Question

We are evaluating a project that costs $1,950,000, has a life of 7 years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 88,800 units per year. Price per unit is $38.49, variable cost per unit is $23.65, and fixed costs are $842,000 per year. The tax rate is 24 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 ±10 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.)

Question:

	OCF	NPV
best-case
worst-case

Answer 1

Net present value is calculated as present value of cash inflow less present value of cash outflow.
In case of best case scenario, sale price and quantity would increase by 10% while variable costs and fixed costs would decrease by 10%.
Calculation of Operating cash flow under best case
Depreciation per year	$278,571.43	(1950000/7)
Projected quantity sold	97,680.00	88800*1.1
Sales price per unit	42.34	38.49*1.1
Sales revenue	4,135,673.52	97680*42.34
Variable costs per unit	$21.29	(23.65*0.90)
Total variable costs	$2,079,118.80	97680*21.29
Fixed costs	$757,800.00	842000*0.90
Sales revenue	$4,135,673.52
Less: Variable costs	-$2,079,118.80
Less: Fixed costs	-$757,800.00
Less: Depreciation	-$278,571.43
Income before taxes	$1,020,183.29
Taxes @ 24%	-$244,843.99
Net income	$775,339.30
Add: Depreciation	$278,571.43
OCF	$1,053,910.73
Calculation of net present value is shown below
Year	Cash flow	Discount factor @ 12%	Present value
0	-$1,950,000.00	1.00000	-$1,950,000.00
1	$1,053,910.73	0.89286	$940,991.72
2	$1,053,910.73	0.79719	$840,171.18
3	$1,053,910.73	0.71178	$750,152.84
4	$1,053,910.73	0.63552	$669,779.32
5	$1,053,910.73	0.56743	$598,017.25
6	$1,053,910.73	0.50663	$533,943.97
7	$1,053,910.73	0.45235	$476,735.69
Net present value			$2,859,791.99
In case of worst case scenario, sale price and quantity would decrease by 10% while variable costs and fixed costs would increase by 10%.
Calculation of Operating cash flow under worst case
Depreciation per year	$278,571.43	(1950000/7)
Projected quantity sold	79,920.00	88800*0.9
Sales price per unit	34.64	38.49*0.9
Sales revenue	2,768,508.72	79920*34.64
Variable costs per unit	$26.02	(23.65*1.1)
Total variable costs	$2,079,118.80	79920*26.02
Fixed costs	$926,200.00	842000*1.1
Sales revenue	$2,768,508.72
Less: Variable costs	-$2,079,118.80
Less: Fixed costs	-$926,200.00
Less: Depreciation	-$278,571.43
Income before taxes	-$515,381.51
Taxes @ 24%	$123,691.56
Net income	-$391,689.95
Add: Depreciation	$278,571.43
OCF	-$113,118.52
Calculation of net present value is shown below
Year	Cash flow	Discount factor @ 12%	Present value
0	-$1,950,000.00	1.00000	-$1,950,000.00
1	-$113,118.52	0.89286	-$100,998.68
2	-$113,118.52	0.79719	-$90,177.39
3	-$113,118.52	0.71178	-$80,515.53
4	-$113,118.52	0.63552	-$71,888.86
5	-$113,118.52	0.56743	-$64,186.48
6	-$113,118.52	0.50663	-$57,309.36
7	-$113,118.52	0.45235	-$51,169.07
Net present value			-$2,466,245.38