©2009 mcgraw-hill ryerson limited 1 of 40 11 cost of capital prepared by: michel paquet sait...

©2009 McGraw-Hill Ryerson Limited1 of 40

1111 Cost of CapitalCost of Capital

Prepared by:

Michel PaquetSAIT Polytechnic

©2009 McGraw-Hill Ryerson Limited


Chapter 11 - Outline

• What is the Cost of Capital?

• Components and Calculation of Cost of Capital

• Optimal Capital Structure

• Use of Cost of Capital

• Capital Asset Pricing Model (CAPM)

• Summary and Conclusions


Learning Objectives

1. Explain that the cost of capital represents the overall cost of financing to the firm. (LO1)

2. Define the cost of capital as the discount rate normally used to analyze an investment. It is an evaluation tool. (LO2)

3. Calculate the cost of capital based on the various valuation techniques from Chapter 10 as applied to bonds, preferred stock and common shares. (LO3)


Learning Objectives

4. Describe how a firm attempts to find a minimum cost of capital by varying the mix of its sources of financing. (LO4)

5. Explain the marginal cost of capital concept. (LO5)


Cost of Capital

• The cost of capital is a measure of the overall cost of financing to a firm.

• It is the discount rate used to discount future cash flows from an investment.

• It is the minimal rate of return that an investment of the same risk as the firm should earn.

• Using the cost of capital to make investment decisions eliminates inconsistency.

LO1/LO2


Cost of Capital

• The cost of capital is a weighted average cost of the various sources of capital, including debt, preferred stock, and common equity (retained earnings):

WACC = Weighted Average Cost of Capital

WACC = The sum of the weighted (aftertax) cost of each source of capital

• If a firm changes its financial leverage (capital structure), its cost of capital will also change accordingly.

LO1/LO2


Table 11-1Cost of capital–Baker Corporation

(1) (2) (3) Cost Weights Weighted (after tax) Cost

Debt . . . . . . . . . . Kd 6.55% 30% 1.97%

Preferred stock . . . . Kp 10.94 10 1.09

Common equity(retained earnings) . . . Ke 12.00 60 7.20

Weighted averagecost of capital . . . . . Ka 10.26%

LO3


Components and Calculation of Cost of Capital

1. Cost of Debt- The cost of debt to the firm is the effective yield

to maturity (or interest rate) paid to its bondholders.

- Two adjustments must be made to the yield: tax and flotation costs.

- Aftertax cost of debt:(1 )

1d

Y TK

F

LO3



2. Cost of Preferred Stock- Preferred stock:

• has a fixed dividend (similar to debt)• has no maturity date• dividends are not tax deductible to the firm

and are expected to be perpetual or infinite- Cost of preferred stock:

LO3

F

PDK pp

p

1

/FP

DK

p

p

p



3. Cost of Common Equity– Common stock equity is available through

retained earnings (R/E) or by issuing new common stock:

Common equity = R/E + New common stock

A. Cost of Retained Earnings• The cost of common equity in the form of retained earnings is

equal to the required rate of return on the firm’s common stock (this is the opportunity cost):

1

0e

DK g

P

LO3



B. Cost of New Common Stock– The cost of new common stock is higher than the

cost of retained earnings because of flotation costs

– Cost of new common stock:

or

• Cost of common equity can also be determined with the Capital Asset Pricing Model (CAPM)

01

0n

n

PDK g

P P

1

0

1

DP

n

gK

F

LO3



C. Capital Asset Pricing Model (CAPM)– An alternative model for calculating the required rate of return on

common stock to the dividend model– Based on a relationship between risk and return: Required return = risk-free rate + risk premium– Cost of retained earnings

– Cost of new common stock

or

j f j m fK R R R

1j

jn

KK

F

0

jn jn

PK K

P

LO3


Optimum Capital Structure

The optimum (best) situation is associated with the minimum overall cost of capital (WACC):– Costs of individual components of financing

weighed by their proportions (weights) in the firm’s capital structure produce WACC

– Optimum capital structure means the lowest WACC– Usually occurs with 40-70% debt in a firm’s capital

structure– Based upon the market value rather than the book

value of the firm’s debt and equity

LO4


FIGURE 11-1Cost of capitalcurve

LO4


Debt/Assets,Selected Companies with Industry Designation Percent

AbitibiBowater (forest products) AXB . . . . . . . . . . . . . . . . . 84Air Canada (airlines) AC.A . . . . . . . . . . . . . . . . 80Bank of Montreal (financials) BMO . . . . . . . . . . . . . . . . 95Canadian Tire (consumer discretion) CTC. . . . . . . . . . . . . . . . . 47Encana (energy) ECA. . . . . . . . . . . . . . . . . 52Nortel (networks) NT. . . . . . . . . . . . . . . . . . 84Melcor (real estate) MRD . . . . . . . . . . . . . . . . 60Potash (fertilizers) POT. . . . . . . . . . . . . . . . . 11Loblaw(consumer staples) L . . . . . . . . . . . . . . . . . . . 59RIM (wireless solutions) RIM . . . . . . . . . . . . . . . . . 28Teck Cominco (mining) TCK.A . . . . . . . . . . . . . . . 41

Table 11-3

Debt (total) to total assets, mid-2008

LO4

Source: www.tsx.com


FIGURE 11-2Cost of capitalover time

LO4


Use of The Cost of Capital

• The cost of capital (WACC) represents the overall rate of return required by a firm’s investors – bondholders, preferred shareholders and common shareholders.

• Investments must be judged against this benchmark regardless of the particular source of funds the firm is using for a particular investment.

• If investments are matched with their financing, investments with lower return may be accepted while those with higher return would be rejected.

LO4


Figure 11-3Cost of capital and investment projects for the Baker Corporation

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

Percent

10 15 19 5039Amount of capital ($ millions)

10.26%

70 85 95

Weighted average cost of capital

Ka

A

BC

D

EF

GH

-----

----

LO2/LO4


Table 11-4Investment projects available to the Baker Corporation

A . . . . 16.00% $10B . . . . 14.00 5C . . . . 13.50 4D . . . . 11.80 20E . . . . 10.40 11F . . . . 9.50 20G . . . . 8.60 15H . . . . 7.00 10

$95

Expected CostProjects Returns ($ millions)

LO2/LO4


Marginal Cost of Capital

• A firm’s cost of debt or preferred stock or common stock increases as it uses more debt or preferred stock or common stock.

• This will lead to a higher cost of capital even if a given capital structure (the weights) is maintained.

• The marginal cost of capital measures a firm’s overall cost of receiving extra dollar from investors.

LO5


First $39 Million Next $11 Million

A/T Weighted A/T WeightedCost Wts. Cost Cost Wts. Cost

Debt . . . . Kd 6.55% .30 1.97% Debt . . . Kd 6.55% .30 1.97%

Preferred. . Kp 10.94 .10 1.09 Preferred . Kp 10.94 .10 1.09

Common Commonequity *. . Ke 12.00 .60 7.20 equity † . . Kn 13.33 .60 8.00

Ka = 10.26% Kmc = 11.06%

*Retained earnings †New common equity

Table 11-5Cost of capital for different amounts of financing

LO5


Over $50 Million

Cost Weighted(after tax) Weights Cost

Debt (higher cost) Kd 7.90% .30 2.37%

Preferred stock Kp 10.94 .10 1.09

Common equity (new common stock) Kn 13.33 .60 8.00

Kmc = 11.46%

Table 11-6Cost of capital for increasing amounts of financing

LO5


Figure 11-4Marginal cost of capital and Baker Corporation investment alternatives

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

Percent

10 15 19 5039Amount of capital ($ millions)

11.46%

70 85 95

Marginal cost of capital

Kmc

A

BC

D EF

GH

11.06%

10.26%

-----

----

LO5


Table 11-7Cost of components in the capital structure

1. Cost of debt Kd = Yield (1-T) = 6.55%

2. Cost of preferred stock

3. Cost of common equity

(retained earnings)

4. Cost of new common stock

KD

P F10.94%p

p

p

Yield = 10.74%

T = Corporate tax rate, 39%

Dp = Preferred dividend, $10.50

Pp = Price of preferred stock, $100

F = Flotation costs, $4

D1 = First year common dividend, $2

Pc = price of common stock, $40

g = growth rate, 7%

Same as above, with Pn =$36.00

F = Flotation costs, $4,

12.0%gPD

K0

1e

13.33%PP

gPD

Kn

0

0

1n

LO3


Capital Asset Pricing Model (CAPM)

• Relates the risk-return trade-offs of individual assets to market returns.

• Suggests that as some portion of risk can be diversified away, the extra return should only be based on the remaining portion of risk that can not be diversified away.

mathematically,

j j mK R e

APP-11A


TABLE 11A-1Performance of PAI and the market

APP-11A


FIGURE 11A-1Linear regressionof returns betweenPAI and the market

APP-11A


Year Kj Rm

1. . . . . 12% 10%2. . . . . 16% 18%3. . . . . 20% 16%4. . . . . 16% 10%5. . . . . 6% 8%

70% 62%

Kj Rm Kj Rm Rm2 ( Rm )

2

936 4,340 844 3,844

n Kj Rm – Kj Rm 5(936) - 4,340j n Rm

2 – ( Rm )2 5(844) - 3,844

Kj – Rm 70 - 0.9 (62)n 5

Figure 11A-1bLinear regression of returns between PAI

and the market

APP-11A


Figure 11A-1cLinear regression of returns between PAI and the marketCalculator

Mode: Stat

Input 10 (x,y) 12 Data

18 (x,y) 16 Data

16 (x,y) 20 Data

10 (x,y) 16 Data

8 (x,y) 6 Data

2ndF a gives 2.79

2ndF b gives .90

2ndF r gives .74

Note that the values for the x axis(Rm) are input first

This is the alpha coefficient

This is the beta coefficient

This is the correlation coefficient, a measure of how well the formula describes the relationship. The closer to 1.00, the better the fit

APP-11A


FIGURE 11A-2The security market line (SML)

APP-11A


FIGURE 11A-3The security market line andchanging interest rates

APP-11A


FIGURE 11A-4The security market line andchanging investor expectations

APP-11A


Capital Structure Theory

• Net Income (NI) Approach

• Net Operating Income (NOI) Approach

• Modigliani and Miller Model

APP-11B


Cost of capital (percent)

Debt/value ratio (percent)

Value of the firm ($)


Ke = Cost of Equity: Kd = Cost of debt; Ka = Cost of capitalValue is the market value of the firm

0 100 0 100

Kd

Ke

Ka

Figure 11B-1Net Income (NI) Approach

APP-11B


Figure 11B-2Net Operating Income (NOI) Approach

Cost of capital (percent) Value of the firm ($)

Debt/value ratio (percent) Debt/value ratio (percent) 0 0 100 100

Ke

Ka

Kd

APP-11B


Figure 11B-3Traditional approach as described by Durand

Ke

Ka

Kd

0 100 0 100

APP-11B

Cost of capital (percent)


Value of the firm ($)



Figure 11B-4Modigliani and Miller with corporate taxes

Cost of capital (percent) Value of the firm ($)

Debt/value ratio (percent) Debt/value ratio (percent)0 100 0 100

Cost of debtadjusted for the tax effect of interest

Ke

Ka

Kd

VL

VU

APP-11B


Figure 11B-5aCombined impact of the corporate tax effect and bankruptcy effect on valuation and cost of capital

0 100

Ka (M +M with tax effect and bankruptcy effect)

Ka (original M + M)

Ka (M + M with tax effect)

APP-11B

A. Cost of capital (percent)



Figure 11B-5bCombined impact of the corporate tax effect and bankruptcy effect on valuation and cost of capital

0 100

VL (M + M with tax effect)

VU (original M +M)

(M + M with tax effect and bankruptcy effect)

APP-11B

B. Value of the firm ($)



Summary and Conclusions

• The cost of capital is calculated as the weighted average of costs from various sources of financing (WACC).

• The weightings are based on the market value of the existing capital structure.

• Firms choose the weights to minimize WACC.• The cost of capital is used as an evaluation tool

to analyze investment proposals.

©2009 mcgraw-hill ryerson limited 1 of 40 11 cost of capital prepared by: michel paquet sait...

Documents