Question

Sunland Real Estate Company management is planning to fund a development project by issuing 10-year zero coupon bonds with a face value of $1,000. Assuming semiannual compounding, what will be the price of these bonds if the appropriate discount rate is 15.4 percent? (Round answer to 2 decimal places, e.g. 15.25.)

Answer 1

Price of the zero coupon bond will be the present value of the bond.

Bond price = Present value of bond payment at maturity

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $1000, PV = Present value, r = rate of interest = 15.4% compounding semi annually, so semi annual rate = 15.4% / 2 = 7.7%, n= time period = 10 * 2 = 20 semi annual periods

now, putting theses values in the above equation, we get,

$1000 = PV * (1 + 7.7%)²⁰

$1000 = PV * (1 + 0.077)²⁰

$1000 = PV * (1.077)²⁰

$1000 = 4.40873571972

PV = $1000 / 4.40873571972

PV = $226.82

So, price of the bonds is $226.82.