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Drake DRAKE UNIVERSITY MBA Stock Valuation A Discounted Cash Flow Approach

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Drake Drake University Fin 200 Common Stock Provides Ownership in the firm, owners have the right to: Share proportionally in dividends paid Vote on stockholder matters Share proportionally in assets remaining after all liabilities are paid in event of liquidation. Dividends are declared by management

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Drake Drake University Fin 200 Preferred Stock Claim prior to common Fixed dividend schedule Missing payment does not constitute default

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Drake Drake University Fin 200 The Market for Common Stocks Secondary Market Transactions Outstanding shares are traded between investors, transactions do not raise money for the firm Sale of additional shares If the firm decides to increase the number of shares outstanding it sells them in the primary market, raising money for the firm Initial Public Offering The initial sale of shares in a firm that was previously privately held.

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Drake Drake University Fin 200 A General Valuation Model The basic components of the valuation are: An estimate of the future cash flow stream from owning the asset The required rate of return for each period based upon the riskiness of the asset The value is then found by discounting each cash flow by its respective discount rate and then summing the PV’s (Basically the PV of an Uneven Cash Flow Stream)

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Drake Drake University Fin 200 The Formal Model The value of the asset should then be equal to: How do we apply the model to find the value of a stock?

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Drake Drake University Fin 200 All Stocks Regardless of type of stock, the return from owning the stock is usually earned in one of two ways: Dividends Dividends are declared by management and paid on a per share basis to the share holder Capital Gains Capital Gains represent the change in the price of the stock

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Drake Drake University Fin 200 General Valuation Model Stocks Assuming that the firms pays dividends, the future expected cash flows received from owning the stock are the dividends that the firm is expected to pay. What about the capital gains?

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Drake Drake University Fin 200 Basic Stock Valuation The firm is a legal entity that continues forever, we are assuming that dividends continue forever (t = infinity) Valuation would then be the PV of the dividends, D t, from t = 0 to t = infinity. The Dividends are discounted at the required rate of return for the investor, r s

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Drake Drake University Fin 200 What about the future price? Let = the stock price in one year There are two future cash flows Dividend one and the future price. 0101

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Drake Drake University Fin 200 Valuation The valuation would then be: What is equal to?

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Drake Drake University Fin 200 Valuation The value of the stock at time 1 must equal the PV of the cash flows that come after it. The PV of D 2, D 3, etc. at time t=1

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Drake Drake University Fin 200 Valuation Substitute forin our equation:

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Drake Drake University Fin 200 Which leaves our original equation

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Drake Drake University Fin 200 Dividends The key to valuing the stock then becomes your assumption about whether dividends change over time. If they do change you need to decide how to estimate possible future changes in dividends. This can in part be determined by the type of stock (common or preferred).

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Drake Drake University Fin 200 Pref Stock Valuation Often it is assumed that the dividends are constant for a preferred stock. If there is no maturity date the valuation is the same as a perpetuity:

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Drake Drake University Fin 200 Dividends For common stock the dividend is usually not expected to remain the same amount forever. Constant dividends formally were often a goal of management, but they represent a decline in real income.

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Drake Drake University Fin 200 Constant Growth in Dividends One possible assumption is that dividends grow at a constant rate. In this case D 1 =D 0 (1+g) D 2 =D 1 (1+g) =D 0 (1+g) 2 D 3 =D 2 (1+g) =D 0 (1+g) 3 etc… Use this in the basic formula in the valuation formula from before.

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Drake Drake University Fin 200 Constant Growth in Dividends

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Drake Drake University Fin 200 Constant Growth continued

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Drake Drake University Fin 200 Constant Growth Substitute

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Drake Drake University Fin 200 Practice Problem How much would you be willing to pay for a share of stock in Bulldog Industries given the following information? Assume that Bulldog just paid $1.00 dividend and that the dividend is expected to grow at 5% each year forever and that the appropriate discount rate for the risk associated with the firm is 10%.

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Drake Drake University Fin 200 Total Return The total return earned by the shareholder has two components:

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Drake Drake University Fin 200 Practice Problem Part 2 Find the the dividend and capital gains yield in the previous problem.

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Drake Drake University Fin 200 Practice Problem Part 2

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Drake Drake University Fin 200 Rates of Return The total return for owning the stock is then the sum of the capital gains yield and the dividend yield. In the previous example, we estimated the future value of the stock at time t+1. Therefore the total return found by adding the capital gains yield to the divided yield would be the expected rate of return,

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Drake Drake University Fin 200 Rates of Return IF you calculated the return after you observed the price at time t+1 then you would have found the actual or realized rate of return ( ). In this case your values for price are not the expected value, but the actual observed value.

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Drake Drake University Fin 200 Note: For a constant growth stock. Given the observed price of the stock and assuming it is equal to value, you can solve for the expected total return by rearranging the constant growth equation.

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Drake Drake University Fin 200 In the case of constant growth, The expected capital gains yield is equal to the expected growth rate

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Drake Drake University Fin 200 Non Constant Growth Assume that the firm grows at a fast rate for a short period of time then starts constant growth Value would equal the PV of each of the early dividends plus the PV of the constant growth portion

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Drake Drake University Fin 200 To find the value of this stock, 1. Discount the dividend received during each period of the supernormal growth period. 2. Find the value of the stock in year m assuming constant growth, the horizon value (use equation above) 3. Discount the PV of the stock in year m (found in 2)) back to the current year.

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Drake Drake University Fin 200 Non Constant Growth Valuation Assume non constant growth is for two periods The PV of the first Two dividends The PV of the Constant Growth From t = 2 to infinity

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Drake Drake University Fin 200 Practice Problem-Data Assume that the average firm in your company’s industry is expected to grow at a constant rate of 7%. Your company is about a risky as the average firm in the industry, and investors are requiring a 15% return for investing in firms in the industry. Your firm has just introduced a new product which it expects to increase earnings each of the next two years. The expectation is that dividends will grow at 40% next year and 20% the year after that then return to the 7% constant growth rate of the industry. The last dividend paid by the firm was $0.75.

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Drake Drake University Fin 200 Practice Problem-questions a) What is the current price of the stock? b) What is the capital gains yield and divined yield if the stock was held for the first year? c) What is the capital gains yield and dividend yield if the stock was bought following the third dividend and held until it paid the fourth dividend? d) Explain your answers in b) and c) (Did the capital gains yield and dividend yield change over time? and if so how? Will you expect it to change after year four? why or why not?)

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