = ($916.42 - $1,000)/$1,000 = -8.36%

total return = [(P₁ - P₀) + D]/P₀ = [($916.42 - $1,000) + $2,820] /$1,000 = 273.64%

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?

accrued interest = $60 x 2/6 = $20

0.075 = {60 + [(1,000 - m)/13]} / [(1,000 + m)/2]

0.03875(1,000 + m) = 136.92 - 0.07692m

38.75 + 0.03875m = 136.92 - 0.07692m

0.11567m = 98.17

m = 98.17 / 0.11567 = 848.71 + 20 (accrued interest) = $868.71

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