1. Business Finance Michael Dimond

2. Michael Dimond School of Business Administration Risk and the costs of capital When considering common equity, preferred equity and debt, the owners of these securities each bear a different level of risk. The higher the risk, the higher the rate of return will be. Usually, this is what you expect: R f < K d < K pfd < K e and… inflation < R f What does this tell you about the return demanded by each type of investor? What does that imply about the risk borne by each? Real Rates, Risk Premium, etc. Market efficiency (the EMH)

3. Michael Dimond School of Business Administration Determining K d with YTM Remember from valuing bonds that the “i” in the TVM relationship is the yield on a bond. Yield is the rate of return demanded by investors in debt. To find the Cost of Debt (K d ), solve for the yield of a bond. Remember: Costs of capital are forward-looking numbers. It is what an investor will demand from future performance. What does this mean for the cost of debt (K d )?

4. Michael Dimond School of Business Administration The “Approximation Formula” The “approximation formula” (PMT+((FV-PV)/n))/((FV+PV)/2) works only when bonds are selling close to par I have tried to eliminate it from the homework, but a couple of multi-part problems require it as one of the parts Because it is not accurate, please do not use the approximation formula unless you are specifically told to. I will not use it on any exams.

5. Michael Dimond School of Business Administration Determining K e with the Dividend Growth Model K e is the required rate of return for equity investors “Cost of Equity” We can derive this from the dividend discount model: P 0 = D 1 /(r-g) :. (r-g) = D 1 /P 0 :. r = D 1 /P 0 + g Since r is the required rate of return, K e = D 1 /P 0 + g How do you test the answer you get? What if you wanted to solve for the expected growth rate? There is another way to find the cost of equity: CAPM

6. Michael Dimond School of Business Administration Determining K e with CAPM Ke is the required rate of return for equity investors “Cost of Equity” The CAPM (Capital Asset Pricing Model) is a formula used to compute K e K e = Rf + β(Rm – Rf) or K e = Rf + β(MRP) MRP is the Market Risk Premium MRP = Rm – Rf Remember: Costs of capital are forward-looking numbers. It is what an investor will demand from future performance. What does this mean for the cost of equity (K e )?

7. Michael Dimond School of Business Administration About beta Beta (β) represents how well an asset’s return correlates with the return on the market. Correlation, not Causality Beta measures sensitivity to economic inputs Beta is the slope of the line showing the relationship of the data What is the difference between Systematic and Unsystematic risk? Can beta be zero? Can beta be negative?

8. Michael Dimond School of Business Administration Can beta really be negative? What does a negative beta imply about the stock performance? What does a negative beta imply about Ke?

9. Michael Dimond School of Business Administration Determining K pfd with the Dividend Discount Model The value of a perpetuity is how we price preferred equity: PV perp = CF/r :. Price = Dividend/K pfd :. Price x K pfd = Dividend :. K pfd = Dividend / Price So… If XYZ Company has 8% preferred stock with a $20.00 par value which is selling for $28.00, what would be the Cost of Preferred Equity? 8% x 20.00 = 1.60 1.60 / 28.00 = 0.0571 = 5.71%

10. Michael Dimond School of Business Administration Market Value vs Book Value Investors have an opinion about the value of a company. A stockholder believes the price of stock is appropriate value, and this is different than what the balance sheet shows for the value of equity. The balance sheet shows the book value. The market price determines the market value. Example: Book Value Example: Market Value (“Market Cap” or Market Capitalization) P/B ratio

11. Michael Dimond School of Business Administration WACC Investors care about market value more than book value. Costs of capital are used in making investing decisions. :. If we wanted to know the overall cost of capital for a company (the cost of equity and the cost of debt combined), we would use a weighted average of the percentages, and weight them based on the market values. The Weighted Average Cost of Capital is called the WACC. WACC = w e x K e + w d x K d (1-t) If there is preferred stock, we just expand the formula: WACC = w pfd x K pfd + w e x K e + w d x K d (1-t)

12. Michael Dimond School of Business Administration Weights of Equity & Debt The weight is the proportion of that type of capital compared with the total capital in the firm. What is the weight of each type of capital below? Equity = E = $600MM Debt = D = $300MM Preferred Stock = Pfd = $100MM Total Capital = TC = 600+300+100 = 1,000 W e = E/TC = 600/1,000 = 0.60 W d = D/TC = 300/1,000 = 0.30 W pfd = Pfd/TC = 100/1,000 = 0.10 Note: the sum of the weights always equals 1.00

13. Michael Dimond School of Business Administration Determining the WACC You may need to compute the WACC from information presented like this: ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125. What is the best approach to solving this problem?

14. Michael Dimond School of Business Administration Break a complicated problem into smaller pieces ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125. Find the market values MV e = $27.50 x 1MM = $27.5MM MV d = 10MM ÷ 1,000 (assumed FV) x $1,125 = $11.25MM MV pfd = $125 x 10,000 = $1.25MM TC = $27.5MM + $11.25MM + $1.25MM = $40.0MM Find the weights & tax shield W e = 27.5 ÷ 40.0 = 0.6875 W d = 11.25 ÷ 40.0 = 0.2813 W pfd = 1.25 ÷ 40.0 = 0.0313 (1-t) = (1 - 0.34) = 0.66

15. Michael Dimond School of Business Administration Break a complicated problem into smaller pieces ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125. Find the different costs of capital K d : Solve for the yield find i, where: n=10x2, PV=-1125, FV=1000, PMT=0.085x1000÷2 [i=3.3800] :. K d = 2x3.38% = 6.76% K e : Use the Dividend Discount Model or the CAPM (based on data available) K e = r = D 1 /P 0 + g K e = [(1.80 x 1.07) / 27.50] + 0.07 = 0.1400 :. K e = 14.00% K pfd : Find the return on a non-growing perpetuity K pfd = r = D 1 /P 0 = (0.09 x 100)/125 = 0.0720 :. K pfd = 7.20%

16. Michael Dimond School of Business Administration From there, put the pieces of the formula in place, then work through the formula in steps WACC = wpfd x Kpfd + we x Ke + wd x Kd x (1-t) WACC = 0.0313 x 0.072 + 0.6875 x 0.14 + 0.2813 x 0.0676 x 0.66 WACC = 0.0023 + 0.0963 + 0.2813 x 0.0446 WACC = 0.0023 + 0.0963 + 0.0126 WACC = 0.1112 = 11.12% By parsing the problem, you avoid errors Try another example: XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25 Determining the WACC 0.0446 is the After-Tax Cost of Debt

17. Michael Dimond School of Business Administration Try another example: XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25 Market Values & Weights MV e = $28,750,000 w e = 0.7095 MV pfd = $ 880,000 w pfd = 0.0217 MV d = $10,890,000 w d = 0.2688 TC = $40,520,000 1.0000 Tax Shield = (1 – t) = (1 - 0.35) = 0.65 Determining the WACC 

18. Michael Dimond School of Business Administration Try another example: XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25 Costs of Capital K e = Rf + β(Rm – Rf) = 0.0315 +1.25(0.1038-0.0315) = 0.1219 = 12.19% K pfd = Dividend / Price = 9.25/110 = 0.0841 = 8.41% K d = Find YTM where i is semiannual and… n = 24 semiannual, PV = -1,100, FV = 1,000, PMT = 41.25 semiannual i = 3.5021 :. YTM = 7.0043% or 0.0700 Determining the WACC

19. Michael Dimond School of Business Administration From there, put the pieces of the formula in place, then work through the formula in steps WACC = wpfd x Kpfd + we x Ke + wd x Kd x (1-t) WACC = 0.0217 x 0.0841 + 0.7095 x 0.1219 + 0.2688 x 0.0700 x 0.65 WACC = 0.0018 + 0.0865 + 0.2688 x 0.0455 WACC = 0.0018 + 0.0865 + 0.0122 WACC = 0.1005 = 10.05% Determining the WACC

20. Michael Dimond School of Business Administration Real life is more complicated Equity can come from retained earnings or from new investment. New issues of stocks and bonds come with flotation costs, price adjustments, etc. which must be factored in. Growth rates are rarely stated, so they must be computed.

21. Michael Dimond School of Business Administration K d with flotation cost ABC Company is in the 40% tax bracket and can sell 15-year bonds ($1,000 par) paying annual interest of 12%. Market rates are slightly below that for bonds of this rating, so the bonds will sell for $1,100. To issue the bonds, ABC will have flotation costs of $30 per bond. Find K d. n = 15 years (annual) i = ?? Solve for YTM (annual) PMT = 12% x 1,000 (annual) outflow PV = 1,100 – 30 (expected proceeds less flotation costs) inflow FV = 1,000 outflow i = 11.0252 YTM = 11.03% K d = 11.03% K d (After-tax) = 11.03% x (1-0.40) = 6.62%

22. Michael Dimond School of Business Administration K pfd with flotation cost XYZ Company is issuing preferred stock with an 8% dividend and a $120 par value. The shares will sell for $129.60 and have flotation costs of $7.20 per share. What is the cost of preferred equity? Par = 120.00 Dividend = 8% x 120 = 9.60 Selling price = 129.60 Flotation costs = 7.20 Net proceeds = 129.60 – 7.20 = 122.40 K pfd = 9.60 / 122.40 = 0.0784 = 7.84%

23. Michael Dimond School of Business Administration K e with flotation cost ABC Company is considering a SEO (Seasoned Equity Offering). Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. The planned dividend per share is $1.45 for the coming year, and they expect the growth of dividends to follow the same average growth it has for the past 5 years. Historic annual DPS are: 20082.12 20092.30 20102.60 20112.92 20123.10 What is their Cost of Equity for the SEO? K e = D 1 / P 0 + g… but what is g?

24. Michael Dimond School of Business Administration K e with flotation cost – finding the growth rate Historic annual DPS for the last 5 years are: 20082.12 20092.30 20102.60 20112.92 20123.10 Growth can be found by solving for the CAGR (Compound Annual Growth Rate) (3.10/2.12) = 1.46 1.46 ^ (1/4) = 1.0997 (a 5-year sample means we see 4 years of compounding) CAGR = 1.0997 – 1 = 0.0997 = 9.97% g = 9.97%

25. Michael Dimond School of Business Administration K e with flotation cost ABC Company is considering a SEO (Seasoned Equity Offering). Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. The planned dividend per share is $1.45 for the coming year, and they expect the growth of dividends to follow the same average growth it has for the past 5 years. Historic annual DPS are: 20082.12 20092.30 20102.60 20112.92 20123.10 What is their Cost of Equity for the SEO? K e = D 1 / P 0 + g K e = 1.45 / P 0 + 0.0997 … what should we use for P 0 ?

26. Michael Dimond School of Business Administration K e with flotation cost Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. Net Proceeds will be 48.22 – 1.00 – 2.86 = 44.36 What is their Cost of Equity for the SEO? K e = D 1 / P 0 + g K e = 1.45 / 44.36 + 0.0997 = 0.1324 = 13.24% What if they used Retained Earnings instead of issuing new stock? K e = 1.45 / 48.22 + 0.0997 = 0.1298 = 12.98% Why is the cost of equity higher for new stock than for retained earnings? What would happen if a company always issued new stock instead of funding growth from retained earnings?