The Cost of Capital

1
Chapter 11
The Cost of Capital
2
Introduction

• This chapter discusses the concept of the cost of
  capital and develops approaches used to measure
  it.

3
Definition

• Cost of Capital (ka) is the return required on
  firms investments.
• Determined by
• how the firm is financed
• equity (common shares)
• debt
• preferred stock
• cost of each source of capital
• cost of equity
• cost of debt
• cost of preferred stock

4
Major Steps

• Steps in determining cost of capital
• First, we need to determine the marginal cost of
  each capital source (component cost)
• Second, determine the relative proportion
  (weight) of each source in the capital structure
• Third, calculate the firms overall cost of
  capital (ka) called the Weighted Average Cost of
  Capital (WACC).

5
Cost of Debt

• Pretax Cost of debt ( kd) is the rate of return
  required by investors in firms long-term debt
  securities.
• Need to adjust it for tax since interest payments
  are tax deductible.
• After-tax cost of debt (Ki)
• ki kd ( 1 - T )

6
Cost of Debt

• Methods for Calculating Kd
• Firm is selling new bonds
• Compute the yield that equates the present value
  of future interest and principal payments to the
  net proceeds to the firm from selling a bond.

7
Cost of Debt

• Example A firm sells a 20-year, 7.8 bond at par
  value of 1000. Net proceeds after issuance costs
  are 980. Tax rate is 40. Interests are paid
  annually.
• Net Proceeds PV -980
• Principal FV 1000
• Interest PMT 78
• n 20
• CPT I/Y
• I/Y Kd 8.00
• Ki 8 (1-0.40) 4.80

8
Cost of Debt

• Methods for Calculating Kd
• Firm is not selling new bonds, but its existing
  bonds are traded in the market.
• use the yield-to-maturity of existing bonds

9
Cost of Debt

• Example A firms 10-year, 8 bonds with a par
  value of 1000 are selling at 950. Tax rate is
  40.
• Market Price PV -950
• Principal FV 1000
• Interest PMT 80
• n 10
• CPT I/Y
• I/Y Kd 8.77
• Ki 8.77 (1-0.40) 5.26

10
Cost of Debt

• Methods for Calculating Kd
• Firm is not selling new bonds, and its existing
  bonds are not traded.
• use the average yield-to-maturity of bonds issued
  by firms having similar risk (similarly rated
  bonds).

11
Cost of Preferred Stock

• Rate of return required by investors on preferred
  stock (Kp)
• Perpetual Preferred Stocks

kp Dp/ Pnet
Example A Company makes an issue of preferred
stocks carrying a dividend of 3 for 30.
Issuance costs are 2 a share.
kp 3/ (30-2) 10.7
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Cost of Preferred Stock

• Redeemable Preferred Stocks
• Calculation is similar to the YTM on bonds

Example A Company makes an issue of preferred
stocks carrying a dividend of 3 for 30.
Issuance costs are 2 a share. These will be
retired in 10 years at par of 30. Net
Proceeds PV -28 Par Value FV
30 Dividend PMT 3 n 10 CPT
I/Y I/Y Kp 11.14
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Cost of Equity

• Two types
• Cost of Internal equity
• Opportunity cost to common stockholders
• Return available to stockholders in alternative
  investments
• Cost of External equity
• Costs of new equity

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Cost of Internal Equity (ke)

• Dividend valuation Approach (Constant Dividend
  Growth Model)
• ke D1/P0 g
• Example A firms stock is selling for
  20. It paid a dividend of 1.00 last year.
  Expected dividend growth rate is 5.

ke 1.00(1.05)/20 0.05 0.102510.25
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Cost of Internal Equity (ke)

• CAPM Approach
• ke rf ?( rm - rf )
• Example A firms stock has a beta of 1.2.
• The Treasury bill rate is 6. The
  expected market risk premium is 8.

ke 6 (1.2 x 8) 15.6
16
Cost of External Equity (k?e)

• Dividend valuation Approach (Constant Dividend
  Growth Model)
• k?e D1/Pnet g
• Example A firm issues new stocks for
• 20. The issuance costs are 1.00 share.
• It paid a dividend of 1.00 last year.
  Expected dividend growth rate is 5.

k?e 1.00(1.05)/19 0.05 0.1053
10.53
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Weighted Average Cost of Capital (WACC)(ka)

• Overall cost of capital of the firm computed as
  the weighted average of the component costs of
  capital.
• Weights represent the proportion of each capital
  component in the target capital structure.

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Calculating WACC
E market value of a firms common equity
B market value of a firms debt

Pf market value of a firms preferred stock Ke
(or Ke)cost of internal (or external)
common equity Kd pretax cost of
debt Kp cost of preferred stock

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WACC Example

• Firms cost of equity is 14, pretax cost of debt
  is 8, and the cost of preferred stock is 10.
  Its target long-term capital structure consists
  of 60 equity, 30 debt and 10 preferred stocks.
  The Marginal corporate income tax rate is 40.
• Ka 0.6 x 0.14 (0.30 x 0.08 x (1-0.4)) 0.10 x
  0.10
• 0.108410.84

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The Weighted (Marginal) Cost of Capital Schedule
MCC Schedule

• Step 1 Calculate the cost of capital for each
  component
• Step 2 Compute the MCC for each increment of
  capital raised

21
Determining the Optimal Capital Budget

• Compare the expected project returns to the
  companys MCC schedule.
• Accomplished by plotting the returns expected
  from the proposed capital expenditure projects
  against the cumulative funds required

22
Optimal Capital Budget

A

EX Major Foods Corporation
B
C
D
MCC
E
F
IRR

23 millions
23
Optimal Capital Budget

• Optimal capital budget contains all projects for
  which the expected return lies above the MCC
• The Major Foods Corporations optimal capital
  budget totals 23 million and includes Projects
  A, B,C, and D. Projects E and F are excluded.