Solutions to Lab Problems for Chapter 14

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Unformatted text preview: Solutions to Lab Problems for Chapter 14 21. Section: 14.2 Estimating and Discounting Cash Flows Learning Objective: 14.2 Level of difficulty: Difficult Solution: Step 1: initial cash flow=-CF0=-\$4,000. Step 2: PV of after-tax operating cash flow Discount rate=0.10, payment=\$2,000*(1-tax rate)=\$2,000*(1-0.4), N=3, and PV=2,984.22. Step 3: PV of CCA tax shield. There is no capital gain, capital recapture, or terminal loss. Using formula [14-7], C0dT/(d+k)=1,200.00, (1+0.5k)/(1+k)=0.954545, SVdT/(d+k)=0, 1/(1+k)n=0.751315, and PV of CCA tax shield=1,145.45 Step 4: PV of ECF Discount rate=0.10, future value=salvage value=0 N=3, and PV=0 Step 5: PV of capital gains taxes paid=0 Step 6: Using formula [14-10], NPV=129.67 This project has a positive NPV. The company should take it. 33. Section: 14.3 Sensitivity to Inputs Learning Objective: 14.3 Level of difficulty: Difficult Solution: a. Year 0 1 2 3 4 Cash flow UCC (open) -\$2,500.00 \$700.00 1,250 \$735.00 2,375 \$771.75 2,137.50 \$810.34 1,923.75 CCA UCC After-tax cash (close) flow -\$2,500.00 \$125.00 2,375 \$556.25 \$237.50 2,137.50 \$610.63 \$213.75 1,923.75 \$632.25 \$192.38 1,731.37 \$655.85 Present value of after-tax cash flows: PV of aftertax cash flow -\$2,500.00 \$519.86 \$533.34 \$516.10 \$500.34 -\$430.35 The asset will be scrapped (salvage = \$0) zero capital gains. As the asset class is large and will continue we do not have to deal with CCA recapture and terminal loss in year 4. b. Worst case Year Base case AfterPV of Cash flow tax cash after-tax flow cash flow Cash flow Best case AfterPV of tax cash after-tax flow cash flow PV of Afterafter-tax tax cash cash flow flow Cash flow Growth rate 2.00% 5.00% 8.00% Year 1 cash flow \$300 \$700 \$ 900 0 1 2 3 4 NPV -2,500 300.00 306.00 312.12 318.36 -2,500 256.25 288.88 287.53 286.87 -2,500 239.49 252.32 234.71 218.85 -\$1,554.63 -2,500 700.00 735.00 771.75 810.34 -2,500 556.25 610.63 632.25 655.85 -2,500 -2,500 519.86 900.00 533.35 972.00 516.10 1,049.76 500.34 1,133.74 -\$430.35 -2,500 706.25 788.38 840.76 898.40 -2,500 660.05 688.60 686.31 685.39 \$220.35 The expected value of the project is: .3*(–1,554.63) + .55*(-430.35) + .15*(220.35) = – \$670.03 c. Year PV of cash flows Growth rate 0.03 0.05 0.07 0.03 0.05 0.07 0.03 0.05 0.07 Year 1 cash 400 400 400 700 700 700 1,000 1,000 1,000 flow NPV -1,278.46 -1,248.18 -1,217.13 -483.34 -430.35 -376.01 311.78 387.48 465.12 Given that this project is only 4 years long, the impact of any errors on the initial cash flow estimate will be more important than growth rate errors. With only 4 years to grow, a small error in the growth rate does not have time to compound into a huge error. d. Using the solver function in Excel, we find that the initial cash flow that results in a break-even or zero NPV is \$857.86 B 47 Year Growth 48 rate Year 1 49 cash flow C CCA D Cash flow 0.05 857.862619935937 E After-tax cash flow F PV of after-tax cash flows 0 1 2 3 4 50 51 52 53 54 55 125 237.5 213.75 192.375 NPV -2500 =D50 =+D52*(1+G\$17) =+D53*(1+G\$17) =+D54*(1+G\$17) -2500 =D52*0.75+\$C52*0.25 =D53*0.75+\$C53*0.25 =D54*0.75+\$C54*0.25 =D55*0.75+\$C55*0.25 =E51/(1.07)^\$B51 =E52/(1.07)^\$B52 =E53/(1.07)^\$B53 =E54/(1.07)^\$B54 =E55/(1.07)^\$B55 =SUM(F51:F55) 45. Section: 14.4 Replacement Decisions Learning Objective: 14.4 Level of difficulty: Challenging Solution: Because we are dealing with a replacement problem, we have to examine the incremental cash flows. As the old machine was fully depreciated 8 years ago and will be scrapped if we replace it, we will assume that the UCC for this asset class at year zero is close to zero (i.e., we will not have to deal with any CCA recapture/loss or capital gains at time zero if we replace the old machine). New machine CCA schedule UCC Year CCA begin 0 1 2 3 4 5 Old machine New machine UCC Rev. Maint. Invest. Maint. New - Old end -25000 12500 22500 18000 14400 11520 2500 4500 3600 2880 2304 Incremental after tax CF 22500 18000 14400 11520 9216 1500 1500 1500 1500 1500 5000 6000 7000 8000 9000 -500 -500 -500 -500 -500 -25000 1980 2640 3300 3960 4620 CCA Tax shield 850 1530 1224 979.2 783.36 Total -25000 2830 4170 4524 4939.2 5403.36 The cash flows are given as nominal values so we need to use the appropriate nominal discount rate: the approximation is 7% +3%= 10%. The more exact value for the nominal rate would be 1.07*1.03 -1 = 10.21% NPV of incremental cash flows: + PV of salvage value of new machine - PV of CCA terminal loss NPV of replacing old machine: -\$8,853.44 3104.60662 890.053461 -\$4,858.78 Based on the analysis above, the old machine should not be replaced. ...
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## This note was uploaded on 01/10/2012 for the course TEFLER 2350 taught by Professor Rentz during the Winter '11 term at University of Ottawa.

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