Gilligan Co.\'s bonds currently sell for $1,150. They have a 6.75% annual coupon

Question

Gilligan Co.'s bonds currently sell for $1,150. They have a 6.75% annual coupon rate and a 15-year maturity, and are callable in 6 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what average annual rate of return should an investor expect to earn if he or she purchases these bonds?

a. 3.92%

b. 4.12%

c. 5.28%

d. 5.55%

e. 4.81%

Show your work please.

Explanation / Answer

We will have to calculate the YTM first, to determine if the coupon rate exceeds the YTM, the bonds will be called and the company will replace them with lower cost bonds. In this case, we will consider YTC as the average rate of return. If the reverse is true (YTM>Coupon Rate), we will take YTM as the average rate.

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Step 1: Calculate YTM

YTM can be calculated with the use of EXCEL/Financial Calculator. The formula/function for calculating YTM is = Rate(Nper,PMT,PV,FV) where Nper is the period, PMT is interest payment, PV is Current Selling Price and FV is Face Value of Bonds)

Here, Nper = 15 Years, PMT = 1000*6.75% = -$1,150 and FV = $1,000

Putting the values in the above function, we get:

YTM = Rate(15,67.50,-1150,1000) = 5.28%

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Since, the coupon rate of 6.75% exceeds the YTM, we will have to calculate the YTC.

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Step 2: Calculate YTC

The formula/function for calculating YTC is same as YTM with the only exception that the callable value will be taken as the face value and we will take the callable period and not the maturity period.

Here, Nper = 6, PMT = 67.50, PV = -$1,150, FV = $1,067.50

Using these values, we get,

YTC = Rate(6,67.50,-1150,1067.50) = 4.81% (which is Option E)

The average annual rate of return the investor expects to earn is 4.81%.

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