Stech Co. is issuing $9 million 12% bonds in a private placement on July 1, 2017. Each $1,000 bond pays interest semi-annually on December 31 and June 30 of each year. The bonds mature in ten years. At the time of issuance, the market interest rate for similar types of bonds was 8%. What is the expected selling price of the bonds

Expected selling price = $ 1,271.81

Explanation:

The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.

These cash flows include interest payment and redemption value

The price of the bond can be calculated as follows:

Step 1

PV of interest payment

coupon rate - 12%, yield - 8%, years to maturity - 10 years

Semi-annual coupon rate = 12%/2 = 6%

Semi-annual Interest payment = (6%*$1000) = $60

Semi annual yield = 8%/2 = 4%

PV of interest payment

= A * (1 - (1+r) ^ (-n)) / r

A - interest payment, r - yield - 4%, n - no of periods - 2 * 10 = 20periods

= 60 * (1 - (1.04) ^ (-10*2)) / 0.04)

= 60 * 13.59032634

=$815.41

Step 2

PV of redemption value (RV)

PV = RV * (1+r) ^ (-n)

RV - redemption value - $1000, n - 2*10 r - 4%

= 1,000 * (1+0.04) ^ (-2*10)

= $456.38

Step 3

Price of bond = PV of interest payment + PV of RV

= $815.41 + $456.38

= $ 1,271.81

Expected selling price = $ 1,271.81