Question

Morin Company's bonds mature in 9 years, have a par value of $1,000, and make an annual coupon interest payment of $70. The market requires an interest rate of 8.0% on these bonds. What is the bond's price?

Answer 1

The bond's price is $909.26.

The Breakdown

To calculate the bond's price, we can use the present value formula for a bond:

Price = (C / (1 + r)¹) + (C / (1 + r)³) + ... + (C / (1 + r)^n) + (M / (1 + r)^n)

Where:

C = Annual coupon interest payment

r = Required interest rate (in decimal form)

n = Number of years until maturity

M = Par value of the bond

In this case:

C = $70

r = 8.0% = 0.08 (decimal form)

n = 9 years

M = $1,000

Plugging in the values into the formula:

Price = (70 / (1 + 0.08)¹) + (70 / (1 + 0.08)²) + ... + (70 / (1 + 0.08)⁹) + (1,000 / (1 + 0.08)⁹)

The bond's price would be:

Price ≈ $70 / (1 + 0.08)¹ + $70 / (1 + 0.08)² + ... + $70 / (1 + 0.08)⁹ + $1,000 / (1 + 0.08)⁹

Price ≈ $64.81 + $59.87 + $55.41 + $51.39 + $47.77 + $44.51 + $41.58 + $39.00 + $36.73 + $468.19

Price ≈ $909.26

Therefore, the bond's price is $909.26.