Question

The Sisyphean Company has a bond outstanding with a face value of $5,000 that reaches maturity in 9 years. The bond certificate indicates that the stated coupon rate for this bond is 8% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 10.3%, then the bond will trade at

A. Par.
B. A discount.
C. A premium.
D. None of the above

The answer is B but please show step by step not through excel why that is the answer please and thank you

Answer 1

A bond reaches its par value at the time of maturity. It doesn't matter whether it was issued at par or at discount. This means that after 9 years it reaches its par value i.e. 5,000 at the time of maturity. Therefore we need to find the present value to know whether it is issued at discount or premium.

We use financial calculator to find pv of the bond

Inputs: Fv = 5,000

I/y = 10.3/ 2 = 5.15 ( because it is a semi annual bond)

Pmt = 8% /2 × 5,000 = 200 ( semiannual bond)

N = 9 × 2 = 18

Pv = compute

We get, Pv = $ 4,335.66

As we can see that present value is less than face value, it means that the bond is trading at discount.