Question

We are evaluating a project that costs $788,400, has a nine-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 75,000 units per year. Price per unit is $52, variable cost per unit is $36, and fixed costs are $750,000 per year. The tax rate is 21 percent, and we require a return of 12 percent on this project. Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±15 percent. Calculate the best-case and worst-case NPV figures. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Initial Investment = Project cost = $788,400

Annual depreciation = (Cost - residual value) / useful life = (788400 - 0) / 9 = $87,600

Annual depreciation tax shield = 87600 * 21% = $18,396

BEST-CASE NPV:

Best-case will be when:

Price and Units per year will increase by 15% and

Variable cost and fixed cost will decrease by 15%.

Price = 52 *(1 + 15%) = $59.80

Units sold = 75000 * (1 + 15%) =86,250

Variable cost per unit = 36 * (1- 15%) = $30.60

Fixed cost = 750000 * (1 - 15%) = $637,500

Annual cash flow = ((59.80 - 30.60) * 86250 - 637500) * (1 - 21%) + 18396

= $1,504,386

NPV = 1504386 * (1 - 1 /(1+12%)^9)/12% - 788400 = $7,227,344.39

WORST-CASE NPV:

Worst-case will be when:

Price and Units per year will decrease by 15% and

Variable cost and fixed cost will increase by 15%.

Price = 52 *(1 - 15%) = $44.20

Units sold = 75000 * (1 - 15%) = 63750

Variable cost per unit = 36 * (1+ 15%) = $41.40

Fixed cost = 750000 * (1 + 15%) = $862,500

Annual cash flow = ((44.20 - 41.40) * 63750 - 862500) * (1 - 21%) + 18396

= - $521964

NPV = -521964 * (1 - 1 /(1+12%)^9)/12% - 788400 = -$3569554.57 or ($3569554.57)

Hence:

Best-case NPV = $7,227,344.39

Worst-case NPV = -$3,569,554.57