We are evaluating a project that costs $710,000, has an thirteen-year life, and

Question

We are evaluating a project that costs $710,000, has an thirteen-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 98,000 units per year. Price per unit is $38, variable cost per unit is $21, and fixed costs are $718,520 per year. The tax rate is 34 percent, and we require a 19 percent return on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 12 percent.

Calculate the best-case NPV

Calculate the best-case NPV

Explanation / Answer

Solution:

a) We will use the tax shield approach in evaluating the OCF. For the best case scenario, we multiply the price and quantity numbers by 1.12 and cost by 0.88.

OCF = [(P – v)Q – FC] (1 – t) + tD

OCF = [($38 x 1.12 - $21 x 0.88) (98,000 x 1.12) - $718,520 x 0.88] (1- 0.34) + 0.34*(710,000/13)

OCF = 1,327,077 + 18,569.23

OCF = $1,345,647

Now, we calculate the NPV using base case projections. Therefore,

NPV = -710,000 + 1,345,647 (PVIFA @ 19%, 13)

NPV – 710,000 + 1,345,647 [(1.19^13-1)/ (0.19*1.19^13)]

NPV = -710,000 + 1,345,647 (4.714709)

NPV = $5,634,332

Hence, the best case NPV is $5,634,332.

b) We will use the tax shield approach in evaluating the OCF. For the worst case scenario, we multiply the price and quantity numbers by 0.88 and cost by 1.12.

OCF = [(P – v)Q – FC] (1 – t) + tD

OCF = [($38 x 0.88 - $21 x 1.12) (98,000 x 0.88) - $718,520 x 1.12] (1- 0.34) + 0.34*(710,000/13)

OCF = 33,500.54 + 18,569.23

OCF = $52,069.77

Now, we calculate the NPV using base case projections. Therefore,

NPV = -710,000 + 52,069.77 (PVIFA @ 19%, 13)

NPV – 710,000 + 52,069.77 [(1.19^13-1)/ (0.19*1.19^13)]

NPV = -710,000 + 52,069.77 (4.714709)

NPV = -$464,506

Hence, worst-case NPV is -$464,506

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