Chapter outline

1. chapter outline Chapter 14 Cost of Capital Read Chapter 14 (except section 14.6) 1. Definition and overview 2. The Cost of Equity 2.1 Dividend growth model approach 2.2 The SML approach 3. The Cost of Debt and Preferred Stock 4. The weighted average cost of capital (WACC) 5. Some fine-tuning

2. 1. Definition and overview Key Issues: What do we mean by cost of capital? How can we estimate cost of capital? Cost of capital, appropriate discount rate, required rate of return ? minimum rate of return that a firm (or investors) requires on firm’s project = Rate of return on alternative project with similar risk. WACC (Weighted average cost of capital): A measure of the cost of capital.

3. 1. Definition and overview.. Who owns the firm? Shareholders: required rate of return ? RE Bondholders: required rate of return ? RD A firm’s cost of capital reflects both its cost of debt and equity. We first look at these costs separately, and then combine them to obtain the weighted cost of capital of a firm. Since we are always interested in valuing after-tax cash flows, we will focus on after-tax cost of capital.

4. 1. Definition and overview.. An accurate estimate of the cost of capital is required for: Capital budgeting: NPV and IRR rules require the appropriate discount rate. Performance evaluation: One can use the cost of capital as a benchmark rate of return for management to meet. Operating decisions: Regulatory agencies use cost of capital to determine the "fair return" in some regulated industries (e.g., electric utilities)

5. 2. The cost of equity There are two approaches to estimate RE 2.1 Dividend growth model approach Recall Rearranging yields

6. 2.1 Dividend growth model.. Implementation D0 and P0 : observable from data Growth rate, g: Estimate it using past data or analyst’s forecast. Example: Geometric growth rate: 4*(1+g)4 = 5.65. Solve for g = 8.969% Average growth rate: (10.00 + 7.95 + 10.53 + 7.62)/4 = 9.025%.

7. 2.1 Dividend growth model.. Pros/Cons: Model is simple and easy to understand. However, the model is applicable only to firms with reasonably stable growth. The model is sensitive to the estimated growth rate. It does not explicitly consider risk, i.e., there is no allowance for the degree of uncertainty on the estimated growth rate in dividends.

8. 2.2 The SML approach Recall CAPM: E(RE) = Rf + ?E [ E(Rm) – Rf ]  Implementation: Estimate ?E, risk-free rate (typically T-bill rate) and market risk premium based on past data. Pros/Cons: The model adjusts for risk, and is applicable for firms other than those with stable dividend growth. Estimates based on past data might not be very reliable in a rapidly changing environment. Estimates might be sensitive to the choice of time periods. However, ?E is reasonably stable in a period of 5 years.

9. 2.2 The SML approach.. Example: Cost of equity  Air BC has a beta of 1.25. Current stock price is $42 per share. The market risk premium is 6.5%. T-bills are currently yielding 5.5%. Air BC’s most recent dividend was $2.20. Dividends are expected to grow at a 4% p.a. indefinitely. What is the best estimate of Air BC’s cost of equity?   Growth model: RE = D0 * (1+g)/P + g = 2.20*(1+4%)/42 + 4% = 9.45%. SML: E(RE) = Rf + ?E [E(Rm) – Rf] = 5.5% + 1.25*6.5% = 13.625% ¦

10. 3. The cost of debt and preferred stock Cost of debt is simply the interest rate that lenders require on firm’s new borrowing. It is normally observable. The yield to maturity (YTM) on existing bonds, or Interest rate on new borrowings of similarly rated bonds. The coupon rate on existing bond is irrelevant: it reflects the firm’s cost of debt at the time of issuance. You want to use today’s yield as a proxy for cost of debt today. Preferred stocks pay fixed amount of dividend. So, dividend yield (dividend/current price) is a reasonable proxy for cost of preferred stock.

11. 3. The cost of debt and preferred stock.. Example: Cost of debt and preferred stock (1) KEC issued a 20-year, 8% semi-annual bond seven years ago. The bond currently sells for 110% of its face value of $1,000. Tax rate is 35%. Find out the pretax and after-tax cost of debt. First find out IRR for the bond: KEC will pay $40 every six months. $1,100 = PV($40 each at the end of 26 periods) + PV($1,000 at the end of 26 periods).  IRR=6.83% p.a.; pre-tax cost of debt = 6.83% p.a. Since interests are tax deductible, after-tax cost of debt is 6.83%*(1 – Tc) = 6.83%*(1 – 0.35) = 4.44%.

12. 3. The cost of debt and preferred stock.. (2) White Teck Co (WTC)’s preferred stock price is $95 per share. There is a $7 stated dividend. What is WKC’s cost of preferred stock?   Cost of preferred stock = $7/$95 = 7.37% ¦

13. 4. The weighted average cost of capital (WACC) WACC 1. Let: E ? the market value of the equity. D ? the market value of the debt. Then: V = E + D, so E/V + D/V = 100% 2. Proportion of E and D in firm’s value V are E/V and D/V. 3. Interest payments on debt are tax-deductible, so the After-tax cost of debt = the pretax cost * (1 - corporate tax rate). = RD ? (1 - Tc) 4. Thus the weighted average cost of capital is WACC = (E/V) ? RE + (D/V) ? RD ? (1 - Tc)

14. 4. The weighted average cost of capital (WACC)… Example: after-tax cost of debt: ABC borrows $1,000 at 10% p.a., TC = 40%. After-tax interest is 10% * (1 – TC). Why? $100 interest is tax deductible and it will reduce the tax bill by $40. So after tax interest is 10% * (1 – TC).

15. 4. The weighted average cost of capital (WACC)… When we say WACC, we refer to the after tax weighted average cost of capital. The table summarizes discussion so far.

16. 4. The weighted average cost of capital (WACC)… Example: Finding the WACC   5 million shares of common shares at $40, and ?E = 1.2. 750,000 shares of 7% preferred stock selling at $75. 250,000 units of 11% semi-annual bonds, par value = $1,000, 15 years-to-maturity selling at 93.5% of the par.  E(Rm) – Rf = 6%, Rf = 4%, TC = 34%. Step 1: find out market value of common, preferred stocks and bonds. See column 1 of table. Step 2: find out fraction in total firm value. See column 2. Step 3: find out after tax cost of common, preferred stocks and bonds. See column 3.

17. 4. The weighted average cost of capital (WACC)… (a) RE = Rf + ?[E(Rm) – Rf] = 4% + 1.2 * 6% = 11.2%   (b) To obtain RD, first find out the bond yield using following approximation formula (or using financial calculator)   Yield ˜ [Coupon + (Face value – Price)/maturity ] / [ (Price + Face value)/2 ] = [110 + (1,000 – 935)/15 ] / [ (1,000 + 935)/2 ] = 11.8% Yield (from a financial calculator) = 11.94% After-tax: 11.94% (1 – TC) = 11.94% * (66%) = 7.88%

18. 4. The weighted average cost of capital (WACC)… Step 4: calculate the weighted average of cost. See column 4.

19. 4. The weighted average cost of capital (WACC)… Example: Using the WACC WallStore’s expansion will cost $50,000 and generate $10,000 p.a. in perpetuity after-tax. Target debt/equity ratio of .50; required return on equity of 15%; return on bond of 10%. Tax rate is 34%. WACC = (E/V) × RE + (D/V)× RD × (1 – TC) = 2/3 × 15%+ 1/3 ×10% × (1 – .34) = 12.2%. WACC is appropriate to use, only when the proposed project is in the same risk class as the firm.

20. 4. The weighted average cost of capital (WACC)… Summary of WACC:  The required return on the firm as a whole. It is the appropriate discount rate for cash flows similar in risk to the firm. I. The Cost of Equity, RE A. Dividend growth model approach: RE = D1/P0 + g B. SML approach: E(RE) = Rf + ?E [ E(Rm) – Rf ]   II. The Cost of Debt, RD Use the yield to maturity on existing debt or similarly rated bonds. III. The Weighted Average Cost of Capital (WACC) WACC = (E/V) * RE + (D/V) * RD * (1 - Tc) where Tc is the corporate tax rate, E is the market value of the firm’s equity, D is the market value of debt, and V = E + D. So, E/V is the % of the firm’s financing (in market value terms) in equity, and D/V is the % in debt.

21. 5. Some fine-tuning What if a project risk is substantially different from the overall firm’s risk? One can not use firm’s overall WACC for the project. What if you still use overall WACC in this case? See next slide and find out what will happen. (Example) divisional cost of capital: Several divisions in a company with different risk should use different cost of capital (conglomerate: food division, computer division).

22. 5. Some fine-tuning

23. 5. Some fine-tuning There are two approaches to remedy the problem:  Pure play approach: pure play ? a company that focuses on a single line of business, e.g. oil drilling, gas exploration, etc. Subjective approach: The firm places projects into one of several risk classes. The firm determines discount rates for each risk class by adding (for high risk) or subtracting (for low risk) an adjustment factor to or from the firm’s WACC.   Project category Adjustment Factor Discount Rate High risk +6% 20% Medium risk +0 14% Low risk -4% 10% Mandatory n.a. n.a.

24. 5. Some fine-tuning..

25. 5. Some fine-tuning.. Example: SML and WACC An all-equity firm with 14% cost of capital considers the projects:   (1) If the firm uses 14% WACC which project does it accept? Project Y.  (2) When the firm considers risk of the projects, which project should it accept? CAPM: E(X) = 5% + 0.85*(14% ? 5%) = 12.65% < expected return 13% CAPM: E(Y) = 5% + 1.15*(14% ? 5%) = 15.35% > expected return 15% So the firm will choose Project X. ¦

26. 6. Questions Example: Eastman Chemical’s WACC Eastman Chemical has 78.26 million shares of common stock outstanding. The book value per share is $22.40 but the stock sells for $58. The market value of equity is $4.54 billion. Eastman’s stock beta is .90. T-bills yield 4.5%, and the market risk premium is assumed to be 9.2%. The firm has four debt issues outstanding. Coupon Book Value Market Value Yield-to-Maturity 6.375% $ 499m $ 501m 6.32% 7.250% 495m 463m 7.83% 7.635% 200m 221m 6.76% 7.600% 296m 289m 7.82% Total $1,490m $1,474m

27. 6. Questions.. Example: Eastman Chemical’s WACC… Cost of equity (SML approach): RE = .045 + .90 ? (.092) = .045 + .0828 = 12.78% Cost of debt: Multiply the proportion of total debt represented by each issue by its yield to maturity; the weighted average cost of debt = 7.15% Capital structure weights: Market value of equity = 78.26 m ? $58 = $4.539 billionMarket value of debt = $501m + $463m + $221m + $289m = $1.474 b V = $4.539 b + $1.474 b = $6.013 b D/V = $1.474b/$6.013b = .2451 E/V = $4.539b/$6.013b = .7549 WACC = .7549 (12.78) + .2451 ? 7.15 ?(1 - .35) = 10.79%

28. 6. Questions.. Some concept questions: 1. What is the relationship between cost of capital and firm value? Given other things being constant, the lower the cost of capital, the higher the value of the firm. 2. When we use the dividend growth model to estimate the firm’s cost of equity, we make a key assumption about future dividends of the firm. What is that assumption? We assume that dividends will grow at a constant growth rate, g. 3. What happens if we use the WACC to evaluate all potential investment projects, regardless of their risk? Estimated NPVs will be understated (overstated) for projects which are less risky (riskier) than the firm.

29. 6. Questions.. Problem 14.16 Elway Mining Corporation has 8 m shares of common stock selling at $35 with a beta of 1.0, 1 m shares of 6 % preferred selling at $60, and 100,000 9 % semiannual coupon bonds, par value $1,000 each. the bonds have 15 years to maturity and sell for 89 percent of par. The market risk premium is 8 percent, T-bills are yielding 5 percent, and the firm’s tax rate is 34 percent. a. What is the firm’s market value capital structure? b. If the firm is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows?

30. 6. Questions.. Solution to Problem 14.16 (continued) a. MVD = 100,000* ($1,000) *(.89) = $89M MVE = 8M*($35) = $280M MVp = 1M*($60) = $60M V = 89M + 280M + 60M = $429M D/V = 89M/429M = .207, E/V = 280M/429M = .653, and P/V = 60M/429M = .140.

31. 6. Questions.. Problem 14.16 b. For projects as risky as the firm itself, the WACC is the appropriate discount rate. So, find out the WACC. RE = .05 + 1.0*(.08) = 13% Bond YTM: $890 = $45(PVIFARD,30) + $1,000(PVIFRD,30) RD = 10.474%, and RD (1 - Tc) = (.10474)(1 - .34) = 6.91% RP = $6/$60 = .10 = 10% WACC = .653 (13) + .207 (6.91) + .14 (10) = 11.32%

32. Problem 14.17 An all-equity firm is considering the following projects. Assume the T-bill rate is 5% and the market expected return is 12%. Project Beta Expected Return (%) W .60 11 X .85 13 Y 1.15 13 Z 1.50 19 a. Which projects have a higher expected return than the firm’s 12 % cost of capital? b. Which projects should be accepted? c. Which projects would be incorrectly accepted or rejected if the firm’s overall cost of capital is used as a hurdle rate? 6. Questions..

33. 6. Questions.. Problem 14.17 (concluded) a. Projects X, Y, and Z with expected returns of 13%, 13%, and 19%, respectively, have higher returns than the firm’s 12% cost of capital. b. Using the firm’s overall cost of capital as a hurdle rate, accept projects W, X, and Z. Compute required returns considering risk via the SML: Project W = .05 + .60(.12 - .05) = .092 < .11, so accept W.Project X = .05 + .85(.12 - .05) = .1095 < .13, so accept X.Project Y = .05 + 1.15(.12 - .05) = .1305 > .13, so reject Y.Project Z = .05 + 1.50(.12 - .05) = .155 < .19, so accept Z. c. Project W would be incorrectly rejected and Project Y would be incorrectly accepted.

34. 6. Questions.. Problem 14.20 True North, Inc. is considering a project that will result in initial after-tax cash savings of $6 million at the end of the first year, and these savings will grow at a rate of 5 % per year indefinitely. The firm has a target debt/equity ratio of .5, a cost of equity of 18 %, and an after-tax cost of debt of 6 %. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and applies an adjustment factor of +2 % to the cost of capital for such risky projects. Under what circumstances should True North take on the project?

35. 6. Questions.. Problem 14.20 WACC = (.3333)(.06) + (.6666)(.18) = .14 Project discount rate = .14 + .02 = .16 NPV = - cost + PV (cash savings) PV (cash savings) = [$6M/(.16 - .05)] = $54.55M So the project should only be undertaken if its cost is less than $54.55M.