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Factor Model

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**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) + ???

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**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-to-market factor.

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**WACC Component costs Adjusting for risk**

The Cost of Capital WACC Component costs Adjusting for risk

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**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?

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**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)?

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**Required rate of return**

Also called: Cost of Capital Hurdle rate Discount rate

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**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.

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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.

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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

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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

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**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.

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**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).

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rd , rp , rs rd: cost of debt=required rate of return for debt investors. rp : cost of preferred stock= required rate of return for preferred stock holders. rs: cost of equity= required rate of return for common stock holders.

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**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)?

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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 = rd(1-T)

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**A 5-year, 12% annual coupon bond sells for $1,075. 81**

A 5-year, 12% annual coupon bond sells for $1, What is the cost of debt (rd)? 5 120 1000 INPUTS N I/YR PV PMT FV OUTPUT 10

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**cost of debt Interest is tax deductible, so After-Tax rd**

= Before Tax rd (1-T) = 10% (1 – T) If T=40% = 6%

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**cost of preferred stock**

WACC = wdrd(1-T) + wprp + wsrs rp is the cost of preferred stock. The rate of return investors require on the firm’s preferred stock.

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**What is the cost of preferred stock?**

The cost of preferred stock can be solved by using this formula: rp = Dp / Pp = $10 / $111.10 = 9%

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**cost of preferred stock**

Preferred dividends are not tax-deductible, so no tax adjustments necessary. Just use rp . rp = Dp / Pp

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**cost of equity WACC = wdrd(1-T) + wprp + wsrs**

rs is the cost of equity. The cost of equity is the return required by equity investors given the risk of the cash flows from the firm

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**Two ways to determine the cost of common equity, rs**

CAPM: rs = rRF + (rM – rRF) β DCF: rs = (D1 / P0) + g

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**If the rRF = 7%, RPM = 6%, and the firm’s beta is 1**

If the rRF = 7%, RPM = 6%, and the firm’s beta is 1.2, what’s the cost of common equity based upon the CAPM? rs = rRF + (rM – rRF) β = 7.0% + (6.0%)1.2 = 14.2%

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**If D0 = $4.19, P0 = $50, and g = 5%, what’s the cost of common equity based upon the DCF approach?**

D1 = D0 (1 + g) D1 = $4.19 ( ) D1 = $4.3995 rs = (D1 / P0) + g = ($ / $50) = 13.8%

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**WACC = wdrd(1-T) + wprp + wcrs = 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%) **

A firm’s capital consists of has 30% in debt, 10% in preferred stock, and 60% in common equity. T=40%, rd=10%,rp=9%, rs=14%. WACC = wdrd(1-T) + wprp + wcrs = 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%) = 1.8% + 0.9% + 8.4% = 11.1%

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The risk of a project When calculating the discount rate of a potential investment project, we have often assumed that the project to be taken has the same risk as the existing business or assets of the firm. If this assumption is valid, then we can use WACC as our discount rate to discount future cash flows from a project. Of course, if the new project has very different risk from existing business, one cannot do so.

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**Should a company use the composite WACC as the hurdle rate for any of its projects?**

Ok for a project with average risk. The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk in the firm. Not Ok for a project with very different risk.

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**Using WACC for All Projects - Example**

What would happen if we use the WACC for all projects regardless of risk? Assume the WACC = 15% Project Required Return Expected Return A 20% 17% B 15% 18% C 10% 12% Ask students which projects would be accepted if they used the WACC for the discount rate? Compare 15% to IRR and accept projects A and B. Now ask students which projects should be accepted if you use the required return based on the risk of the project? Accept B and C. So, what happened when we used the WACC? We accepted a risky project that we shouldn’t have and rejected a less risky project that we should have accepted. What will happen to the overall risk of the firm if the company does this on a consistent basis? Most students will see that the firm will become riskier.

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**If using one WACC for all projects**

You might mistakenly reject project C and take project A. That is, you tend to favor risky projects. If you keep making such mistakes, the firm may become more and more risky.

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**We should consider the project’s risk**

If the project is more risky than the firm, use a discount rate greater than the WACC If the project is less risky than the firm, use a discount rate less than the WACC

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**Questions What are the approaches for computing the cost of equity?**

How do you compute the cost of debt and the after-tax cost of debt? How do you compute the capital structure weights required for the WACC? What happens if we use the same WACC as the discount rate for projects with very different risks?

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**Exercises Using the company cost of capital to evaluate a project is:**

A. Always correct B. Always incorrect C. Correct for projects that are about as risky as the average of the firm's other assets

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If a firm uses the same company cost of capital for evaluating all projects, which of the following is likely? A. Rejecting good low risk projects B. Accepting poor high risk projects C. Both A and B D. Neither A nor B

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**The (pretax) cost of debt for a firm ____.**

A) is always greater than the cost of equity B) normally cannot be observed, directly or indirectly, in the marketplace C) is equal to the yield to maturity on the firm's outstanding bonds D) is greater than the average coupon rate on the firm's outstanding bonds E) is equal to the average coupon rate on the firm's outstanding bonds

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**A common stock issue is currently selling for $31 per share**

A common stock issue is currently selling for $31 per share. You expect the next dividend to be $1.40 per share. If the firm has a dividend growth rate of 5% that is expected to remain constant indefinitely, what is the firm's cost of equity? A)9.5% B)11.3% C)13.8% D)14.2% E)15.1%

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**What is the required return on the firm’s existing assets?**

A firm’s cost of capital is the required return on the firm’s existing assets; it is also the weighted average required rates of return for all investors of the firm. Investors may include debt investor, preferred stock investor, and common stock investor.

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**What factors influence a company’s composite WACC?**

Interest rates Tax rates. The firm’s capital structure and dividend policy. The firm’s investment policy. Firms with riskier projects generally have a higher WACC.

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