Question

Cost of debt. Kenny Enterprises has just issued a bond with a par value of ​$1,000​, a maturity of twenty​ years, and a coupon rate of 8.9​% with semiannual payments. What is the cost of debt for Kenny Enterprises if the bond sells at the following​ prices? What do you notice about the price and the cost of​ debt?

a.  ​$956.14

b.  ​$1,000.00

c.  ​$1,035.22

d.  ​$1,137.07

Answer 1

a.Information provided:

Par value= future value= $1,000

Time= 20 years*2= 40 semi-annual periods

Coupon rate= 8.9%/2= 4.45%

Coupon payment= 0.0445*1,000= $44.50

Current price= present value= $956.14

The cost of debt is calculated by computing the yield to maturity.

The yield to maturity is computed by entering the below in a financial calculator:

FV= 1,000

N= 40

PMT= 44.50

PV= -956.14

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.6950%.

Therefore, the cost of debt is 4.6950%*2= 9.39%.

b. Information provided:

Par value= future value= $1,000

Time= 20 years*2= 40 semi-annual periods

Coupon rate= 8.9%/2= 4.45%

Coupon payment= 0.0445*1,000= $44.50

Current price= present value= $1,000

The cost of debt is calculated by computing the yield to maturity.

The yield to maturity is computed by entering the below in a financial calculator:

FV= 1,000

N= 40

PMT= 44.50

PV= -1,000

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.45%.

Therefore, the cost of debt is 4.50%*2= 8.90%.

c. Information provided:

Par value= future value= $1,000

Time= 20 years*2= 40 semi-annual periods

Coupon rate= 8.9%/2= 4.45%

Coupon payment= 0.0445*1,000= $44.50

Current price= present value= $1,035.22

The cost of debt is calculated by computing the yield to maturity.

The yield to maturity is computed by entering the below in a financial calculator:

FV= 1,000

N= 40

PMT= 44.50

PV= -1,035.22

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 4.2650%.

Therefore, the cost of debt is 4.2650%*2= 8.53%.

d. Information provided:

Par value= future value= $1,000

Time= 20 years*2= 40 semi-annual periods

Coupon rate= 8.9%/2= 4.45%

Coupon payment= 0.0445*1,000= $44.50

Current price= present value= $1,137.07

The cost of debt is calculated by computing the yield to maturity.

The yield to maturity is computed by entering the below in a financial calculator:

FV= 1,000

N= 40

PMT= 44.50

PV= -1,137.07

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 3.78%.

Therefore, the cost of debt is 3.78%*2= 7.56%.

It is noticeable that as the price of the bond increases, the cost of debt reduces.

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