Question

Find the cost of debt

​(r​d),

and the​ after-tax cost of debt for each of the following​ bonds:

Bond	Par Value	Coupon Rate	Maturity	Current Value	Tax Rate
A	​1,000	​10%	30 Years	​1,455	​40%
B	​1,000	​12%	13 Years	954	​35%
C	​1,000	​8%	5 Years	875	​45%

Bond​ A, Cost of Debt​ (rd) :

Bond A, After Tax Cost of​ Debt:

​

Bond​ B, Cost of Debt​ (rd):

Bond​ B, After Tax Cost of​ Debt:

​Bond​ C, Cost of Debt​ (rd):

Bond​ C, After Tax Cost of​ Debt:

​

Answer 1

A.Information provided:

Par value= future value= $1,000

Coupon rate= 10%

Coupon payment= 0.10*1,000= $100

Time= 30 years

Current price= present value= $1,455

Tax rate= 40%

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

Enter the below in a financial calculator to compute the yield to maturity:

FV= 1,000

PMT= 100

N= 30

PV= -1,455

The value obtained is 6.51.

Therefore, the cost of debt is 6.51%.

After tax cost of debt= before tax cost of debt*(1- tax rate)

                                        = 6.51%*(1- 0.40)

                                        = 3.91%.

B. Information provided:

Par value= future value= $1,000

Coupon rate= 12%

Coupon payment= 0.12*1,000= $120

Time= 13 years

Current price= present value= $954

Tax rate= 35%

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

Enter the below in a financial calculator to compute the yield to maturity:

FV= 1,000

PMT= 120

N= 13

PV= -954

The value obtained is 12.74.

Therefore, the cost of debt is 12.74%.

After tax cost of debt= before tax cost of debt*(1- tax rate)

                                        = 12.74%*(1- 0.35)

                                        = 8.28%.

C. Information provided:

Par value= future value= $1,000

Coupon rate= 8%

Coupon payment= 0.08*1,000= $80

Time= 5 years

Current price= present value= $875

Tax rate= 45%

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

Enter the below in a financial calculator to compute the yield to maturity:

FV= 1,000

PMT= 80

N= 5

PV= -875

The value obtained is 11.42.

Therefore, the cost of debt is 11.42%.

After tax cost of debt= before tax cost of debt*(1- tax rate)

                                        = 11.42%*(1- 0.45)

                                        = 6.28%.

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