suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Price of bond = €875.09

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 would  be worked out as follows:

Step 1  

Calculate the PV of interest payments

Annual interest payment

= 3.8% × 1,000 = 38

PV of interest payment = A ×(1- (1+r)^(-n))/r

r- annual yield = 4.7%

n- 23

PV of interest payment= 38 × (1-(1.047^(-23)/0.047 =  €527.37

Step 2

PV of redemption Value

PV = RV × (1+r)^(-n)

PV = 1,000  × (1.047)^(-23)  = €347.717

Step 3

Price of bond

=  527.37+  347.717 = €875.09

Price of bond = €875.09