9 -1 Lecture Eleven The Overall Cost of

9 -1 Lecture Eleven The Overall Cost of Capital n Cost of Capital Components l. Debt l. Preferred l. Common Equity n WACC n MCC n IOS

Cost of Capital 9 -2 1. For capital budgeting purposes - “opportunity cost”, “hurdle rate”, “cut off rate” 2. For measure of effective or desirable capital structure. ie. Relative merit of varying degrees of leverage (D/TA) or (D/E) 3. For growth of the economy. If estimate of overall cost of capital is higher than the actual, investment (I), will be less that is economically justified and the economy will slow down Estimation of the cost of capital for the firm is very important but quite difficult to do. So we may settle for a range or a “worry zone” concept.

Theoretical Definition of the Cost of Capital 9 -3 I. Gordon’s “The cost of capital for a given firm is a discount rate with the property that an investment with a rate of profit above (below) this rate will raise (lower) the value of the firm. ” II. Johnson’s Financial manager may measure his firm’s cost of capital and his policies may affect the cost of capital. But the ultimate determination of the cost of capital rest in the market place and is established by investors who manage this portfolio to achieve what each views as his optimal balance between ask and return. III. Van Horne’s “In general, the over all cost of capital is the discount rate that equates the present value of the funds received by the firm, net of underwriting and other costs, with the present value of expected outflows. ”

The outflows may be: 9 -4 1. Interest payments (adjusted for taxes) 2. Repayments of principal 3. Dividends 4. Stock purchases by the firm from its shareholders In mathematical notation, this definition is: Where: Io = Net amount of funds received by the firm at time zero (known) Ct = Outflow in period t (known) K = The discount factor & cost of capital (unknown, i. e. what you solve for).

9 -5 What types of long-term capital do firms use? Long-term debt Preferred stock Common equity: Retained earnings New common stock

Cost of Capital Equations Summary 9 -6 Kd = cost of new debt --- investment banker quote; use bond valuation mode solving for Kd Kd(1 - T) = after tax cost of debt Kp = cost of preferred stock Ka=Weighted Average Cost of Capital (WACC)= Kd(1 -T)(Wd)+Kp(Wp)+Ks(Ws) or Ke(We)

9 -7 Should we focus on before-tax or after-tax capital costs? Stockholders focus on A-T CFs. Thus, focus on A-T capital costs, i. e. , use A-T costs in WACC. Only kd needs adjustment.

9 -8 Should we focus on historical (embedded) costs or new (marginal) costs? The cost of capital is used primarily to make decisions which involve raising new capital. So, focus on today’s marginal costs (for WACC).

9 -9 A 15 -year, 12% semiannual bond sells for $1, 153. 72. What’s kd? 0 1 i=? 60 30 N OUTPUT 30 . . . -1, 153. 72 INPUTS 2 60 60 + 1, 000 -1153. 72 60 I/YR PV PMT 5. 0% x 2 = kd = 10% 1000 FV

9 - 10 Component Cost of Debt n Interest is tax deductible, so kd AT = kd BT(1 - T) = 10%(1 - 0. 40) = 6%. n Use nominal rate. n Flotation costs small. Ignore.

9 - 11 What’s the cost of preferred stock? PP = $113. 10; 10%Q; Par = $100; F = $2. Use this formula:

9 - 12 Picture of Preferred 0 -111. 1 kps = ? 1 2 2. 50 . . . ì 2. 50

9 - 13 Note: n Flotation costs for preferred are significant, so are reflected. Use net price. n Preferred dividends are not deductible, so no tax adjustment. Just kps. n Nominal kps is used.

9 - 14 Is preferred stock more or less risky to investors than debt? n More risky; company not required to pay preferred dividend. n However, firms try to pay preferred dividend. Otherwise, (1) cannot pay common dividend, (2) difficult to raise additional funds, (3) preferred stockholders may gain control of firm.

9 - 15 Why is yield on preferred lower than kd? n Corporations own most preferred stock, because 70% of preferred dividend are nontaxable to corporations. n Therefore, preferred often has a lower BT yield than the B-T yield on debt. n The A-T yield to an investor, and the A-T cost to the issuer, are higher on preferred than on debt. Consistent with higher risk of preferred.

9 - 16 Example: kps = 8. 84% kd = 10% T = 40% kps, AT = kps - kps (1 - 0. 7)(T) = 8. 84% - 8. 84%(0. 3)(0. 4) = 7. 78% kd, AT = 10% - 10%(0. 4) = 6. 00% A-T Risk Premium on Preferred = 1. 78%

9 - 17 Why is there a cost for retained earnings? n Earnings can be reinvested or paid out as dividends. n Investors could buy other securities, earn a return. n Thus, there is an opportunity cost if earnings are retained.

9 - 18 n Opportunity cost: The return stockholders could earn on alternative investments of equal risk. n They could buy similar stocks and earn ks, or company could repurchase its own stock and earn ks. So, ks is the cost of retained earnings.

9 - 19 Three ways to determine cost of retained earnings, ks: 1. CAPM: ks = k. RF + (k. M - k. RF)b. 2. DCF: ks = D 1/P 0 + g. 3. Own-Bond-Yield-Plus-Risk Premium: ks = kd + RP.

What is the Capital Asset Pricing Model sp (%) 35 9 - 20 (CAPM) slides 9 -16 to 9 -26 Company Specific Risk Stand-Alone Risk, sp 20 Market Risk 0 10 20 30 40 2, 000+ # Stocks in Portfolio

9 - 21 n As more stocks are added, each new stock has a smaller riskreducing impact. n sp falls very slowly after about 40 stocks are included. The lower limit for sp is about 20% = s. M.

9 - 22 Stand-alone Market Firm-specific = risk + risk Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific risk is that part of a security’s stand-alone risk which can be eliminated by proper diversification.

9 - 23 n By forming portfolios, we can eliminate about half the riskiness of individual stocks (35% vs. 20%).

9 - 24 If you chose to hold a one-stock portfolio and thus are exposed to more risk than diversified investors, would you be compensated for all the risk you bear?

9 - 25 n NO! n Stand-alone risk as measured by a stock’s s or CV is not important to a well-diversified investor. n Rational, risk averse investors are concerned with sp , which is based on market risk.

9 - 26 n There can only be one price, hence market return, for a given security. Therefore, no compensation can be earned for the additional risk of a one-stock portfolio.

9 - 27 n Beta measures a stock’s market risk. It shows a stock’s volatility relative to the market. n Beta shows how risky a stock is if the stock is held in a welldiversified portfolio.

9 - 28 Use the SML to calculate the required returns. SML: ki = k. RF + (k. M - k. RF)bi. n Assume k. RF = 8%. ^ n Note that k. M = k. M is 15%. (Equil. ) n RPM = k. M - k. RF = 15% - 8% = 7%.

9 - 29 Expected vs. Required Returns ^ HT k 17. 4% k 17. 0% Market USR 15. 0 13. 8 15. 0 12. 8 T-bills Coll. 8. 0 1. 7 8. 0 2. 0 Undervalued: ^ k>k Fairly valued Overvalued: ^ k

9 - 30 SML: ki = 8% + (15% - 8%) bi. ki (%) SML . HT k. M = 15 k. RF = 8 . Coll. -1 . . . T-bills 0 1 USR 2 Risk, bi

9 - 31 What’s the cost of retained earnings based on the CAPM? k. RF = 7%, MRP = 6%, b = 1. 2. ks = k. RF + (k. M - k. RF )b. = 7. 0% + (6. 0%)1. 2 = 14. 2%.

9 - 32 What’s the DCF cost of retained earnings, ks? Given: D 0 = $4. 19; P 0 = $50; g = 5%.

9 - 33 Suppose the company has been earning 15% on equity (ROE = 15%) and retaining 35% (dividend payout = 65%), and this situation is expected to continue. What’s the expected future g?

9 - 34 Retention growth rate: g = b(ROE) = 0. 35(15%) = 5. 25%. Here b = Fraction retained. Close to g = 5% given earlier. Think of bank account paying 10% with b = 0, b = 1. 0, and b = 0. 5. What’s g?

9 - 35 Could DCF methodology be applied if g is not constant? n YES, nonconstant g stocks are expected to have constant g at some point, generally in 5 to 10 years. n But calculations get complicated.

9 - 36 Find ks using the own-bond-yield-plusrisk-premium method. (kd = 10%, RP = 4%. ) ks = kd + RP = 10. 0% + 4. 0% = 14. 0% n This RP = CAPM RP. n Produces ballpark estimate of ks. Useful check.

9 - 37 What’s a reasonable final estimate of ks?

9 - 38 How do we find the cost of new common stock, ke? Use DCF formula, but adjust P 0 for flotation cost. End up with ke > ks.

9 - 39 New common, F = 15%:

9 - 40 Flotation adjustment: ke - ks = 15. 4% - 13. 8% = 1. 6%. Add the 1. 6% flotation adjustment to average ks = 14% to find average ke : ke = ks + Floatation adjustment = 14% + 1. 6% = 15. 6%.

9 - 41 Why is ke > ks? 1. Investors expect to earn ks. 2. Company gets money as retained earnings; earns ks; everything’s O. K. 3. But investors put up money to buy new stock; F pulled out; so net money must earn > ks to provide ks on money investors put up.

9 - 42 Example 1. ks = D 1/P 0 + g = 10%; F = 20%. 2. Investors put up $100, expect EPS = DPS = 0. 1($100) = $10. 3. But company nets only $80. 4. If earn ks = 10% on $80, EPS = DPS = 0. 10($80) = $8. Too low. Price falls. 5. Need to earn ke = 10% /0. 8 = 12. 5%. 6. Then EPS = 0. 125($80) = $10. Conclusion: ke = 12. 5% > ks = 10. 0%.

9 - 43 What’s WACC using only retained earnings for equity component of WACC 1? WACC 1 = wdkd(1 - T) + wpskps + wceks = 0. 3(10%)(0. 6) + 0. 1(9%) + 0. 6(14%) = 1. 8% + 0. 9% + 8. 4% = 11. 1%. = Cost per $1 until retained earnings used up.

9 - 44 WACC with New CS F = 15% WACC 2 = wdkd(1 - T) + wpskps + wceke = 0. 3(10%)(0. 6) + 0. 1(9%) + 0. 6(15. 6%) = 1. 8% + 0. 9% + 9. 4% = 12. 1%.

9 - 45 Summary to this Point WACC rises because equity cost is rising.

9 - 46 MCC Schedule Definition n MCC shows cost of each dollar raised. n Each dollar consists of $0. 30 of debt, $0. 10 of Preferred and $0. 60 of equity (retained earnings or new sommon stock). n First dollars cost WACC 1 = 11. 1%, then WACC 2 = 12. 1%.

9 - 47 How large will capital budget be before must issue new CS? Capital Budget = Capital Raised Debt = 0. 3 Capital Raised Preferred = 0. 1 Capital Raised Equity = 0. 6 Capital Raised = 1. 0 Total Capital Equity = RE = 0. 6 Capital Raised, so Capital Raised = RE/0. 6.

9 - 48 Find Retained Earnings Break Point BPRE Dollars of RE = Fraction of equity $300, 000 = $500, 000. = 0. 60 $500, 000 total can be financed with retained earnings, debt, and preferred.

9 - 49 WACC (%) 15 WACC 1 = 11. 1% WACC 2=12. 1% 10 $500 $2, 000 Dollars of New Capital (in thousands)

9 - 50 Investment Opportunities (Capital Budgeting Projects) Which to accept?

9 - 51 % A = 17 B = 15 MCC 12. 1 C = 11. 5 11. 1 IOS Optimal Capital Budget 500 1, 200 2, 000 $

9 - 52 n Projects A and B would be accepted (IRR exceeds the MCC). n Project C would be rejected (IRR is less than the MCC). n Capital Budget = $1. 2 million.

9 - 53 Would the MCC remain constant beyond $2 million? n No. WACC would eventually rise above 12. 1%. n Costs of debt, preferred stock would rise. n Large increases in capital budget may also increase the perceived risk of the firm, increasing WACC.