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 + ßCapstone(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, 99.67$61.64$92.161.64$082.0110101 PPPCFPPRT 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 risk-free rate is 7%. Stock Investment Beta A $ 200,000 1.50 B 300,000 .65 C 500,000 1.25 Solution:Portfolio Beta = piNiiw1 A 200,000 20% B 300,000 30% C 500,000 50% Total 1,000,000 100% p.20(1.50) + .30(.65) + .50(1.25) = 1.12 E(RPortfolio) = Rrf + βPortfolio (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 0$455,437.9NPVkFCFNPVnttt438,235,2$000,780,1$12.0)12.1(11000,450$000,780,1$)1(80 Since NPV > 0, try IRR > k. Try IRR = 20%. $53,278722,726,1$000,780,1$20.0)20.1(11000,450$000,500,1$)1(080ntttIRRFCFNPV Try IRR = 19%. 0$535 465,779,1$000,780,1$19.0)19.1(11000,450$000,780,1$)1(080ntttIRRFCFNPV 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 PVCF0 $(42,000) $(42,000) $(42,000) $(42,000) 1 12,800 (29,200) 11,636 (30,364) 2 12,800 (16,400) 10,579 (19,785) 3 8,900 (7,500) 6,687 (13,098) 4 8,900 1,400 6,079 (7,019) 5 5,000 6,400 3,105 (3,914) 6 5,000 11,400 2,822 (1,092) 7 5,000 16,400 2,566 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 Year 2 Year 3 Year 4 Year 5 Year 6 Cost Savings $ 380,000 $ 380,000 $ 380,000 $ 280,000 $ 280,000 $ 280,000 Depreciation 200,000 200,000 200,000 200,000 200,000 200,000 EBIT $ 180,000 $ 180,000 $ 180,000 $ 80,000 $ 80,000 $ 80,000 Taxes (32%) 57,600 57,600 57,600 25,600 25,600 25,600 Net income $ 122,400 $ 122,400 $ 122,400 $ 54,400 $ 54,400 $ 54,400 Beginning BV 1,200,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000 Less:Depreciation 200,000 200,000 200,000 200,000 200,000 200,000 Ending BV $ 1,000,000 $ 800,000 $ 600,000 $ 400,000 $ 200,000 $ 0 Average after-tax income = $88,400 Average book value of equipment = $600,00014.7%000,600$400,88$book value Averageincometax -after Average return of rate Accounting Since the project’s ARR is below the acceptance rate of 20 percent, the machinery should not be purchased. 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 required rate of return. 10.