Question

Jerome Corporation's bonds have 15 years to maturity, an 8.75% coupon paid semiannually, and a $1,000 par value. The bond has a 6.50% nominal yield to maturity, but it can be called in 6 years at a price of $1,050. What is the bond's nominal yield to call?

Answer 1

The nominal yield to call is computed as shown below:

First we need to compute the present value of the bond as follows:

The coupon payment is computed as follows:

= 8.75% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 43.75

The YTM will be as follows:

= 6.50% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.25% or 0.0325

N will be as follows:

= 15 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 30

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 43.75 x [ [ (1 - 1 / (1 + 0.0325)³⁰ ] / 0.0325 ] + $ 1,000 / 1.0325³⁰

= $ 43.75 x 18.98191741 + $ 383.0876842

= $ 1,213.546571

So, the nominal yield to call is computed as follows:

= [ Coupon payment + [ (Price at which bond can be called - current price) / (Year after which bond can be called x 2) ] / [ (Price at which bond can be called + current price) / 2 ]

= [ $ 43.75 + [ ($ 1,050 - $ 1,213.546571) / (6 x 2) ] / [ ($ 1,050 + $ 1,213.546571) / 2 ]

= [ $ 43.75 + [ - $ 163.5465709 / 12 ] / $ 1,131.773285

= $ 30.12111909 / $ 1,131.773285

= 2.661409267%

To get the annualized yield to call, we need to multiply the above figure by 2 as shown below:

= 2.661409267% x 2

= 5.32% Approximately

Feel free to ask in case of any query relating to this question