Question

A bond has a coupon rate of 3%, pays interest semiannually, sells for $950, and matures in 3 years. Face value=1000

a) Calculate the approximate YTM (yield to maturity).

b) Calculate the YTM, using a financial calculator.

c) What is the difference between the approximate YTM and the Real YTM in (b)?

Answer 1

a)

No of periods = 3 years * 2 = 6 semi-annual periods

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

Coupon per period = (3% / 2) * $1000

Coupon per period = $15

Approximate Semi-annual YTM = (Coupon + (Face value - Price) / no of periods) /  ((Face value - Price) / 2)

Approximate Semi-annual YTM = ($15 + ($1000 - $950) / 6) / (($1000 + $950) / 2)

Approximate Semi-annual YTM = 2.3932%

Bond Equivalent yield = 2 * Approximate Semi-annual YTM

Bond Equivalent yield = 2 * 2.3932%

Bond Equivalent yield = 4.7863%

b)

Using the Texas Instruments BA 2 plus calculator

SET N = 6, PV = -950, FV = 1000, PMT = 15

CPT ---> I/Y = 2.4049

YTM = 2 * I/Y

YTM = 2* 2.4049

YTM = 4.8097%

c)

Differeence between Approximate & Real YTM

Approximate YTM - Real YTM = 4.7863 - 4.8097%

Approximate YTM - Real YTM = -0.0234%