Question

Gilligan Co.'s bonds currently sell for $1,010. 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 rate of return should an investor expect to earn if he or she purchases these bonds, the YTC or the YTM?

Select the correct answer. a. 6.77% b. 7.47% c. 7.12% d. 6.42% e. 6.07%

Answer 1

No of periods = 15 years

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (6.75% / 1) * $1000

Coupon per period = $67.50

Let us compute Yield to Maturity (YTM)

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

$1010 = $67.5 / (1 + YTM)¹ + $67.5 / (1 + YTM)² + ...+ $67.5 / (1 + YTM)¹⁵ + $1000 / (1 + YTM)¹⁵

Using Texas Instruments BA 2 plus calculator

SET N = 15, PMT = 67.5, FV = 1000, PV = -1010

CPT --> I/Y = 6.6426

YTM = 6.6426% or 6.64%

Let us compute Yield to Call(YTC)

Bond Price = Coupon / (1 + YTC)^period + Call price/ (1 + YTC)^period

$1010 = $67.50 / (1 + YTM)¹ + $67.50 / (1 + YTC)² + ...+ $67.50 / (1 + YTC)⁶ + $1067.50 / (1 + YTC)⁶

Using Texas Instruments BA 2 plus calculator

SET N = 6, PMT = 67.50, FV = 1000, PV = -1010

CPT --> I/Y = 7.4697

YTC = 7.4697% or 7.47%

The investor would expect to earn YTC = 7.47%