Question

Problem 7-8 Yield to call Seven years ago the Singleton Company issued 26-year bonds with a 12% annual coupon rate at their $1,000 par value. The bonds had a 7% 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. (select multiple choice answer) -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. -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. -Since the bonds have been called, investors will receive a call premium and can declare a capital gain on their tax returns. -Since the bonds have been called, investors will no longer need to consider reinvestment rate risk. -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.

Answer 1

a)
Issue Price = $ 1000
Annual Coupon Interest = 12% * 1000 = $ 120
Redemption Value = 1000 + 7% of 1000 = $ 1070
Period = 7 Years

Actual Return will be the rate at which

Issue Price = Present Value of Future Cash Flow
Issue Price = Present Value of Annual Coupon Interest for 7 years + PV of Redemption value at 7th year
1000 = [120/(1+r)¹ + 120/(1+r)² + 120/(1+r)³ + 120/(1+r)⁴ + 120/(1+r)⁵ + 120/(1+r)⁶ + 120/(1+r)⁷ ] + 1070/(1+r)7
This rate is called IRR ( Internal Rate of Return)
It is difficult to solve directly, so either use financial calculator or excel to solve
In below image i have shown how to calculate IRR in Excel

It will give r = 12.68%
So, realized rate of return for an investor = 12.68%

b)
Generally Company's call bonds earlier because when they have funds available at a lower cost compared to existing bonds, thus

The investor should not be happy that Singleton called them - 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.