Question

You are considering a new product launch. The project will cost $800,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 200 units per year; price per unit will be $18,300, variable cost per unit will be $15,300, and fixed costs will be $630,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 34 percent.

a) Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±12 percent. What are the best and worst cases for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios?

b) Evaluate the sensitivity of your base-case NPV to changes in fixed costs.

Answer 1

Total cash PVIFe Sales Sale Variable Contributi Fixed Depreciat Deprecia Operating | Present value Year units price cost on per unit |costs | ion Tax@34% |PAT 2% PBT 800,000) 1.000(800,000.00) 48,200 0.893$43,035.71 48,200 0.797 $ 38,424.74 48,200 $ 34,307.81 48, (800,000) 2 200 18,300 3 200 18,300 15,300 4 200 18,30015,300 3,000 630,000 200,000 (230,000) (78,200)151,800) 200,00048,200 3,000 630,000 200,000 (230,000) (78,200)151,800) 200,00048,200 3,000 630,000 200,000 (230,000 ( 48,200 0.712 200 0.636 30,631.97 (78,200)151,800) 200,000 S (653,599.76) Base case NPV Sales Sale Variable Contributi Fixed Depreciat Deprecia Operating Total cash PVIF IPAT PBT Year units price cost on per unit costs ion Tax@34% cash flows Investment flows 1296 | Presentvalue (800,000) (800,000) 1.000$ (800,000.00) 37,142.86 41faxo en..es/ $ 爁4,1ได้琺汱/ 0 1200 18,300 15,300 2 200 18,300 3 200 18,300 15,300 4 200 18,30015,300 3,000 640,000 200,000 (240,000(81,600)(158,400)200,000 41,600 41,600 0.893 3,000 640,000 200,000 (240,000)(81,600) (158,400) 200,00041,600 0.797 33,163.27 41,600 $29,610.06 41,600 0.636 $ 26,437.55 0.712 200,000(240,000(81,600 158,400) 200,000 (673,646.27) NPV with FC change Sales Sale Vriable Contributi Fixed Depreciat Deprecia Operating ioum Total cash PVIF@ l present value Year units price cost on per unit costs ion cash flows Investment flows 12% PBT Tax@34% |PAT (800,000) (800,000) 1.000(800,000.00) 417,050 0.893 372,366.29 417,050 0.797 332,469.90 417,050 296,848.12 417,050 0.636 265,042.97 0.712 3 224 18,30013,464 4,836 | 554,400 | 200,000 | 328,864「 111,814 217,050 | 200,000 | 417,050 466,727.27 st case NPV

ia Operating Total cash PVIF Sales Sale Variable Contributi Depreciat Depreci tion 12% | Present value PBT on per unit Fixed costs ion Tax@34% |PAT cash flows Investment flows 03 1 176 18,300 17,136 1,164 2 176 18,300 17,136$ 1,164 3 176 18,300 17,1361,164 4 176 18,300 $ 17,136$ 1,164705,600 200,000 (700,736) (238,250(462,486)200,000 (262,486 (262,486) 0.893 (234,362.29 (209,252.04 (262,486) 0.712 186,832.1 (262,486) 0.636 $ (166,814.45 705,600 200,000 (700,736) (238,250)(462,486) 200,000 (262,486 705,600200,000 (700,736) (238,250 (462,486 200,000 (262,486 705,600200,000 (700,736) (238,250) (262,486) 0.797 (462,486) 200,000 (262,486 (1,597,260.95 Worst case NPV

f(P68-P59)/10000 E101 AB $ 466,727.27 -$1,597,260.95 -$653,599.76 $2.00 98 NPV best 99 NPV worst oNPV base NPV falls by 100 101