We are evaluating a project that costs $1,100,000, has a ten-year life, and has

Question

We are evaluating a project that costs $1,100,000, has a ten-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 42,000 units per year. Price per unit is $50, variable cost per unit is $25, and fixed costs are $820,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.

Calculate the best-case and worst-case NPV figures.

We are evaluating a project that costs $1,100,000, has a ten-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 42,000 units per year. Price per unit is $50, variable cost per unit is $25, and fixed costs are $820,000 per year. The tax rate is 35 percent, and we require a return of 10 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent.

Explanation / Answer

Annual depreciation = (cost of asset – salvage value)/ Life

                                        = (1,100,000 – 0)/10

                                        = 110,000

Depreciation tax shield = Annual depreciation x tax rate

                                                = 110,000x 35%

                                                = 38,500

Base Case

Best Case

Worst case

Sales

42000

46200

37800

Price

50

55

45

Variable cost

25

22.5

27.5

Fixed cost

820000

738000

902000

Base Case

Best Case

Worst case

Sales revenue

2100000

2541000

1701000

Total variable cost

-1050000

-1039500

-1039500

Fixed cost

-820000

-738000

-902000

EBIT

230000

763500

-240500

Taxes 35%

-80500

-267225

84175

Net Income

149500

496275

-156325

Depreciation tax shield

38500

38500

38500

Operating cash flow

188000

534775

-117825

PV of annuity factor 10%

6.1446

6.1446

6.1446

PV= PV factor x OCF

$1,155,178.62

$3,285,960.87

-$723,983.62

NPV = PV of OCF – initial cash outflow

NPV best case = $1,155,178.62-1,100,000

                                = $55,178.62

Worst case NPV= -$723,983.62- 1,100,000

                                = -$1,823,983.62

Base Case

Best Case

Worst case

Sales

42000

46200

37800

Price

50

55

45

Variable cost

25

22.5

27.5

Fixed cost

820000

738000

902000

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