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We are evaluating a project that costs $993,000, has an eight-year life, and has no salvage value
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We are evaluating a project that costs $993,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 94,000 units per year. Price per unit is $41, variable cost per unit is $28, and fixed costs are $1,009,881 per year. The tax rate is 37 percent, and we require a 13 percent return on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 20 percent. |
| Required: | |
| (a) | Calculate the best-case NPV. (Do not round your intermediate calculations.) |
|
(Click to select) $4,703,003 $5,924,242 $5,628,030 $6,220,454 $883,581 |
|
| (b) | Calculate the worst-case NPV. (Do not round your intermediate calculations.) |
|
(Click to select) $-3,837,745 $883,581 $-1,291,464 $6,220,454 $-4,618,205 |
Expert Solution
a
| Time line | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
| Cost of new machine | -993000 | |||||||||||
| =Initial Investment outlay | -993000 | |||||||||||
| 100.00% | ||||||||||||
| Unit sales | 112800 | 112800 | 112800 | 112800 | 112800 | 112800 | 112800 | 112800 | ||||
| Profits | =no. of units sold * (sales price - variable cost) | 3023040 | 3023040 | 3023040 | 3023040 | 3023040 | 3023040 | 3023040 | 3023040 | |||
| Fixed cost | -807904.8 | -807904.8 | -807904.8 | -807904.8 | -807904.8 | -807904.8 | -807904.8 | -807904.8 | ||||
| -Depreciation | Cost of equipment/no. of years | -124125 | -124125 | -124125 | -124125 | -124125 | -124125 | -124125 | -124125 | 0 | =Salvage Value | |
| =Pretax cash flows | 2091010.2 | 2091010.2 | 2091010.2 | 2091010.2 | 2091010.2 | 2091010.2 | 2091010.2 | 2091010.2 | ||||
| -taxes | =(Pretax cash flows)*(1-tax) | 1317336.426 | 1317336.426 | 1317336.426 | 1317336.4 | 1317336.4 | 1317336.4 | 1317336.426 | 1317336.4 | |||
| +Depreciation | 124125 | 124125 | 124125 | 124125 | 124125 | 124125 | 124125 | 124125 | ||||
| =after tax operating cash flow | 1441461.43 | 1441461.43 | 1441461.43 | 1441461.4 | 1441461.4 | 1441461.4 | 1441461.43 | 1441461.4 | ||||
| +Tax shield on salvage book value | =Salvage value * tax rate | 0 | ||||||||||
| =Terminal year after tax cash flows | 0 | |||||||||||
| Total Cash flow for the period | -993000 | 1441461.43 | 1441461.43 | 1441461.43 | 1441461.4 | 1441461.4 | 1441461.4 | 1441461.43 | 1441461.4 | |||
| Discount factor= | (1+discount rate)^corresponding period | 1 | 1.13 | 1.2769 | 1.442897 | 1.6304736 | 1.8424352 | 2.0819518 | 2.35260548 | 2.6584442 | ||
| Discounted CF= | Cashflow/discount factor | -993000 | 1275629.584 | 1128875.738 | 999005.078 | 884075.29 | 782367.51 | 692360.63 | 612708.5234 | 542219.93 | ||
| NPV= | Sum of discounted CF= | 5924242 |
b
| Time line | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
| Cost of new machine | -993000 | |||||||||||
| =Initial Investment outlay | -993000 | |||||||||||
| 100.00% | ||||||||||||
| Unit sales | 75200 | 75200 | 75200 | 75200 | 75200 | 75200 | 75200 | 75200 | ||||
| Profits | =no. of units sold * (sales price - variable cost) | -60160 | -60160 | -60160 | -60160 | -60160 | -60160 | -60160 | -60160 | |||
| Fixed cost | -1211857.2 | -1211857.2 | -1211857.2 | -1211857 | -1211857 | -1211857 | -1211857.2 | -1211857 | ||||
| -Depreciation | Cost of equipment/no. of years | -124125 | -124125 | -124125 | -124125 | -124125 | -124125 | -124125 | -124125 | 0 | =Salvage Value | |
| =Pretax cash flows | -1396142.2 | -1396142.2 | -1396142.2 | -1396142 | -1396142 | -1396142 | -1396142.2 | -1396142 | ||||
| -taxes | =(Pretax cash flows)*(1-tax) | -879569.586 | -879569.586 | -879569.586 | -879569.6 | -879569.6 | -879569.6 | -879569.586 | -879569.6 | |||
| +Depreciation | 124125 | 124125 | 124125 | 124125 | 124125 | 124125 | 124125 | 124125 | ||||
| =after tax operating cash flow | -755444.59 | -755444.59 | -755444.59 | -755444.6 | -755444.6 | -755444.6 | -755444.59 | -755444.6 | ||||
| +Tax shield on salvage book value | =Salvage value * tax rate | 0 | ||||||||||
| =Terminal year after tax cash flows | 0 | |||||||||||
| Total Cash flow for the period | -993000 | -755444.59 | -755444.59 | -755444.59 | -755444.6 | -755444.6 | -755444.6 | -755444.59 | -755444.6 | |||
| Discount factor= | (1+discount rate)^corresponding period | 1 | 1.13 | 1.2769 | 1.442897 | 1.6304736 | 1.8424352 | 2.0819518 | 2.35260548 | 2.6584442 | ||
| Discounted CF= | Cashflow/discount factor | -993000 | -668535.035 | -591623.925 | -523560.996 | -463328.3 | -410025.1 | -362854 | -321109.764 | -284167.9 | ||
| NPV= | Sum of discounted CF= | -4618205 |
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