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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 Tutorial #5 Problem Set Oct.20/21 2011 1. A company will generate $1,000,000 in earnings next year and will pay it all out in dividends. The company has 200,000 shares outstanding and its discount rate is 10%. (a) If the company expects to generate the same earnings each year in the future and will keep paying them out, what is its price per share? (5 marks) (b) Suppose the company can reinvest $200,000 next year (and reduce dividend pay- ment at that time). The return on retained earnings is 14% (i.e., the reinvested amount will pay off 14% per year forever). What is the NPV of the next year’s reinvestment, expressed in today’s dollars? (5 marks) (c) If the company takes the opportunity described in (b) (invests next year and pays out all earnings each year after next year), what should be its current share price? (5 marks) (d) The company decides to change its strategy. It will reinvest 30% of its earnings every year, starting next year. As in (b), future investments will pay off 14% forever, starting a year after the investment is made. What is the per-share NPVGO (net present value of growth opportunities)? (5 marks) Solution: (a) We will use the constant dividend model. The value of the company is $1 M/ . 1 = $10 M . Thus, one share is worth $10 M/ 200 , 000 = $50 . 00. (b) NPV =- $200 , 000 + . 14 × $200 , 000 . 1 1 . 1 = $72 , 727 . (c) The new value of the company will be $10,072,727: the initial value plus NPV we got in (b). Hence, the share price should be P = $10 , 072 , 727 / 200 , 000 = $50 . 36. An alternative solutions is to use the dividends directly. The company will payout $800,000 next year. Each year after that, it will pay out $1.028M ($1M as before plus 14% of the amount reinvested, 0 . 14 × $200 , 000 = $28 , 000). Hence, its total value is $800 , 000 1 . 1 + $1 . 028 M . 1 1 . 1 = $10 , 072 , 727 , which gives the same price per share....
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This note was uploaded on 12/20/2011 for the course RSM 332 taught by Professor Raymondkan during the Fall '08 term at University of Toronto.
- Fall '08