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TBS 907-Spring 2005 - Tutorial 2- NPV Analysis- Solutions
Course: FIN FIN, Spring 2009School: Baptist College of...
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907- TBS SPRING 2005 TUTORIAL 2- NPV ANALYSIS Question 1 As winner of a breakfast cereal competition, you can choose one of the following prizes: a. b. c. d. e. $100,000 now. $180,000 at the end of five years. $11,400 a year forever. $19,000 for each of 10 years $6,500 next year and increasing thereafter by 5 per year forever. If the interest rate is 12 percent, which is the most valuable prize. Answer: a. b. c....
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907- TBS SPRING 2005 TUTORIAL 2- NPV ANALYSIS
Question 1 As winner of a breakfast cereal competition, you can choose one of the following prizes: a. b. c. d. e. $100,000 now. $180,000 at the end of five years. $11,400 a year forever. $19,000 for each of 10 years $6,500 next year and increasing thereafter by 5 per year forever.
If the interest rate is 12 percent, which is the most valuable prize. Answer: a. b. c. d. PV = $100,000 PV = $180,000/1.125 = $102,137 PV = $11,400/0.12 = $95,000 PV = $19,000 [Annuity factor, 12%, t = 10] PV = $19,000 5.650 = $107,350 e. PV = $6,500/(0.12 - 0.05) = $92,857 Prize (d) is the most valuable because it has the highest present value.
Question 2 Consider the following three stocks: a. b. c. Stock A is expected to provide a dividend of $10 per share forever. Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4 percent per year forever. Stock C is expected to pay a dividend of $5 next year. Thereafter dividend growth is expected to be 20 percent a year for 5 years (i.e. until year 6) and zero thereafter.
Answer: DIV1 $10 = = $100.00 r 0.10 DIV1 5 = = $83.33 r - g 0.10 - 0.04 DIV1 DIV2 DIV3 DIV4 DIV5 DIV6 DIV7 1 + + + + + + 1 2 3 4 5 6 1.10 1.10 1.10 1.10 1.10 1.10 0.10 1.106
PA = PB = PC =
PC =
5.00 6.00 7.20 8.64 10.37 12.44 12.44 1 + + + + + + = $104.50 1 2 3 4 5 6 1.10 1.10 1.10 1.10 1.10 1.10 0.10 1.10 6
At a capitalization rate of 10 percent, Stock C is the most valuable. For capitalization a rate of 7 percent, the calculations are similar. The results are: PA = $142.86 PB = $166.67 PC = $156.48 Therefore, Stock B is the most valuable.
Question 3 The furniture division of Playfurn Ltd., a profitable, diversified company, purchased a machine 5 years ago for $7,500. When it was purchased the machine had an expected useful life of 15 years and an estimated value of zero at the end of its life. The machine currently has a market value of $1000. the division manager reports that he can buy a new machine for $16,000 ( including installation) which, over its 10-year life, will result in an expansion of sales from $10,000 to $11,000 per annum. In addition, it is estimated that the new machine will reduce annual operating costs from $7,000 to $5,000. If the required rate of return is 10 percent per annum, should Playfurn buy the new machine? Answer: Compare machines over a life of 10 years. Assume that at the end of 10 years, the scrap value of the new machine is zero. Continue to operate old machine: Net Cash Flow : $10,000 - $7,000 = $3,000 per year for 10 years 1 10 1 - 1.1 - $1000 = $17,434 NPV = $3000 0.10 Purchase New Machine now: Cost Disposal of Old Machine Net Cash Flow = $16,000 = $1,000 = $11,000 - $5,000 = $6,000
1 10 1 - 1.1 - $1000 = $21,867 NPV = -$16,000 + $1,000 + $6000 0.10 As the NPV of purchasing the new machine exceeds the NPV of continuing to operate the old machine, the new machine should be purchased now.
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