Question

1. Four years ago, Swift Bicycles issues a 20-year callable bond with a $1,000 maturity value and a 7.5% coupon rate of interest (paid semi-annually). The bond is currently selling a $1,050.
   1. What is the bonds yield to maturity (YTM)? (see hint above)

1. If the bond can be called in six years for a redemption price of $1,090, what is the bond’s yield to call (YTC)?Four years ago, Swift Bicycles issues a 20-year callable bond with a $1,000 maturity value and a 7.5% coupon rate of interest (paid semi-annually). The bond is currently selling a $1,050.
2. a. What is the bonds yield to maturity (YTM)? (see hint above)
3. b. If the bond can be called in six years for a redemption price of $1,090, what is the bond’s yield to call (YTC)?

Answer 1

No of periods = 16 years * 2 = 32 semi-annual periods

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

Coupon per period = (7.5% / 2) * $1000

Coupon per period = $37.5

Let us compute Yield to Maturity(YTM)

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

$1050 = $37.5 / (1 + YTM / 2)¹ + $37.5 / (1 + YTM / 2)² + ...+ $37.5 / (1 + YTM / 2)³² + $1000 / (1 + YTM / 2)³²

Using Texas Instruments BA 2 plus Calculator

SET N = 32, PMT = 37.5, FV = 1000, PV = -1050

CPT ---> I/Y = 3.4882

YTM = 2 * I/Y

YTM = 2 * 3.4882%

Yield to Maturity (YTM) = 6.9764% or 6.98%

Let us compute Yield to Call(YTC) to be called 6 years from now i,e 12 semi annual periods

Bond Price = Coupon / (1 + YTC / 2)^period + Face value / (1 + YTC / 2)^period

$1050 = $37.5 / (1 + YTC / 2)¹ + $37.5 / (1 + YTC / 2)² + ...+ $37.5 / (1 + YTC / 2)¹² + $1090 / (1 + YTC / 2)¹²

Using Texas Instruments BA 2 plus Calculator

SET N = 12, PMT = 37.5, FV = 1000, PV = -1050

CPT ---> I/Y = 3.8275

YTC = 2 * I/Y

YTC = 2 * 3.8275%

Yield to Call (YTC) = 7.6550% or 7.66%