Question

We are evaluating a project that costs $1,160,000, 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 44,000 units per year. Price per unit is $45, variable cost per unit is $20, and fixed costs are $645,000 per year. The tax rate is 35 percent, and we require a return of 20 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.

Answer 1

We first need to find the depreciation for each year. The depreciation is:

Depreciation = $1,160,000/10

Depreciation = $116,000 per year

We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. For thebest-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so wewill multiply the base case numbers by 0.9, a 10 percent decrease. Doing so, we get:

OCF_best= {[($45)(1.1) – ($20)(0.9)](44,000)(1.1) – $1,160,000(0.9)}(0.65) + 0.35($116,000)

OCF_best= $352,990.00

The best-case NPV is:

NPV_best= –$1,160,000 + $352,990.00(PVIFA_20%,10)

NPV_best= –$1,160,000 + $352,990.00*4.1925

NPV_best= $319,910.575

For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by 0.9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent,so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get:

OCF_worst= {[($45)(0.9) – ($20)(1.1)](44,000)(0.9) – $1,160,000(1.1)}(0.65) + 0.35($116,000)

OCF_worst= -$312,610

The worst-case NPV is:

NPV_worst= –$1,160,000 – $312,610.00(PVIFA20%,10)

NPV_worst= –$1,160,000 – $312,610.00*4.1925

NPV_worst= -$2,470,617.425