Question

You are considering a new product launch. The project will cost $920,000, have a 5-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 310 units per year; price per unit will be $15,915, variable cost per unit will be $11,800, and fixed costs will be $605,000 per year. The required return on the project is 10 percent and the relevant tax rate is 24 percent. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent.

a. What are the best-case and worst-case NPVs with these projections?

b. What is the base-case NPV?

c. What is the sensitivity of your base-case NPV to changes in fixed costs?

Answer 1

a)

best case NPV:

projected sales units = 310

since we are doing best case scenario we should add 10%

sales under best case = 310 + 10% = 341

variable cost = 11800 - 10% = $10,620

fixed costs = 605,000 - 10% = 544,500

sale price = 15915 (there is no change in price)

tax rate = 24%

depreciation = 920,000 / 5 = $184,000

operating cash flow = [(sale price - variable cost) * number of units - fixed costs - depreciation](1-tax) +depreciation

operating cash flow = [(15915 - 10620) * 341 - 544,500 - 184,000](1 - 0.24) + 184,000

= 1002592.2

require return(r) = 10%

number of years(n)= 5%

PVIFA(n = 5 ; r = 10 ) = 3.7908

present value of cash flows = 1002592.2 * 3.7908

= 3800626.51

out flow = $920,000

NPV = 3800626.51 - 920,000

= 2880626.51

worst case NPV:

projected sales units = 310

under worst case = 310 - 10% = 279

variable cost = 11800 + 10% = 12980

fixed cost = 605,000 + 10% = 665,500

sales price = 15,915 (no change in sales price)

tax rate = 24%

depreciation = 920,000 / 5 = 184,000

operating cash flow = [(sale price - variable cost) * number of units - fixed costs - depreciation](1-tax) +depreciation

operating cash flow = [(15915 - 12980) * 279 - 665,500 - 184,000](1 - 0.24) + 184,000

= $160,717.4

require return(r) = 10%

number of years(n)= 5%

PVIFA(n = 5 ; r = 10 ) = 3.7908

present value of cash flows = 160,717.4 * 3.7908

= $609,247.52

NPV = 609,247.52 - 920,000

= - 310,752.48

b) base case NPV:

sales units = 310

selling price = 15915

variable cost = 11800

fixed cost = 605,000

depreciation = 184,000

tax rate = 24%

operating cash flow = [(sale price - variable cost) * number of units - fixed costs - depreciation](1-tax) +depreciation

operating cash flow = [(15915 - 11800) * 310 - 605,000 - 184,000](1- 0.24) + 184,000

operating cash flow = 553,854

PVIFA(n = 5 ; r = 10 ) = 3.7908

present value of cash flows = 553,854 * 3.7908

= $2099549.74

outflow = 920,000

NPV = 2099549.74 - 920,000 = 1179549.74

c) sensitivity:

to calculate sensitivity of NPV to changes in fixed costs we have to choose another value of fixed cost lets just assume fixed cost is 650,000 instead of 605,000

operating cash flow = [(sale price - variable cost) * number of units - fixed costs - depreciation](1-tax) +depreciation

operating cash flow = [(15915 - 11800) * 310 - 650,000 - 184,000](1- 0.24) + 184,000

= $519,654

PVIFA(n = 5 ; r = 10 ) = 3.7908

present value of cash flows = 519,654 * 3.7908

= $1969904.38

sensitivity of NPV = change in NPV / change in fixed costs

= (2099549.74 - 1969904.38) / (650,000 - 605,000)

= 129645.36 / 45,000

  = $2.88

for every dollar of increase in fixed costs NPV falls by 2.88