Answer:
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
