* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Topic Note-3
Private equity wikipedia , lookup
Financialization wikipedia , lookup
Investment management wikipedia , lookup
Greeks (finance) wikipedia , lookup
Modified Dietz method wikipedia , lookup
Rate of return wikipedia , lookup
Early history of private equity wikipedia , lookup
Mark-to-market accounting wikipedia , lookup
Lattice model (finance) wikipedia , lookup
Investment fund wikipedia , lookup
Pensions crisis wikipedia , lookup
Stock trader wikipedia , lookup
Short (finance) wikipedia , lookup
Internal rate of return wikipedia , lookup
Financial economics wikipedia , lookup
Present value wikipedia , lookup
Private equity in the 1980s wikipedia , lookup
Mergers and acquisitions wikipedia , lookup
1 MF807 Prof. Thomas Chemmanur Topic Note-3 STOCK AND FIRM VALUATION Common stock represents ownership of the firm: stockholders elect the board of directors which controls the firm and are entitled to the cash flows generated by the firm. However, stock holders are residual claimants: they get only the cash flow left over after paying interest to debt holders and other claimants. However, at this stage, we will assume that the firm is 100% equity financed, postponing a discussion of the impact of other claims till we talk about the firm's capital structure choice. 1. Stock valuation with the constant dividend growth model Consider a firm which pays dividends D1, D2, ...etc for the first H periods. Let PH be the price of the stock at t = H. Then, from our present value class, we know that the current market price of the stock, P0 is given by, (1) D1 D2 D3 DH +PH P0 = (1+r) + (1+r)2 + (1+r)3 +...+ (1+r)H where r is the discounting rate which corresponding to the riskiness of the stock. But we know that PH is given by, (2) PH DH 1 D H 2 2 ... (1 r ) (1 r ) 2 (3) P0 D3 D1 D2 DH DH 1 DH 2 ... ... 2 3 H H 1 (1 r ) (1 r ) (1 r ) (1 r ) (1 r ) (1 r ) H 2 Using (2) in (1) and simplifying, The problem in using (3) is that, to begin with, we don't know what the dividend stream is! Let us make the simplifying assumption that dividends grow at a constant rate g. Then, if D0 was the dividend in the last (current) period, D1 = D0 (1 + g); D2 = D1 (1+g) = D0(1+g)2; D3 = D0(1+g)3, etc. Using this assumption in (3), (4) 1 g (1 g ) (1 g ) 2 (1 g ) 3 (1 g ) P0 D0 ... 1 2 3 1 r (1 r ) (1 r ) (1 r ) (1 r ) H H , (1 r ) H ......... The term in the square brackets is an infinite geometric series of the form I talked about in the class on present values, with common ratio (1+g)/(1+r). Applying the formula for the sum of an infinite geometric series, (4) reduces to: (5) P0 = D0(1+g) D1 = r-g r-g (5) is often referred to as the constant growth formula for stock valuation. The above formula can be used only when r > g, since otherwise the common ratio (1+g)/(1+r) of the geometric series is greater than 1, and the stock price becomes 3 infinity. It is important to remember that (5) is true only if the underlying assumption of a constant growth rate in dividends is true (which is often not the case). The above formula assumes that we know r and g, and want to find the price P 0. If we do not know g, we have to make additional assumptions to find it. 3. Approximating g from ROE and the plow-back ratio It is important to remember that return on equity (ROE) is an accounting concept. Unfortunately, accounting numbers represent the past, while in finance, we want to know about future cash flows to value securities. (Accounting figures also have the problem that they can differ according to the choice of accounting method). However, they can act as a starting place. Earnings per share (EPS) = Net Income (obtained from the income statement)/Number of shares Book Value per share = Book value of equity (obtained from the balance sheet)/Number of shares. Return on equity (ROE) = EPS/Book Value Per Share Dividend payout ratio = Dividend per share/EPS Plow-back ratio = 1 - Dividend payout ratio. Then g ≈ Plow-back ratio x ROE, assuming that the firm's earnings re-invested in the company earn the same return as in the past. (Again, it goes without saying that this assumption may not always be true). 3. Finding r given P0, D0 and g From (5), 4 D1 r = P + g 0 (6) Again assuming constant dividend growth. 4. Stock Valuation with different growth rates in dividends Often, the assumption of a constant growth rate in dividends is not at all realistic. The dividend may grow at a certain rate for the first few years, and then settle down to a steady rate afterward. To illustrate how to price equity in this case, consider the following problem. Problem 1: A company's dividend grows at 10% rate for the first five years, and thereafter settles down to a steady growth rate of 6%. If stockholders expect a rate of return of 14% from investing in the equity, what is its share price? D0 = $2 per share. 5. Stock valuation from the NPV of growth opportunities Sometimes, it may be easier to value equity as the sum of two components: (a) The value of a share if the firm does not make any future investment, and therefore pays out all earnings as dividends (b) The NPV of future growth opportunities.1 (a) If the firm does not make any investment, let us assume that it will earn EPS1 next year, and continue to earn the same amount for ever. In this case, its value will be EPS1/r, since the earnings stream will be a perpetuity. (b) If the firm does make the investment, it will plow back a fraction of EPS1 into the firm. In that case, it will obtain additional earnings from this new project. Denote the NPV of this new investment per share by PVGO. Then, price per share, 1Notice that we are adding only the NPV of growth opportunities. The investment required for these is assumed to come from retaining earnings from existing projects, which is part of (a). Therefore adding the investment for the growth opportunities in (b) will be double-counting. 5 (7) P0= (a) + (b) = EPS1 r + PVGO Re-arranging (7) we get, (8) EPS1 PVGO P0 = r 1 - P0 The importance of (8) is that it gives a relationship between the earnings-to-price ratio of a company and its market capitalization rate r (rate of return expected by investors from the equity). When PVGO is zero (i.e., when the firm has no growth opportunities) both are the same. Problem 2: Consider a firm with existing assets that generate an EPS of $5. If the firm does not invest any further, EPS is expected to remain constant at this level. However, starting next year, the firm has the chance to invest $3 per share a year in developing a newly discovered geothermal steam source for electricity generation. Each investment is expected generate a perpetual 20 % return. However, the source will be fully developed by the fifth year. What will be the stock price and earnings-price ratio assuming investors require a 12% rate of return? Problem 3: Consider a firm with the following data: D1 = $10 per share; dividends are expected to grow by 5% a year; the company plows back 20% of earnings. (i) What is the price of a share? (ii) What is next year's expected earnings? (iii) What is the return on book equity? (iv) What is PVGO? (r = 15%). 6. Stock price as the present value of free cashflow per share: We can also express the price per share as: 6 t (9) P0 t 1 Free cash flow per share at date t (1 r ) t where Free cash flow = Revenue - Costs - Investment. However, free cash flow per share is the amount that the firm is free to pay out as dividends per share. Therefore (9) is essentially identical to (3). 7. A note on the price-earnings (P/E) ratio The P/E ratio is available in financial newspapers. It is the reciprocal of the EPS/Price ratio. Therefore, from (8), we can see that the P/E ratio of a company will be higher if (a) if its r is low or (b) it has higher growth opportunities (i.e., a higher PVGO), or a combination of the two. It is sometimes useful in stock valuation. If we can find a similar firm with the same riskiness and growth opportunities, we can use the following rule: Value of the firm's equity = Earnings of the firm to be valued x P/E of the similar firm. (The problem is, of course in finding such a very similar firm).