We may approach these problems is 2 ways: – Given the current price and the expected future price and dividend, we can solve for the return (discount rate) – for the 1-year case, this is akin to solving for the “i” in a lump-sum TVM problem – Or, we may be given an expected future price and dividend and a required rate of return (or, discount rate) and then use the rate of return to discount the future expected cash flows to get our price (PV) today FIN 300 - Stocks Pt. 1 16
What About Non-Dividend Payers? • Actually, many firms pay no dividends – In particular, young, high-growth (tech, especially) firms – Generally dividend-payers are larger, more-established, mature firms • How do we price non-dividend-paying stocks? – Well, if we have an expectation of a future selling price for the stock and a discount rate, we can solve for the PV of the future sale price – In practice, many investors apply a couple of methods: • Look at similar firms and calculate the stock price (per share) and divide by the earnings-per-share (EPS) – then multiply the comparable firms P/E by your firm’s EPS – to get a price estimate • Or, more sophisticated “discounted cash flow (DCF) methods” – where, an analyst projects the future cash flows (based on the projected future accounting numbers of a firm and then applies a discount rate to estimate the value of the company FIN 300 - Stocks Pt. 1 17 Just an FYI: Not on the exam!
Dividend-Paying Stocks • In this class, we will focus on dividend-paying stocks • When we focus on stock pricing, we are generally talking about common shares • However, what we are doing (in terms of the math) is pretty generic • As we have discussed before, preferred shares are generally seen to pay a level dividend that never changes – In the last part of this chapter’s coverage we will do some examples that speak specifically to “perpetual” preferred shares of stock FIN 300 - Stocks Pt. 1 18
Extending Stock Pricing to 2 Years • For example, let’s assume that we can look 2 years (or, 2 periods) ahead: FIN 300 - Stocks Pt. 1 19 DIV 2 + P 2 P 0 0 2y 1y DIV 1 Dividends Paid at the ends of the 1 st and 2 nd years (t=1 & t=2) Expected Sale Price (of the share) in 2 yrs. (t=2) 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 (1 + 𝑅𝑅 ) + ( 𝐷𝐷𝐷𝐷𝐷𝐷 2 + 𝑃𝑃 2 ) (1 + 𝑅𝑅 ) 2 R = expected total return (or, discount rate) per period for the stock
Stock Pricing Out 3 or More Years FIN 300 - Stocks Pt. 1 20 DIV 3 + P 3 P 0 0 3y 1y DIV 1 DIV 2 2y 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 (1 + 𝑅𝑅 ) + 𝐷𝐷𝐷𝐷𝐷𝐷 2 (1 + 𝑅𝑅 ) 2 + 𝐷𝐷𝐷𝐷𝐷𝐷 3 + 𝑃𝑃 3 (1 + 𝑅𝑅 ) 3 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 (1 + 𝑅𝑅 ) + 𝐷𝐷𝐷𝐷𝐷𝐷 2 (1 + 𝑅𝑅 ) 2 + 𝐷𝐷𝐷𝐷𝐷𝐷 3 (1 + 𝑅𝑅 ) 3 + 𝐷𝐷𝐷𝐷𝐷𝐷 4 + 𝑃𝑃 4 (1 + 𝑅𝑅 ) 4 Or, 4 years 𝑃𝑃 0 = 𝐷𝐷𝐷𝐷𝐷𝐷 1 (1 + 𝑅𝑅 ) + 𝐷𝐷𝐷𝐷𝐷𝐷 2 (1 + 𝑅𝑅 ) 2 + 𝐷𝐷𝐷𝐷𝐷𝐷 3 (1 + 𝑅𝑅 ) 3 + 𝐷𝐷𝐷𝐷𝐷𝐷 4 (1 + 𝑅𝑅 ) 4 + ⋯ to ∞ Or, forever!
Price (PV) of an Infinite Stream of Dividends •