Question

A $1,000 par value bond is currently valued at $1,050. The bond pays interest semi-annually, has 9 years to maturity, and has a yield to maturity of 7.72 percent. The coupon rate is _____ percent and the current yield is _____ percent.

Multiple Choice

a. 7.80; 6.21

b. 8.00; 7.31

c. 8.00; 7.51

d. 8.08; 7.66

e. 8.50; 8.10

Answer 1

Information provided:

Par value= future value= $1,000

Current price= present value= $1,050

Time= 9 years*2= 18 semi-annual periods

Yield to maturity= 2.72%/2= 1.36% per semi-annual period

The coupon rate is computed by first calculating the coupon payment.

Enter the below in a financial calculator:

FV= 1,000

PV= -1,050

N= 18

I/Y= 3.86

Press the CPT key and PMT to compute the coupo payment.

The value obtained is 42.50 per semi-annual period.

The annual coupon payment is $42.50*2= $85

Coupon rate is calculated using the below formula:

Coupon rate= Annual coupon payment/ Par value

                        = $85/ $1,00

                        = 0.0850*100

                        = 8.50%

Current yield is calculated using the below formula:

Current Yield= Annual interest/Current price

                         = $85/ $1,050

                         = 0.0810*100

                         = 8.10%.

Hence, the answer is option d.

In case of any query, kindly comment on the solution.