1

From CAPM (single factor model) to multi-factor model

The CAPM has not been verified completely. Investors seem to be concerned with both market risk and other risk factors. Therefore, the it may not produce a correct estimate of ri.

ri = rRF + βi (rM – rRF) + ???

2

Fama-French 3 factor model

The required return is based on 3 factors. In addition to the market factor, there are also a size factor and book-tomarket factor.

Rt R f , t *( Rm , t R f ,t ) s * SMBt h * HMLt t

3

The Cost of Capital

WACC

Component costs

Adjusting for risk

4

As a financial manager in a firm

You are often faced with the decision whether to invest in some potential projects.

For example, should a firm buy a new production line?

5

Discount rate = required return

From the project, we need to earn at least the required return to compensate our investors for the financing they have provided.

The required return is the same as the appropriate discount rate and is based on the risk of the cash flows from the project.

How to decide the appropriate discount rate

(to discount future FCFs from the project)?

6

Required rate of return

Also called:

Cost of Capital

Hurdle rate

Discount rate

7

Estimate discount rate in a project One simple approach is to ASSUME that the new project has the same risk as the existing business or assets in the firm.

We can estimate what is the required return on the firm’s existing assets.

Then use this required return as the discount rate for the new project.

Of course, if the new project has risk very different from the existing business, one CANNOT do this.

8

Cost of Capital

Company Cost of Capital (COC) is the required return on the existing firm assets. It is based on the risk of assets.

The risk of firm’s overall assets is equal to the weighted average risks of firm’s debt, preferred stock and common equity. Thus the cost of capital of a firm equals the weighted average of the cost of debt, the cost of preferred stock, and the cost of common equity.

9

Example:

Suppose the company 785.com has the following classes of assets:

2/3 Intangible, good will & New technology

Beta=2.0

1/6 Machine & Plant

Beta=1.3

1/6 Working assets

Beta=0.6

Beta of firm assets

=1.3*(2/3)+1.3/6+0.6/6=1.18

10

Same example

Suppose the same company is owned by stockholders (70% in value) and debt holders (30% in value).

Beta of stock=1.51, beta of debt=0.41

Beta of the portfolio that contains all stocks and debts =0.41*30%

+1.51*70%=1.18

11

Firm Cost of Capital =

WACC

WACC is the weighted average of the after-tax cost of each of the sources capital used by a firm to finance its project, where the weight reflects the proportion of total financing raised from each source. 12

Calculating the weighted average cost of capital

WACC = wdrd(1-T) + wprp + wsrs

The w’s refer to the firm’s capital structure weights.

Use market values to determine the weights (proportions).

13

rd , rp , rs rd: cost of debt=required rate of return for debt investors.

r : cost of preferred stock= p required rate of return for preferred stock holders.

r cost of equity= required rate of s: return for common stock holders.

14

cost of debt

WACC = wdrd(1-T) + wprp + wcrs

rd is the cost of debt capital.

The yield to maturity on outstanding L-T debt is often used as a measure of rd.

Why tax-adjust, i.e. why rd(1-T)?

15

cost of debt

We are concerned with after-tax cash flows, so we need to consider the effect of taxes on the various components of costs of capital.

Interest expense reduces our tax liability

This reduction in taxes reduces our cost of debt

After-tax cost of debt = r (1-T) d 16

A 5-year, 12% annual coupon bond sells for $1,075.81. What is the cost of debt

(rd)?

INPUTS

5

N

OUTPUT

I/YR

-1075.81

120

1000

PV

PMT

FV

10

17

cost of debt

Interest is tax deductible, so

After-Tax rd

= Before Tax rd (1-T)

=