# ch19 - Chapter 19 - Solutions Overview: Problem Length {S}...

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Chapter 19 - Solutions Overview: Problem Length Problem #’s {S} 1, 2, 15,16,17 {M} 3,4,5, 7, 10,11,12, 14 {L} 6, 8, 9, 13 1.{S}The models should give identical results. Using 2003 expected dividends of \$4.50, a discount rate r of 20%, and growth rate g of 15%, we find that: The dividend payout ratio for both 2002 (\$4.05/\$10.03 = 40.4%) and 2003 (\$4.50/\$11.40 = 39.5%) is approximately 40%. The long term growth rates for earnings and dividends differ. This is possible only if the payout rate will change over time. Thus, in an earnings-based model using the earnings growth rate of 14%, we must use another (higher than 40%) estimate for the payout ratio. A payout ratio of 47.5% would result in the same valuation: Based on these models, Emfil shares are not attractive at a price of \$115, and should not be added to the portfolio. 19-1 \$90 = .15 - .20 \$4.50 = g - r D = P P = kE r - g = (.475)(\$11.40) .20-.14 = \$90

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2.{S}a. P/E 1 = r r 1 = E P r E = P For a firm with a P/E ratio of 12 r = 8.25% b. (i) The increase of \$3 is transitory. The market is saying that the price/earnings ratio should reflect only the "normal" earnings of \$10 per share. (ii) The increase of \$3 is permanent and earnings in the future are expected to remain at \$13. The market value is based on \$13 per share of normal earnings. (iii)The increase of \$3 implies not only permanence but growth as future earnings are expected to increase above the present level of \$13. 19-2
3.{M}a. The P/E ratio with a dividend payout of k , discount rate of r and growth rate equal to g can be derived as: For the Lo Company: b. Hi's P/E ratio must be identical to that of Lo (3.467) as both firms have the same market value and earnings. c. Lo Company 2001 2002 2003 2004 2005 1) Earnings/share 2) Number of shares 3) Net income 4) Dividends paid 5) New investment 6) Firm value at period end 7) Price per share 8) P/E ratio \$ 1.00 1,000 \$1,000 200 800 3,467 3.47 3.467 \$ 1.04 1,000 \$1,040 208 832 3,605 3.61 3.467 \$ 1.08 1,000 \$1,082 216 865 3,750 3.75 3.467 \$ 1.12 1,000 \$1,125 225 900 3,900 3.90 3.467 \$ 1.17 1,000 \$1,170 234 936 4,056 4.06 3.467 Calculations: 1) Given 2) Since no new financing and no stock dividends or splits, shares must remain constant over time. 3) Earnings per share x number of shares 4) Dividends per share (given) x number of shares 5) Net income - dividends paid 6) (.2 x next year's income)/(.10-.04); 2005 value assumes that net income continues to grow at 4% rate. 7) Firm value/number of shares 8) Firm value/current year net income 19-3 P = kE(1+ g) r - g and P E = k(1+ g) r - g P E = .2(\$1+.04) .10-.04 = 3.467

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Hi Company 2001 2002 2003 2004 2005 1) Earnings/share 2) Number of shares 3) Net income 4) Dividends paid 5) New investment 6) New financing 7) Firm value at period end 8) Price/share before new issue 9) P/E ratio 10) Shares issued 11) Price/share at new issue \$ 1.00 1,000 \$1,000 1,000 800 800 3,467 3.47 3.467 300 \$ 2.67 \$ 0.80 1,300 \$1,040 1,040 832 832 3,605 2.77 3.467 390 \$ 2.13 \$ 0.64 1,690 \$1,082 1,082 865 865 3,750 2.22 3.467 507 \$ 1.71 \$ 0.51 2,197 \$1,125 1,125 900 900 3,900 1.77 3.467 659 \$ 1.37 \$ 0.41 2,856 \$1,170 1,170 936 936 4,056 1.42 3.467 857 \$ 1.09 Calculations based on issuance of shares at end of year: 1) Given 2) 2001 given; From 2001 on, previous year shares plus new shares issued 3) Earnings per share x number of shares 4) Dividends per share (given) x number of shares 5) Identical in amount to that computed for Lo Company 6) Equal to (5) 7) Identical to Lo Company [(.2 x next year's income)/ (.10-.04)]; 2001 value assumes that net income continues to grow at 4% rate.
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## This note was uploaded on 04/15/2009 for the course ACCOUNTING BUSI0027 taught by Professor Guan during the Spring '09 term at HKU.

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ch19 - Chapter 19 - Solutions Overview: Problem Length {S}...

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