Question

6. Calculated Numeric: Using Zero Rate table A Estima... Points: 15 Question Using Zero Rate table A Estimate the cash price of a bond with a face value of $100 that will mature in 24 months and pays a coupon of 4 semiannually per annum Answer Answer range ..

Answer 1

Price of bond = present value of its cash flows.

The cash flows are the coupon payments and face value payable at maturity.

Semiannual coupon payment = face value * annual coupon rate / 2

Semiannual coupon payment = $100 * 4% / 2= $2.

There are 4 semiannual coupon payments over 24 months, with the first occurring in 6 months, the second in 12 months, the third in 18 months and the last in 24 months. Hence, we use the corresponding zero rates to value the cash flows.

Present value of each cash flow = cash flow * e^-rt,

where r = zero rate,

and t = time of cash flow (in years).

Price of bond = ($4 * e^-0.042*0.5) + ($4 * e^-0.045*1.0) + ($4 * e^-0.047*1.5) + ($4 * e^-0.05*2.0) + ($100 * e^-0.05*2.0)

Price of bond = $105.57