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# ACT349 1st Assignment and solutions

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Department
Actuarial Science
Course
ACT349H1
Professor
All Professors
Semester
Fall

Description
ACT349 F13 Assignment for Sep 18, 2013 4:00pm Tutorial Brealey Myers Allen 11th Ed 'Principles of Corporate Finance' (North American or Global edition) These questions are from the text and given here for your convenience. But it will be easier to answer them if you have the text and you’ll need the text for the next assignment – please get it fast-certainly in time to do the assignment for the Sep 25 tutorial. Sorry, but copyright law is a constraint. 1. (BMAGL11-098 ;BMA11-Ch04-Q04v00) Company Y does not plough back any earnings and is expected to produce a level dividend stream of \$5 a share. If the current stock price is \$40, what is the market capitalization rate? Solution g=0 since no ploughback ▯▯▯ ▯ 40=P= ▯▯▯= ▯▯▯ r=12.5% 2. (BMAGL11-099 ;BMA11-Ch04-Q05v00) Company Z’s earnings and dividends per share are expected to grow indefinitely by 5% a year. If next year’s dividend is \$10 and the market capitalization rate is 8%, what is the current stock price? Solution g=0.05 ▯▯▯ ▯▯ P= = = \$333.33 ▯▯▯ ▯.▯▯▯▯.▯▯ 3. (BMAGL11-099 ;BMA11-Ch04-Q07v00) Company Z’s earnings and dividends per share are expected to grow indefinitely by 5% a year. Next year’s dividend is \$10 and the market capitalization rate is 8%. If Company Z were instead to distribute all its earnings, it could maintain a level dividend stream of \$15 a share. How much is the market actually paying per share for growth opportunities? Solution: P(g=0.05)= ▯▯▯= ▯▯ = \$333.33 ▯▯▯ ▯.▯▯▯▯.▯▯ ▯▯ P(g=0)= = \$187.50 ▯.▯▯▯▯ PVGO =PV(Grow Ops)= P(g=0.05) – P(g=0.00)=\$145.83 Comment from Keith Sharp: This is assuming that the amazingly competent management can give a higher return on capital than the overall market can give. This gets pretty deep, and would involve considering e.g. that if the stockholder re-invests then he/she will be a ‘marginal’ investor whereas the first few dollars of investment get the factory electricity turned on and give a big return. Getting beyond ACT349, don’t worry about it. 4. (BMAGL11-100 ;BMA11-Ch04-Q18v00) Consider the following three stocks: a) Stock A is expected to provide a dividend of \$10 a share forever. b) Stock B is expected to pay a dividend of \$5 next year. Thereafter, dividend growth is expected to be 4% a year forever. c) Stock C is expected to pay a dividend of \$5 next year. Thereafter, dividend growth is expected to be 20% a year for five years (i.e. until year 6) and zero thereafter. If the market capitalization rate for each stock is 10%, which stock is the most valuable? What if the capitalization rate is 7%? (From Keith Sharp: assume end-of-year dividends, with the first dividend coming 12 months from now. Assume that the 20% growth is for 60 months after Div1, hence 20% till time 6 years from now. The time 7 dividend is the same as the time 6 dividend. Any question like this in an ACT349 exam will be clearer about the timing than is the text question) Solution: For part c) we’ll use ‘horizon’ analysis, wh6re h=6 P = ▯▯▯▯ (1+ ▯▯▯ ▯⋯..▯▯ ▯▯▯) ) + + ▯ P 0 ▯▯▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯▯ h ▯▯▯▯ ▯▯▯ h ▯▯▯ ▯ = (1- ▯ ) )/ (1- ▯ ))/ + + ▯ Ph ▯▯▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯ ▯▯▯▯ ▯▯▯ h ▯ = ▯▯▯▯▯ (1- ▯▯▯) )+ + ▯▯▯ ▯ Ph A B C r=0.10 ▯▯▯▯ ▯▯ ▯▯▯▯ ▯ ▯▯▯▯ ▯∗▯.▯▯▯ P0= ▯▯▯ =▯.▯▯▯▯.▯▯ P 0 ▯▯▯ = ▯.▯▯▯▯.▯▯\$83.33 P h ▯▯▯ = ▯.▯▯▯▯.▯▯124.416 =\$100 ▯ ▯.▯ ▯ P 0= (1 - ▯) + ▯ 124.416 ▯.▯▯▯▯.▯▯ ▯.▯ ▯.▯ = 34.276 + 70.229=\$104.50 r=0.07 P 0 P = ▯▯▯▯= ▯ =\$166.67 ▯▯▯▯ ▯∗▯.▯▯▯ 0 ▯▯▯ ▯.▯▯▯▯.▯▯ P h ▯▯▯ = ▯.▯▯▯▯.▯▯177.737 ▯▯▯▯ ▯▯ = ▯▯▯= ▯.▯▯▯▯.▯▯ ▯ ▯.▯ ▯ P 0 (1 - ▯) + ▯*177.737 ▯.▯▯▯▯.▯▯ ▯.▯▯ ▯.▯▯ =\$142.86 = 38.065+118.434 = 156.50 5. (BMAGL11-100 ;BMA11-Ch04-Q20v00) Company Q’s current return on equity (ROE) is 14%. It pays out one-half of earnings as cash dividends (payout ratio=0.5). Current book value per share is \$50. Book value per share will grow as Q reinvests earnings. Assume that the ROE and payout ratio stay constant for the next four years. After that, competition forces the ROE down to 11.5% and the payout ratio increases to 0.8. The cost of capital is 11.5% What are Q’s EPS and dividends next year? How will EPS and dividends grow in years 2, 3, 4, 5 and subsequent years? Solution ROE=0.14 g=ROE*payback ratio=0.14*(1-0.5)= 0.07 for years 1-4 (time 0 to 4) g=0.115 * (1-0.8) = 0.023 for years 5+ (t> 4 ) EPS(1)= 50*ROE = \$7 Year Time at year end End-year EPS End-year div 1 (0
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