Question

Morin Company’s annual bonds mature in 8 years, have a par value of $1,000, and currently sells for $903.04. The market requires an interest rate of 8.2% on these bonds. What is the bond’s coupon rate? 7.50% 7.25% 6.50% 6.25% 6.10%

Answer 1

6.50%

Working:

Current selling price of a bond is the present value of cash flow from bond which is nothing but present value of par value and

present value of annual coupon interest .

Step-1:Calculate present value of par Value

Present value of par value

=

Par Value x Present Value of $ 1 to be received in year 8

=

1000

x

(1+0.082)^-8

=

$ 532.33

Step-2:Present Value of annual coupon interest amount

Current Selling price of bond

$     903.04

Less:Present value of par value

$     532.33

Present value of coupon interest amount

$     370.71

Step-3:Calculate annual coupon interest amount

Present Value of annual coupon interest amount

=

Annual coupon amount x Present value of annuity of $ 1

or,

$ 370.71

=

Annual coupon amount x 5.7033

or,

Annual coupon amount

=

$ 370.71

/

5.7033

or,

Annual coupon amount

=

$    65.00

Working:

Present value of annuity of $ 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.082)^-8)/0.082

i

8.20%

=

5.7033

n

8

Step-4:Calculate annual coupon rate

Annual coupon rate

=

Annual coupon amount/Par Value

=

$    65.00

/

$       1,000

=

6.50%