Principles of Managerial Finance

CHAPTER 11 The Cost of Capital 475

The initial $960 inflow is followed by annual interest outflows of $90 (9%

coupon interest rate$1,000 par value) over the 20-year life of the bond. In year

20, an outflow of $1,000 (the repayment of the principal) occurs. We can deter-

mine the cost of debt by finding the IRR, which is the discount rate that equates

the present value of the outflows to the initial inflow.

Calculator Use [Note:Most calculators require either the present (net proceeds)

or the future (annual interest payments and repayment of principal) values to be

input as negative numbers when we calculate cost to maturity. That approach is

used here.] Using the calculator and the inputs shown at the left, you should find

the before-tax cost (cost to maturity) to be 9.452%.

Approximating the Cost

The before-tax cost of debt, kd, for a bond with a $1,000 par value can be

approximated by using the following equation:

kd

I

(11.1)

where

Iannual interest in dollars

Ndnet proceeds from the sale of debt (bond)

nnumber of years to the bond’s maturity

EXAMPLE Substituting the appropriate values from the Duchess Corporation example into

the approximation formula given in Equation 11.1, we get

kd

I



 9



.



4



%

This approximate before-tax cost of debt is close to the 9.452% value calculated

precisely in the preceding example.

After-Tax Cost of Debt

However, as indicated earlier, thespecific costof financing must be stated on

an after-tax basis. Because interest on debt is tax deductible, it reduces the

firm’s taxable income. The after-tax cost of debt,ki, can be found by multiply-

ing the before-tax cost,kd, by 1 minus the tax rate,T, as stated in the following

equation:

kikd(1T) (11.2)

$92



$980

$960$1,000



2

$90 2



$980

$1,000$960



20

Nd$1,000



2

$1,000Nd



n

9.452

20 N

PV

FV

CPT

I

PMT

960
 90
 1000

Solution

Input Function