Chapter 7_7 to 7_8
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Chapter 7_7 to 7_8

Course Number: ACSTC 371, Fall 2011

College/University: Waterloo

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ActSc 371 7.7 and 7.8 Practice Problems 1. What is the profitability index for the following cash flows, if the relevant discount rate is 15%? Year 0 Year 1 Year 2 Year 3 $-10,000 $6,500 $4,000 $2,500 A) 1 B) 1.03 C) 1.3 D) 1.05 E) 1.11 Solution: PV of cash flows after the initial investment is: 10,320.54. The PI is this value divided by the absolute value of the original investment This is 10320.54/10000=1.03...

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371 ActSc 7.7 and 7.8 Practice Problems 1. What is the profitability index for the following cash flows, if the relevant discount rate is 15%? Year 0 Year 1 Year 2 Year 3 $-10,000 $6,500 $4,000 $2,500 A) 1 B) 1.03 C) 1.3 D) 1.05 E) 1.11 Solution: PV of cash flows after the initial investment is: 10,320.54. The PI is this value divided by the absolute value of the original investment This is 10320.54/10000=1.03 2. The Ziggy Trim and Cut Company can purchase equipment on sale for $4,300. The asset has a three-year life, will produce a cashflow of $1,200 in the first and second year, and $3,000 in the third year. The interest rate is 12%. Calculate the project's discounted payback and Profitability Index assuming end of year cash flows. Should the project be taken? Solution: CF0=-4300 CF1=1200 CF2=1200 CF3=3000 Step 1: Calculate the NPV using the calculator = -136.60 Because NPV is less than zero, discounted payback cannot be calculated. Step 2: to calculate the PI, first calculate the NPV without including the initial cashflow (i.e. 4300). This is: 4163.40. Then, divide this value by the absolute value of the initial investment (i.e. 4300). PI=0.97. Because PI is less than 1, we should reject the project. Therefore, under both methods we should reject the project. Both methods indicate that your cost of capital is not being covered. 3. The Walker Landscaping Company can purchase a piece of equipment for $3,600. The asset has a two-year life, will produce a cashflow of $600 in the first year and $4200 in the second year. The interest rate is 15%. Calculate the project's discounted payback and Profitability Index assuming steady cashflows. Should the project be taken? If the accounting rate of return was positive, how would this affect your decision? Answer: CF0=-3600 CF1=600 CF2=4200 Step 1: Calculate the NPV: 97.54 NPV is positive, so we can calculate the projects payback. 600 600/1.15 521.74 4200 4200/1.15^2 3175.80 Given discounted the initial investment was -3600: after 1 year, payback is 3078.26. The proportion of the second year cash inflow that goes towards payback is: 3078.26/3175.80=0.97. Therefore, the projects discounted payback is 1.97 years. Step 2: Calculate PI using PV of Cashflows without initial investment: 3697.54. Divide this value by the absolute value of the original investment: 3697.54/3600=1.03. Since it is greater than 1, we should accept this project. Both measures indicate acceptance. A positive accounting rate of return would be consistent with this decision. Reliance on AAR should not be the key, as DPP and PI indicate earning a rate greater than cost of capital. 4. An investment project has the cashflow stream of -250, 75, 125, 100, and 50. The cost of capital is 12%. What is the discount payback period? -250 75 75/1.12 66.96 125 125/1.12^2 99.65 100 100/1.12^3 71.18 50 50/1.12^4 31.78 The sum of the PVs first three cash inflows is 237.79. Therefore, 250-237.79=12.21 of the fourth cash flow needs to be applied. This is the ratio: 12.21/31.78=0.38. Therefore, the answer is 3.38 years. 5. Halloween Co. wish to buy a new sewing machine to being costume manufacturing for next year in order to increase productivity. The initial net cash outlay is 15,600. The cashflows associated with the acquisition of the new sewing machine are as follows: Year Cash Flow from Operation 1 6,610 2 5,650 3 4,690 4 4,630 5 3,670 Assuming the required rate of return is 10% 4. What is the Net Present Value for this project? 4,043.31 Since this value is positive, you should accept this investment. 5. What is the Profitability Index? The PV of cash flows after the initial investment is: 19,643.31. Then, divide this by the initial investment: 1.26. Since this value is greater than 1, you should accept the project.

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