Question

We are evaluating a project that costs $982,000, has a life of eight years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 113,000 units per year. Price per unit is $37, variable cost per unit is $21, and fixed costs are $1,000,658 per year. The tax rate is 24 percent, and we require a return of 13 percent on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 16 percent.

  

a. Calculate the best-case NPV.

  

b. Calculate the worst-case NPV.

Answer 1

Cost of Project = $982,000
Salvage Value = 0
No of Years = 8

Annual Depreciation = (Cost of Project – Salvage Value)/No of Years
                                = (982,000 – 0) / 8
                           =$122,750

a. Best case NPV. (Highest Sales Quantity, Highest Selling price per unit, lowest variable cost per unit and lowest fixed costs)
Sales Quantity = 113,000 * 1.16 = 131,080
Selling price per unit = $37 * 1.16 = $42.92
Variable cost per unit = $21 * 0.84 = $17.64
Fixed Costs = $1,000,658 * 0.84 = $840,552.72

NPV = PV of Cash Inflows - Initial Cash Outflow
Since the annual cash flows are same we can use Present Value annuity factor instead of Present Value Factor.

Calculation of PV of Cash Inflows :

PARTICULARS	Year	1 to 8
SALES		5625953.6
VARIABLE COST		2312251.2
FIXED COST		840552.72
DEPRECIATION		122750
INCREMENTAL EBIT		2350399.68
INCOME TAX @24%		564095.92
UNLEVERED NET INCOME		1786303.76
ADD : DEPRECIATION		122750.00
POUND FREE CASH FLOW		1909053.76
PVAF (13%,8)		4.79877029
PRESENT VALUE @13%		9161110.45

Best Case NPV = $9,161,110.45 - $982,000
                          = $8,179,110.45

b. Worst case NPV. (Lowest Sales Quantity, Lowest Selling price per unit, Highest variable cost per unit and Highest fixed costs)
Sales Quantity = 113,000 * 0.84 = 94,920
Selling price per unit = $37 * 0.84 = $31.08
Variable cost per unit = $21 * 1.16 = $24.36
Fixed Costs = $1,000,658 * 1.16 = $1,160,763.28

NPV = PV of Cash Inflows - Initial Cash Outflow

Calculation of PV of Cash Inflows :

PARTICULARS	Year	1 to 8
SALES		2950113.6
VARIABLE COST		2312251.2
FIXED COST		1160763.28
DEPRECIATION		122750
INCREMENTAL EBIT		-645650.88
INCOME TAX @24%		-154956.21
UNLEVERED NET INCOME		-490694.67
ADD : DEPRECIATION		122750.00
POUND FREE CASH FLOW		-367944.67
PVAF (13%,8)		4.79877029
PRESENT VALUE @13%		-1765681.95

Worst Case NPV = -$1,765,681.95 - $982,000
= -$2,747,681.95

NOTE : Present Value Factor have been calculated as = (1/1+r)n

Where
r= Required rate of Return (Discount rate)
n= No of Periods

PVAF (13%,8) is calculated by adding the PV Factor of 13% for 8 years.