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# BREAK-EVEN ANALYSIS Based On NPV (in thousands of \$) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Key Assumptions Sales Growth Rate Change...

Suppose a firm is considering the following project where all of the dollar figures are in thousands of dollars. In year 0, the project requires \$24,490 investment in plant and equipment, is depreciated using the straight-line method over seven years and there is a salvage value of \$5,800 in year 7. The project is forecast to generate sales of 4,800 units in year 1 and grow at a sales growth rate of 72.0% in year 2. The sales growth rate is forecast to decline by 12.0% in year 3, to decline by 15.0% in year 4, to decline by 18.0% in year 5, to decline by 23.0% in year 6, to decline by 29.0% in year 7. Unit sales will drop to zero in year 8.

The inflation rate is forecast to be 2.7% in year 1 and rising to 3.5% in year 7. The real cost of capital is forecast to be 10.2% in year 1, rising to 11.9% in year 7. The tax rate is forecast to be a constant 38.0%. Sales revenue per unit is forecast to be \$12.20 in year 1 and then grow with inflation. Variable cost per unit is forecast to be \$7.30 in year 1 and then grow with inflation. Cash fixed costs are forecast to be \$6,740 in year 1 and then grow with inflation. What is the project NPV? What is the NPV Break-Even Point in Year 1 Unit Sales, where NPV equals zero? What is the NPV Break-Even Point in the Year 2 Sales Growth Rate, where NPV equals zero? What is the NPV Break-Even Contour in the two-dimensional space of Year 1 Unit Sales and Year 2 Sales Growth Rate?

Based On NPV (in thousands of \$) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Key Assumptions Sales Growth Rate 72.0% 60.0% 45.0% 27.0% 4.0% -25.0% Change in Sales Growth Rate -12.0% -15.0% -18.0% -23.0% -29.0% Inflation Rate 2.7% 2.8% 2.9% 3.0% 3.2% 3.4% 3.5% Real Cost of Capital 10.2% 10.5% 10.8% 11.1% 11.4% 11.7% 11.9% Tax Rate 38.0% 38.0% 38.0% 38.0% 38.0% 38.0% 38.0% Discounting Discount Rate = Cost of Capital 13.2% 13.6% 14.0% 14.4% 15.0% 15.5% 15.8% Cumulative Discount Factor 0.0% 13.2% 28.6% 46.6% 67.7% 92.8% 122.7% 157.9% Price or Cost / Unit Unit Sales 4,800 8256 13210 19154 24325 25298 18974 Sales Revenue / Unit \$12.20 \$12.54 \$12.91 \$13.29 \$13.72 \$14.18 \$14.68 Variable Cost / Unit \$7.30 \$7.50 \$7.72 \$7.95 \$8.21 \$8.49 \$8.78 Cash Fixed Costs \$6,740 \$6,929 \$7,130 \$7,344 \$7,579 \$7,836 \$8,110 Cash Flow Forecasts Sales Revenue \$58,560 \$103,543 \$170,474 \$254,603 \$333,693 \$358,840 \$278,549 Variable Costs \$35,040 \$61,956 \$102,005 \$152,344 \$199,669 \$214,716 \$166,673 Gross Margin \$23,520 \$41,587 \$68,469 \$102,259 \$134,024 \$144,124 \$111,876 Cash Fixed Costs \$6,740 \$6,929 \$7,130 \$7,344 \$7,579 \$7,836 \$8,110 Depreciation \$2,670 \$2,670 \$2,670 \$2,670 \$2,670 \$2,670 \$2,670 Total Fixed Costs \$9,410 \$9,599 \$9,800 \$10,014 \$10,249 \$10,506 \$10,780 Operating Profit \$14,110 \$31,988 \$58,669 \$92,245 \$123,776 \$133,618 \$101,096 Taxes \$5,362 \$12,156 \$22,294 \$35,053 \$47,035 \$50,775 \$38,416 Net Profit \$8,748 \$19,833 \$36,375 \$57,192 \$76,741 \$82,843 \$62,679 Add Back Depreciation \$2,670 \$2,670 \$2,670 \$2,670 \$2,670 \$2,670 \$2,670 Operating Cash Flow \$11,418 \$22,503 \$39,045 \$59,862 \$79,411 \$85,513 \$65,349 Investment in Plant & Equip (\$24,490) \$5,800 Cash Flows (\$24,490) \$11,418 \$22,503 \$39,045 \$59,862 \$79,411 \$85,513 \$71,149 Present Value of Each Cash Flow (\$24,490) \$10,089 \$17,504 \$26,638 \$35,689 \$41,181 \$38,396 \$27,583 Net Present Value \$172,590 By trial and error the Solver adjusts the value of the Year 1 Unit Sales in cell C16 until the Net P This results in a NPV Break-Even Point in Year 1 Unit Sales of 851. By trial and error the Solver adjusts the value of the Sales Growth Rate in cell D5 until the Net P Data Table: Sensitivity of Net Present Value to Year 1 Unit Sales and Year 2 Sales Growth Rate Output Formula: Input Values for Year 1 Unit Sales Net Present Value \$172,590 3,200 4,000 4,800 5,600 52.0% \$49,149 \$70,740 \$92,331 \$113,923 Input Values for Year 2 62.0% \$72,436 \$99,849 \$127,261 \$154,674 Sales Growth Rate 72.0% \$102,655 \$137,623 \$172,590 \$207,558 82.0% \$141,643 \$186,357 \$231,072 \$275,786 92.0% \$191,610 \$248,816 \$306,023 \$363,229 B REAK- E VEN A NALYSIS in Sales Growth Rate of -9.6% 52.0% 62.0% 72.0% 82.0% 92.0% \$0 \$50,000 \$100,000 \$150,000 \$200,000 \$250,000 \$300,000 \$350,000 \$400,000 3,200 4,000 4,800 5,600 NPV Break-Even Contour (Based On NPV = 0) Across Year 1 Unit Sales And Year 2 Sales Growth Rate Year 2 Sales Growth Rate Net Present Value Year 1 Unit Sales NPV Break-Even Contour

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BREAK-EVEN ANALYSIS Based On NPV (in thousands of \$)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Key Assumptions
Sales Growth Rate
Change in Sales Growth Rate
Inflation Rate
Real Cost...

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