# UT FIN 357 - ReviewTest2withsolutions (9 pages)

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## ReviewTest2withsolutions

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## ReviewTest2withsolutions

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University of Texas at Austin
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REVIW TEST 2 with Solutions by M L Poloskey These are some questions I wrote for another text that you can use for practice Note Not all topics in our text are covered here 1 Using the following information from Capstone Corporation what price would CAPM predict that this company s stock will trade for 1 year from today if you assume a risk free rate of 3 and a market risk premium of 8 Beta 65 Current Price 64 61 Estimated Forward Annual Dividend 1 92 Solution Using CAPM we find E RCapstone Rrf Capstone E Rm Rrf 0 03 65 0 08 E RCapstone 082 or 8 2 Then using the formula for an asset s return during a period P P0 CF1 P 64 61 1 92 RT 1 0 082 1 P1 67 99 P0 64 61 2 How are covariance and correlation different Solution Both covariance and correlation measure the co movements of returns The covariance is the expected product of the deviations of two returns from their means To compute the correlation the covariance is divided by the standard deviation of each return This scales the result so it is always between 1 and 1 and makes it easier to interpret 3 Calculate the beta of this portfolio and use the capital asset pricing model CAPM to determine its expected rate of return The market expected rate of return is 15 and the riskfree rate is 7 Stock A B C Solution Investment 200 000 300 000 500 000 Beta 1 50 65 1 25 Portfolio Beta p N w i 1 A B C Total i i 200 000 300 000 500 000 1 000 000 20 30 50 100 p 20 1 50 30 65 50 1 25 1 12 E RPortfolio Rrf Portfolio E RM Rrf E RPortfolio 07 1 12 15 07 1596 or 15 96 4 What would you recommend to an investor who is considering an investment which according to its beta plots below the security market line SML Solution Recommend the investor does not invest An investment that plots below the SML has high risk relative to return CAPM would predict an investment with that beta should have a higher return 5 Why does an investor want a diversified portfolio Can an investor eliminate all risk Solution An investor of a diversified portfolio reduces risk by investing in two or more assets whose values do not always move in the same direction at the same time Through diversification the investor can eliminate unsystematic or unique risk but still faces systematic or market risk 6 Testco Corp is considering adding a new product line The cost of the factory and equipment to produce this product is 1 780 000 and the company expects increased cash flows from the sale of this product to be 450 000 for each of the next eight years If the company uses a discount rate of 12 percent what is the net present value of this project What is the internal rate of return of this project Solution Cost of this project 1 780 000 Annual cash flows 450 000 Required rate of return 12 Length of project n 8 years 1 1 FCFt 1 12 8 NPV 1 780 000 450 000 t 0 12 t 0 1 k 1 780 000 2 235 438 n NPV 455 437 90 Since NPV 0 try IRR k Try IRR 20 1 1 n FCFt 1 20 8 NPV 0 1 500 000 450 000 t 0 20 t 0 1 IRR 1 780 000 1 726 722 53 278 Try IRR 19 1 1 n FCFt 1 19 8 NPV 0 1 780 000 450 000 t 0 19 t 0 1 IRR 1 780 000 1 779 465 535 0 The IRR is approximately 19 percent Using the financial calculator we find that the IRR is 18 99 percent 7 Flowers Unlimited is considering purchasing an additional delivery truck The cost of the new truck will be 42 000 Cost savings are expected to be 12 800 for the next two years and 8 900 for the following two years and 5 000 for the last 3 years of the truck s useful life What is the payback period for this project What is the discounted payback period for this project assuming a discount rate of 10 percent Solution Discount rate k 10 Year CF Cumulative CF PVCF Cumulative PVCF 0 1 2 3 4 5 6 7 42 000 12 800 12 800 8 900 8 900 5 000 5 000 5 000 42 000 29 200 16 400 7 500 1 400 6 400 11 400 16 400 42 000 11 636 10 579 6 687 6 079 3 105 2 822 2 566 42 000 30 364 19 785 13 098 7 019 3 914 1 092 1 474 PB Years before cost recovery Remaining cost to recover Cash flow during the year 3 7 500 8 900 3 84 years Discounted PB Years before cost recovery Remaining cost to recover PV Cash flow during the year 6 1 092 2 566 6 43 years 8 What is the average accounting rate of return ARR on equipment that will initially cost 1 2 million and will result in pretax cost savings of 380 000 for the next three years and then 280 000 for the following three years The machinery will be depreciated to a salvage value of 0 over 6 years using the straight line method The company s tax rate is 32 percent and the firm s acceptance decision on any project is based on an ARR of 20 percent Should this machinery be purchased Solution Year 1 380 000 200 000 180 000 57 600 122 400 Year 2 380 000 200 000 180 000 57 600 122 400 Year 3 380 000 200 000 180 000 57 600 122 400 Year 4 280 000 200 000 80 000 25 600 54 400 Year 5 280 000 200 000 80 000 25 600 54 400 Year 6 280 000 200 000 80 000 25 600 54 400 Beginning BV 1 200 000 Less Depreciation 200 000 Ending BV 1 000 000 5 000 000 200 000 800 000 4 000 000 200 000 600 000 3 000 000 200 000 400 000 2 000 000 200 000 200 000 1 000 000 200 000 0 Cost Savings Depreciation EBIT Taxes 32 Net income Average after tax income 88 400 Average book value of equipment 600 000 Average after tax income Average book value 88 400 14 7 600 000 Since the project s ARR is below the acceptance rate of 20 percent the machinery should not be purchased Accounting rate of return 9 If a project has a positive NPV what do we know about that project s IRR Solution If a project has a positive NPV the IRR of that project is greater than the required rate of return Since the IRR is the discount rate that makes the NPV equal zero a positive NPV results from the project s IRR being greater than the …

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