The market price of a €500,000, ten-year, 12% (pays interest semiannually) bond issue sold to yield an effective rate of 10% is

Question

Quizplus · Accepted Answer

Step 1: Calculate the semi-annual coupon payment 
Coupon payment = (Face value x Coupon rate) / 2 = (500,000 x 12%) / 2 = €30,000

Step 2: Calculate the number of semi-annual periods (n) 
n = 10 years x 2 semi-annual periods per year = 20

Step 3: Calculate the present value of the semi-annual coupon payments using the semi-annual discount rate (i) 
i = 10% / 2 = 5% 
PV of coupon payments = (Coupon payment x [1 - (1 + i)^-n] )/ i = (30,000 x [1 - (1 + 5%)^-20]) / 5% = €358,312

Step 4: Calculate the present value of the face value using the semi-annual discount rate (i) 
PV of face value = Face value / (1 + i)^n = 500,000 / (1 + 5%)^20 = €204,000

Step 5: Add the present value of the coupon payments and the present value of the face value 
Market price = PV of coupon payments + PV of face value = €358,312 + €204,000 = €562,312

Therefore, the correct answer is B, €562,312.

The Market Price of a €500,000, Ten-Year, 12% (Pays Interest