Cost of Capital
^
CF1

^
CF2

^
CFn

Asset
+…+
+
=
Value
(1 + r)1 (1 + r)2
(1 + r)n r= firm’s required rate of return, which represents the return investors receive for providing funds to the firm

1

Chapter Essentials—The Questions






What types of capital do firms use to finance investments?
What is the cost of capital?
How is the cost of capital used to make financial decisions?
Why do funds generated through retained earnings have a cost?
Who determines a firm’s cost of capital?

2

Cost of Capital
 Introduction
 Cost of Debt, rdT
 Cost of Equity, rps and (rs or re)
 Marginal Cost of Capital (MCC)
 MCC and Investment Opportunity
(IOS) Schedules

3

Basic Definitions
 Capital—refers to the long-term funds used by a firm to finance its assets.
 Capital components—the types of capital used by a firm— long-term debt and equity
 Cost of capital—the cost associated with the various types of capital used by the firm, which is based on the rate of return required by the investors who provide the funds to the firm.
 Weighted average cost of capital, WACC—the average percentage cost, based on the proportion of each type of capital, of all the funds used by the firm to finance its assets.  Capital structure—the mix of the types of capital used by the firm to finance its assets.
 Optimal capital structure—the mix of capital that minimizes the firm’s WACC, thus maximizes its value.
4

Weighted Average Cost of Capital
(WACC)—Logic
 A firm generally uses different types of funds to finance its assets—that is, debt and equity.
 Costs associated with different types of capital (funds) usually are not the same—e.g., debt generally is cheaper than equity.
 The overall cost, or average, should be weighted based on the proportion of each type of funds used by the firm.
 Example: A firm is financed with debt and equity with the following characteristics:
Cost Proportion
Debt rdebt
=
8% 10%
Equity rstock
=
12% 90%
The average cost of each dollar of financing is:
Weighted average = 8%(0.1) + 12%(0.9) = 11.6%
5

Cost of Capital
 Investors who are the participants in the financial markets determine the firm’s costs of funds.
 The firm’s costs of funds change when




conditions in the financial markets change investors’ general risk aversion changes firm’s risk changes

6

Cost of Debt, rdT
 rd—the before-tax cost of debt is simply

the yield to maturity (YTM) of the debt
 YTM—bondholders’ required rate of

return = rd
 rdT—the after-tax cost of debt s' required
 Bondholder
  rdT  rateof return



rd


Tax savings 



 associatedwithdebt rd T
 rd(1  T)

T = marginal tax rate
7

Cost of Debt, rdT—Example
A firm has debt with the following characteristics:
Maturity value, M $1,000.00
Coupon rate, C
8.0% (paid semiannually)
Years to maturity 6 yrs
Market price
$1,099.50
Marginal tax rate
40.0%
Based on this information, we know that the following relationship exists:
Vd $1,099.50

$40
(1  rd)1



$40
(1  rd)2

 

$1,040
(1  rd)12

Solving for rd gives us the YTM for this bond
8

Cost of Debt, rdT—Example
Solve using:
 Trial-and-error process (numerical solution)  approximation equation

 Financial calculator
 Spreadsheet

9

Cost of Debt, rdT—Example rd approximation



M  Vd

Approximat e yield INT  N

to maturity
2(Vd )  M





3

$40










$1,000 $1,099.50
12



2($1,099.5
0)  $1,000
3

$31.71

0.02972.97%
$1,066.33

rd/2 = 2.97% per six-month period (interest payment) rd = 2.97% x 2 = 5.94% ≈ 6%
10

Cost of Debt, rdT—Example
Financial calculator solution:
N
=
12 = 6 years x 2
PV =-1,099.50
PMT =
40 = (0.08 x 1,000)/2
FV =
1,000
I/Y =
? = 3.0% per six-month period rd

= 3.0% x 2 = 6.0% per year = YTM
11

Cost of Debt, rdT—Example
 Bondholders/investors demand a 6 percent

rate of return to invest in this firm’s long-term debt.  rd = YTM = 6% is the rate of return paid to

bondholders.
 The firm pays $80 interest per year, which is a

tax