We are evaluating a project that costs $927,000, has an fourteen-year life, and

Question

We are evaluating a project that costs $927,000, has an fourteen-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 143,000 units per year. Price per unit is $36, variable cost per unit is $25, and fixed costs are $936,270 per year. The tax rate is 33 percent, and we require a 17 percent return on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 15 percent.

  

(Click to select)

$8,008,838

$7,608,396

$7,024,734

$8,409,280

$2,703,444

(Click to select)

$8,409,280

$2,703,444

$152,293

$-3,041,704

$-3,797,279

We are evaluating a project that costs $927,000, has an fourteen-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 143,000 units per year. Price per unit is $36, variable cost per unit is $25, and fixed costs are $936,270 per year. The tax rate is 33 percent, and we require a 17 percent return on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 15 percent.

Explanation / Answer

(a) Computation of the best-case NPV.We have,

Sales price = 36( 1 + 0.15) = $ 41.40

Quantity = 143,000 (1 + 0.15) = 164,450

Variable cost = 25 ( 1 - 0.15) = $ 21.25

Fixed Cost = 936,270 (1 - .15) = $ 795,830

Depeciation(Straight line basis) = 927,000 / 14 = $ 66,214

Step1: Computation of free-cash inflow for the project.We have,

Step2: Computation of NPV.We have,

NPV = Present value of cash inflow - Cash outflow

NPV = ( 1,708,802 x PVIFA(17%, 14 year)) - 927,000

NPV = ( 1,708,802 x 5.22929906) - 927,000

NPV = 8,935,338 - 927,000 = $ 8,008,338

Hence, the best-case NPV is $ 8,008,338.

(b) Computation of the worst-case NPV.We have,

Sales price = 36( 1 - 0.15) = $ 30.60

Quantity = 143,000 (1 - 0.15) = 121,550

Variable cost = 25 ( 1 + 0.15) = $ 28.75

Fixed Cost = 936,270 (1 +.15) = $ 1,076,711

Depeciation(Straight line basis) = 927,000 / 14 = $ 66,214

Step1: Computation of free-cash inflow for the project.We have,

Step2: Computation of NPV.We have,

NPV = Present value of cash inflow - Cash outflow

NPV = ( 1,708,802 x PVIFA(17%, 14 year)) - 927,000

NPV = ( - 548,885 x 5.22929906) - 927,000

NPV = -2,870,279 - 927,000 = - $ 3,797,279

Hence, the best-case NPV is - $ 3,797,279.

Particulars Amount in $ Sales price 41.40 Less: Variable cost 21.25 Contribution 20.15 Contribution for whole units 164,450 x 20.15 3,313,668 Less: Fixed cost 795,830 Less: Depreciation 66,214 Profit before tax 2,451,624 Less: Tax@ 33% 2,451,624 x 33% 809,036 Profit after tax 1,642,588 Add: depreciation 66,214 Free cash flow for project $ 1,708,802

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