In: Finance
Chapter 10.3
Blooper’s analysts have come up with the following revised estimates for its magnoosium mine:
Range |
||||||||
Pessimistic | Optimistic | |||||||
Initial investment | + | 40 | % | – | 15 | % | ||
Revenues | – | 15 | % | + | 20 | % | ||
Variable costs | + | 25 | % | – | 20 | % | ||
Fixed cost | + | 40 | % | – | 20 | % | ||
Working capital | + | 45 | % | – | 25 | % |
Conduct a sensitivity analysis for each variable and range and compute the NPV for each. Use Spreadsheet 10.1 and accompanying data as a starting point for the analysis. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers in thousands rounded to the nearest whole dollar.)
A. Inputs | |||||||
Initial investment ($ thousands) | 10,000 | ||||||
Salvage value ($ thousands) | 2,000 | ||||||
Initial revenues ($ thousands) | 15,000 | ||||||
Variable costs (% of revenues) | 40.0% | ||||||
Initial fixed costs ($ thousands) | 4,000 | ||||||
Initial total expenses ($ thousands) | 10,000 | ||||||
Inflation rate (%) | 5.0% | ||||||
Discount rate (%) | 12.0% | ||||||
Receivables (% of sales) | 16.7% | ||||||
Inventory (% of next year's costs) | 15.0% | ||||||
Tax rate (%) | 35.0% | ||||||
Year: | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
B. Fixed assets | |||||||
Investments in fixed assets | 10,000 | ||||||
Sales of fixed assets | 1,300 | ||||||
Cash flow from fixed assets | -10,000 | 1,300 | |||||
C. Operating cash flow | |||||||
Revenues | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | ||
Variable expenses | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | ||
Fixed expenses | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | ||
Depreciation | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | ||
Pretax profit | 3,000 | 3,250 | 3,513 | 3,788 | 4,078 | ||
Tax | 1,050 | 1,138 | 1,229 | 1,326 | 1,427 | ||
Profit after tax | 1,950 | 2,113 | 2,283 | 2,462 | 2,650 | ||
Operating cash flow | 3,950 | 4,113 | 4,283 | 4,462 | 4,650 | ||
D. Working capital | |||||||
Working capital | 1,500 | 4,075 | 4,279 | 4,493 | 4,717 | 3,039 | 0 |
Change in working capital | 1,500 | 2,575 | 204 | 214 | 225 | -1,679 | -3,039 |
Cash flow from investment in working capital | -1,500 | -2,575 | -204 | -214 | -225 | 1,679 | 3,039 |
0.408 | 0.408 | 0.408 | 0.408 | 0.250 | |||
E. Project valuation | |||||||
Total project cash flow | -11,500 | 1,375 | 3,909 | 4,069 | 4,238 | 6,329 | 4,339 |
Sensitivity Analysis of Initial Investment | Pessimistic | Optimistic | |||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||
Revenue | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | |||||
Less: Variable expenses | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | |||||
Less: Fixed Expenses | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | |||||
Less: Depreciation | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | |||||
Pre tax Profit | 3,000 | 3,250 | 3,513 | 3,787 | 4,078 | 3,000 | 3,250 | 3,513 | 3,787 | 4,078 | |||||
Tax | 1,050 | 1,138 | 1,229 | 1,326 | 1,427 | 1,050 | 1,138 | 1,229 | 1,326 | 1,427 | |||||
Profit after tax | 1,950 | 2,113 | 2,283 | 2,462 | 2,651 | 1,950 | 2,113 | 2,283 | 2,462 | 2,651 | |||||
Operating cash flow | 3,950 | 4,113 | 4,283 | 4,462 | 4,651 | 3,950 | 4,113 | 4,283 | 4,462 | 4,651 | |||||
Working Capital | |||||||||||||||
Working capital | 1,500 | 4,075 | 4,279 | 4,493 | 4,717 | 3,039 | 0 | 1,500 | 4,075 | 4,279 | 4,493 | 4,717 | 3,039 | 0 | |
Change in working capital | 1,500 | 2,575 | 204 | 214 | 225 | -1,679 | -3,039 | 1,500 | 2,575 | 204 | 214 | 225 | -1,679 | -3,039 | |
Cash flow from investment in working capital | -1,500 | -2,575 | -204 | -214 | -225 | 1,679 | 3,039 | -1,500 | -2,575 | -204 | -214 | -225 | 1,679 | 3,039 | |
Initial Investment in Fixed assets | -14000 | -7500 | |||||||||||||
Sale of fixed assets | 1300 | 1300 | |||||||||||||
Total Project cash flow | -15,500 | 1,375 | 3,909 | 4,069 | 4,237 | 6,330 | 4,339 | -9,000 | 1,375 | 3,909 | 4,069 | 4,237 | 6,330 | 4,339 | |
Discounting factor @ 6.67% | 1 | 0.9374707 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | 1 | 0.937471 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | |
Present value of cashflow | -15,500 | 1,289 | 3,435 | 3,353 | 3,272 | 4,583 | 2,945 | -9,000 | 1,289 | 3,435 | 3,353 | 3,272 | 4,583 | 2,945 | |
NPV | 3,378 | 9,878 | |||||||||||||
Sensitivity Analysis of Sales | Pessimistic | Optimistic | |||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||
Revenue | 12,750 | 13,388 | 14,057 | 14,759 | 15,498 | 18,000 | 18,900 | 19,846 | 20,837 | 21,880 | |||||
Less: Variable expenses | 5,100 | 5,355 | 5,623 | 5,904 | 6,199 | 7,200 | 7,560 | 7,938 | 8,335 | 8,752 | |||||
Less: Fixed Expenses | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | |||||
Less: Depreciation | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | |||||
Pre tax Profit | 1,650 | 1,833 | 2,024 | 2,225 | 2,437 | 4,800 | 5,140 | 5,497 | 5,871 | 6,266 | |||||
Tax | 578 | 641 | 709 | 779 | 853 | 1,680 | 1,799 | 1,924 | 2,055 | 2,193 | |||||
Profit after tax | 1,073 | 1,191 | 1,316 | 1,446 | 1,584 | 3,120 | 3,341 | 3,573 | 3,816 | 4,073 | |||||
Operating cash flow | 3,073 | 3,191 | 3,316 | 3,446 | 3,584 | 5,120 | 5,341 | 5,573 | 5,816 | 6,073 | |||||
Working Capital | |||||||||||||||
Working capital | 1,365 | 3,563 | 3,741 | 3,928 | 4,124 | 2,588 | 0 | 1,680 | 4,770 | 5,009 | 5,259 | 5,522 | 3,654 | 0 | |
Change in working capital | 1,365 | 2,198 | 178 | 187 | 196 | -1,536 | -2,588 | 1,680 | 3,090 | 239 | 251 | 263 | -1,868 | -3,039 | |
Cash flow from investment in working capital | -1,365 | -2,198 | -178 | -187 | -196 | 1,536 | 2,588 | -1,680 | -2,575 | -204 | -214 | -225 | 1,679 | 3,039 | |
Initial Investment in Fixed assets | -10000 | -10000 | |||||||||||||
Sale of fixed assets | 1300 | 1300 | |||||||||||||
Total Project cash flow | -11,365 | 875 | 3,013 | 3,129 | 3,250 | 5,120 | 3,888 | -11,680 | 2,545 | 5,137 | 5,359 | 5,591 | 7,752 | 4,339 | |
Discounting factor @ 6.67% | 1 | 0.9374707 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | 1 | 0.937471 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | |
Present value of cashflow | -11,365 | 820 | 2,648 | 2,578 | 2,510 | 3,707 | 2,639 | -11,680 | 2,386 | 4,515 | 4,415 | 4,319 | 5,613 | 2,945 | |
NPV | 3,538 | 12,513 | |||||||||||||
Sensitivity Analysis of Variable costs | Pessimistic | Optimistic | |||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||
Revenue | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | |||||
Less: Variable expenses | 7,500 | 7,875 | 8,269 | 8,682 | 9,117 | 4,800 | 5,040 | 5,292 | 5,556 | 5,835 | |||||
Less: Fixed Expenses | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | |||||
Less: Depreciation | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | |||||
Pre tax Profit | 1,500 | 1,675 | 1,859 | 2,051 | 2,255 | 4,200 | 4,510 | 4,836 | 5,177 | 5,536 | |||||
Tax | 525 | 586 | 651 | 718 | 789 | 1,470 | 1,579 | 1,693 | 1,812 | 1,938 | |||||
Profit after tax | 975 | 1,089 | 1,208 | 1,333 | 1,465 | 2,730 | 2,932 | 3,143 | 3,365 | 3,599 | |||||
Operating cash flow | 2,975 | 3,089 | 3,208 | 3,333 | 3,465 | 4,730 | 4,932 | 5,143 | 5,365 | 5,599 | |||||
Working Capital | |||||||||||||||
Working capital | 1,725 | 4,316 | 4,532 | 4,759 | 4,997 | 3,045 | 0 | 1,320 | 3,891 | 4,086 | 4,290 | 4,504 | 3,045 | 0 | |
Change in working capital | 1,725 | 2,591 | 216 | 227 | 238 | -1,952 | -3,045 | 1,320 | 2,571 | 195 | 204 | 214 | -1,459 | -3,039 | |
Cash flow from investment in working capital | -1,725 | -2,591 | -216 | -227 | -238 | 1,952 | 3,045 | -1,320 | -2,575 | -204 | -214 | -225 | 1,679 | 3,039 | |
Initial Investment in Fixed assets | -10000 | -10000 | |||||||||||||
Sale of fixed assets | 1300 | 1300 | |||||||||||||
Total Project cash flow | -11,725 | 384 | 2,873 | 2,982 | 3,095 | 5,417 | 4,345 | -11,320 | 2,155 | 4,728 | 4,929 | 5,140 | 7,278 | 4,339 | |
Discounting factor @ 6.67% | 1 | 0.9374707 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | 1 | 0.937471 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | |
Present value of cashflow | -11,725 | 360 | 2,525 | 2,457 | 2,391 | 3,922 | 2,949 | -11,320 | 2,020 | 4,155 | 4,061 | 3,970 | 5,270 | 2,945 | |
NPV | 2,879 | 11,101 | |||||||||||||
Sensitivity Analysis of Fixed cost | Pessimistic | Optimistic | |||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||
Revenue | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | |||||
Less: Variable expenses | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | |||||
Less: Fixed Expenses | 5,600 | 5,880 | 6,174 | 6,483 | 6,807 | 3,200 | 3,360 | 3,528 | 3,705 | 3,890 | |||||
Less: Depreciation | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | |||||
Pre tax Profit | 1,400 | 1,570 | 1,749 | 1,935 | 2,133 | 3,800 | 4,090 | 4,395 | 4,714 | 5,050 | |||||
Tax | 490 | 550 | 612 | 677 | 747 | 1,330 | 1,432 | 1,538 | 1,650 | 1,768 | |||||
Profit after tax | 910 | 1,021 | 1,137 | 1,258 | 1,386 | 2,470 | 2,659 | 2,857 | 3,064 | 3,283 | |||||
Operating cash flow | 2,910 | 3,021 | 3,137 | 3,258 | 3,386 | 4,470 | 4,659 | 4,857 | 5,064 | 5,283 | |||||
Working Capital | |||||||||||||||
Working capital | 1,740 | 4,332 | 4,549 | 4,776 | 5,015 | 3,045 | 0 | 1,380 | 3,954 | 4,152 | 4,359 | 4,577 | 3,045 | 0 | |
Change in working capital | 1,740 | 2,592 | 217 | 228 | 239 | -1,970 | -3,045 | 1,380 | 2,574 | 198 | 208 | 218 | -1,532 | -3,045 | |
Cash flow from investment in working capital | -1,740 | -2,592 | -217 | -228 | -239 | 1,970 | 3,045 | -1,380 | -2,574 | -198 | -208 | -218 | 1,532 | 3,045 | |
Initial Investment in Fixed assets | -10000 | -10000 | |||||||||||||
Sale of fixed assets | 1300 | 1300 | |||||||||||||
Total Project cash flow | -11,740 | 318 | 2,804 | 2,909 | 3,019 | 5,356 | 4,345 | -11,380 | 1,896 | 4,461 | 4,649 | 4,846 | 6,815 | 4,345 | |
Discounting factor @ 6.67% | 1 | 0.9374707 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | 1 | 0.937471 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | |
Present value of cashflow | -11,740 | 298 | 2,464 | 2,397 | 2,332 | 3,878 | 2,949 | -11,380 | 1,777 | 3,920 | 3,830 | 3,743 | 4,935 | 2,949 | |
NPV | 2,579 | 9,775 | |||||||||||||
Sensitivity Analysis of Working capital | Pessimistic | Optimistic | |||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||
Revenue | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | 15,000 | 15,750 | 16,538 | 17,364 | 18,233 | |||||
Less: Variable expenses | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | 6,000 | 6,300 | 6,615 | 6,946 | 7,293 | |||||
Less: Fixed Expenses | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | 4,000 | 4,200 | 4,410 | 4,631 | 4,862 | |||||
Less: Depreciation | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | 2,000 | |||||
Pre tax Profit | 3,000 | 3,250 | 3,513 | 3,787 | 4,078 | 3,000 | 3,250 | 3,513 | 3,787 | 4,078 | |||||
Tax | 1,050 | 1,138 | 1,229 | 1,326 | 1,427 | 1,050 | 1,138 | 1,229 | 1,326 | 1,427 | |||||
Profit after tax | 1,950 | 2,113 | 2,283 | 2,462 | 2,651 | 1,950 | 2,113 | 2,283 | 2,462 | 2,651 | |||||
Operating cash flow | 3,950 | 4,113 | 4,283 | 4,462 | 4,651 | 3,950 | 4,113 | 4,283 | 4,462 | 4,651 | |||||
Working Capital | |||||||||||||||
Working capital | 2,175 | 3,734 | 296 | 310 | 326 | -2,435 | 0 | 1,125 | 1,931 | 153 | 161 | 169 | -1,259 | 0 | |
Change in working capital | 2,175 | 1,559 | -3,438 | 15 | 16 | -2,761 | 2,435 | 1,125 | 806 | -1,778 | 8 | 8 | -1,428 | 1,259 | |
Cash flow from investment in working capital | -2,175 | -1,559 | 3,438 | -15 | -16 | 2,761 | -2,435 | -1,125 | -806 | 1,778 | -8 | -8 | 1,428 | -1,259 | |
Initial Investment in Fixed assets | -10000 | -10000 | |||||||||||||
Sale of fixed assets | 1300 | 1300 | |||||||||||||
Total Project cash flow | -12,175 | 2,391 | 7,550 | 4,269 | 4,446 | 7,411 | -1,135 | -11,125 | 3,144 | 5,891 | 4,276 | 4,454 | 6,079 | 41 | |
Discounting factor @ 6.67% | 1 | 0.9374707 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | 1 | 0.937471 | 0.878851 | 0.823897 | 0.77238 | 0.724083 | 0.678807 | |
Present value of cashflow | -12,175 | 2,242 | 6,636 | 3,517 | 3,434 | 5,366 | -770 | -11,125 | 2,947 | 5,177 | 3,523 | 3,440 | 4,401 | 28 | |
NPV | 8,250 | 8,391 | |||||||||||||
Sensitivity Analysis | Pessimistic | Optimistic | |||||||||||||
NPV Change in Initial Investment | 3378 | 9878 | |||||||||||||
NPV Change in revenue | 3538 | 12513 | |||||||||||||
NPV Change in Variable cost | 2879 | 11101 | |||||||||||||
NPV Change in Fixed cost | 2579 | 9775 | |||||||||||||
NPV Change in working capital | 8250 | 8391 |