PS2 - ECO 362 PROBLEM SET 2 FINANCIAL INVESTMENTS Professor...

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ECO 362 October 11, 2007 PROBLEM SET 2 FINANCIAL INVESTMENTS Professor: Burt Malkiel Exercise 1 (a) Gordon’s model states P 0 = D 0 (1 + g ) r g , and we know that D 1 = D 0 (1 + g ) = 2 . 16 , P 0 = 51 . 43 and g = 0 . 068 . So, what we have to do is to fi nd r , say P 0 = D 0 (1 + g ) r g = r g = D 0 (1 + g ) P 0 = r = g + D 1 P 0 ; hence r = 0 . 068 + 2 . 16 51 . 43 = (growth)+(dividend yield) = 11% . (b) In this case, calculations are straightforward. We want to fi nd P 0 for D 1 = D 0 (1 + g ) = 2 . 16 , g = 0 . 068 and r = 0 . 10 , then P 0 = D 0 (1 + g ) r g = 2 . 16 0 . 10 0 . 068 = 67 . 5 . Hence, C should sell at 67 . 5 . Exercise 2 (a) Since CISCO pays no dividend, we have to use formula 4 in classnotes on Stock Valuation (October 3). Recall that P 0 E 0 = m S & P (1 + g ) N (1 + r ) N where m S & P is the market multiple (using information on S & P 500 ), say P S & P /E S & P . In this case, we have that m S & P = 15 . Next, following the hint we obtain the dividend yield of the S & P as follows D 1 P 0 = D 1 /E 1 P 0 /E 1 = 30% 15 = 2% , so that, together with an anticipated long-run growth rate for earnings and dividends of 6% , implies a discount rate for S & P of 8% = 6% + 2% . Hence, the appropriate discount rate (during the next 5 years) applied to CISCO is 10% = 8% + 2% = (market return) + (risk premium). Finally, as g = 15% , substituting into formula 4 in the classnotes P CISCO E CISCO = 15 (1 . 15) 5 (1 . 10) 5 = 18 . 733 1
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ECO 362 October 11, 2007 from where, P CISCO = 18 . 733 × E CISCO = 18 . 733 × 1 . 10 = 20 . 60 . (b) Since CISCO’s market price and earnings per share are 27 . 50 and 1 . 10 , respectively; we have that P/E = 25 , and hence —using r = 10% and m S & P = 15 — we get P 0 E 0 = m s μ 1 + g 1 + r N = 1 + g 1 + r = μ 1 m s P 0 E 0 1 /N = g = μ 1 m s P 0 E 0 1 /N (1 + r ) 1 g = μ 1 15 25 1 / 5 (1 . 10) 1 = 21 . 83% . Exercise 3 (a) Rewriting the Gordon formula in terms of the next period’s dividends, P 0 = D 1 r g so that r = D 1 P 0 + g i.e. the rate of return equals the dividend yield plus growth rate. In this case, we have D 1 /P 0 = 1 . 5% and g = 6% , therefore r = 7 . 5% . (b) Doing the same calculations as in part (a) yields Dividend growth rate ( g ) 5% 6% 7% 8% 9% Rate of return ( r ) 6 . 5% 7 . 5% 8 . 5% 9 . 5% 10 . 5% (c) Write dividend yield = D 1 P 0 = E 1 ( D 1 /E 1 ) P 0 where D 1 /E 1 is the payout rate. Then, D 1 E 1 = μ D 1 P 0 P 0 E 1 = μ D 1 P 0 P 0 E 0 (1 + g ) = 0 . 015 × 25 (1 + g ) = 0 . 375 1 + g .
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