On January 1, Applied Technologies Corporation (ATC) issued $570,000 in bonds that mature in 10 years. The bonds have a stated interest rate of 9 percent. When the bonds were issued, the market interest rate was 9 percent. The bonds pay interest once per year on December 31.

Required: Determine the price at which the bonds were issued and the amount that ATC received at issuance.

Bonds issued at $570,000 the company also recieve this amount

Explanation:

As the bonds coupon interest is 9% and the market rate which, represent the investor desired return for similar risk matches this amount the bonds will issue at par.

That is, the company will recieve exactly their face value from the bonds as the discounted value of the coupon and maturity atches the bond nominal return.

Price of Bond = $ 570,000

Amount received = $ 570,000.

Explanation:

The value of the bond is the present value (PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).

Value of Bond = PV of interest + PV of RV

The value of bond for Applied Technologies Corporation can be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment

= 9% * 570,000*=

=51,300

PV of interest =

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

51300 * (1 - (1.09) ^ (-10)

= 329,225.8401

Step 2

PV of Redemption Value

= 570,000 * (1.09) ^ (-10)

= 240,774.16

Price of bond

= 329,225.8401 + 240,774.16

= $ 570,000.00

Price of Bond = $ 570,000.00

Amount received = $ 570,000.