Question

PT MAJU's corporate bonds can currently be sold for $ 1,150. These bonds have a nominal value of $ 1,000 with an annual coupon rate of 7% per year and a age of 10 years. However, the bond could be withdrawn from circulation after 6 years at a price of $ 1,067. In this case it is assumed that there are no transaction costs except for the call premium which is given at the time of withdrawal and refund of bonds and the yield curve is horizontal, with rates that remain constant at the current level to the future.

Question

With the conditions mentioned above, what is the rate of return that investors expect if they buy the bonds, whether they are kept to maturity (Yield To Maturity) or if they arrive at withdrawal before maturity (Yield To Call)?

Answer 1

No of periods = 10 years

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

Coupon per period = (7% / 1) * $1000

Coupon per period = $70

Let us compute Yield to Maturity (YTM)

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

$1150 = $70 / (1 + YTM)¹ + $70 / (1 + YTM)² + ...+ $70 / (1 + YTM)¹⁰ + $1000 / (1 + YTM)¹⁰

Using Texas Instruments BA 2 plus calculator

SET N = 10, PMT = 70, FV = 1000, PV = -1150

CPT --> I/Y = 5.0525

YTM = 5.0525% or 5.05%

Let us compute Yield to Call(YTC)

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

$1150 = $70 / (1 + YTM)¹ + $70 / (1 + YTC)² + ...+ $70 / (1 + YTC)⁶ + $1067 / (1 + YTC)⁶

Using Texas Instruments BA 2 plus calculator

SET N = 6, PMT = 70, FV = 1067, PV = -1150

CPT --> I/Y = 5.0266

YTC = 5.0266% or 5.03%

The investor would expect to earn YTC= 5.03%