A $50,000, level-coupon Eurobond has a 6% coupon and matures in ten years. At what price should the bond sell today if the prevailing interest rate is 8% per annum? Round your answer
To the nearest dollar.

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the present value formula:
PV = C*(1 - 1/(1+r)^n)/r + F/(1+r)^n
where PV is the present value (what we are trying to find), C is the annual coupon payment, r is the interest rate, n is the number of years to maturity, and F is the face value or maturity value of the bond.

Plugging in the given values, we get:
PV = 3,000*(1 - 1/(1+0.08)^10)/0.08 + 50,000/(1+0.08)^10
PV = $43,290 (rounded to the nearest dollar)

Therefore, the correct answer is B. To calculate the price of the bond, we need to use the formula:

Price = (Coupon payment / (1 + Market interest rate)^1) + (Coupon payment / (1 + Market interest rate)^2) + … + (Coupon payment + Face value) / (1 + Market interest rate)^n

Where, 
Coupon payment = $50,000 x 6% = $3,000 
Face value = $50,000 
Market interest rate = 8% 
n = 10

Plugging the values in the formula:

Price = ($3,000 / 1.08^1) + ($3,000 / 1.08^2) + … + ($3,000 + $50,000) / 1.08^10

Price = $43,290

Therefore, the bond should sell at $43,290 today.

A $50,000, Level-Coupon Eurobond Has a 6% Coupon and Matures