We may approach these problems is 2 ways Given the current price and the

# We may approach these problems is 2 ways given the

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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

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