Problem 7-8 Yield to call Seven years ago the Singleton Company issued 25-year b
ID: 2739108 • Letter: P
Question
Problem 7-8 Yield to call Seven years ago the Singleton Company issued 25-year bonds with a 11% annual coupon rate at their $1,000 par value. The bonds had a 6% call premium, with 5 years of call protection. Today Singleton called the bonds. a.Compute the realized rate of return for an investor who purchased the bonds when they were issued and held them until they were called. Round your answer to two decimal places. % b.Explain why the investor should or should not be happy that Singleton called them. I.Since the bonds have been called, interest rates must have risen sufficiently such that the YTC is greater than the YTM. If investors wish to reinvest their interest receipts, they can now do so at higher interest rates. II.Since the bonds have been called, interest rates must have risen sufficiently such that the YTC is greater than the YTM. If investors wish to reinvest their interest receipts, they must do so at lower interest rates. III.Since the bonds have been called, investors will receive a call premium and can declare a capital gain on their tax returns. IV.Since the bonds have been called, investors will no longer need to consider reinvestment rate risk. V.Since the bonds have been called, interest rates must have fallen sufficiently such that the YTC is less than the YTM. If investors wish to reinvest their interest receipts, they must do so at lower interest rates. -Select-
Explanation / Answer
a) Realized return = 11.95%
It is the irr of the cash flows when the bond is held till it is called. Therefore, it is the value of 'i' in the following equation.
1000 = 110/(1+r)^1 + 110/*1+r)^2 + 110/(1+r)^3 + 110/(1+r)^4 + 110/(1+r)^5 + 1060/(1+r)^5
The value of 'i' has to be found out by trial and error by using different values for i such that the PV of RHS in above equation = 1000.
b) Option (V) - Investors will not be happy. Since the bonds have been called, interest rates must have fallen sufficiently such that the YTC is less than the YTM. If investors wish to reinvest their interest receipts, they must do so at lower interest rates
1 2 3 4 5 Total cash inflows 110 110 110 110 1170 pvif @ 12% 0.892857143 0.7971939 0.71178025 0.6355181 0.5674269 PV 98 88 78 70 664 998 pvif @ 11% 0.900900901 0.8116224 0.73119138 0.658731 0.5934513 PV 99 89 80 72 694 1036 Exact value of i = 12 - (1000-998)/(1036-998) = 11.95