Gugenheim, Inc., has a bond outstanding with a coupon rate of 6.5 percent and annual payments. The yield to maturity is 7.7 percent and the bond matures in 21 years. What is the market price if the bond has a par value of $2,000?

Price of bond=$1,753.96

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 Gugenheim, Inc can be worked out as follows:

Step 1  

Calculate the PV of interest payments

Annual interest payment

= 6.5%% × 2000 = 130

PV of interest payment

PV = A× (1- 1+r)^(-n)

A- 130, r- 7.7, n- 21

= 130 × (1-(1.077)^(-21)/0.077)  = 1,332.743

Step 2

PV of redemption Value

PV = RV × (1+r)^(-n)

RV - 2000, r- 7.7%, n- 21

PV = 2000 × (1.077)^(-21)  = 421.2115063

Step 3

Price of bond

=  1,332.743 + 421.211

=$1753.955

Price of bond=$1,753.96

cash flow statement possibly