Question

We are evaluating a project that costs $972,000, has a life of twelve years, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 117,000 units per year. Price per unit is $35, variable cost per unit is $25, and fixed costs are $989,496 per year. The tax rate is 22 percent, and we require a return of 21 percent on this project. The projections given for price, quantity, variable costs, and fixed costs are all accurate to within +/- 11 percent. a. Calculate the best-case NPV. b. Calculate the worst-case NPV.

Answer 1

a. Best Case NPV -

Preparing a proforma Income statement using details available

Particulars	Best Case
Sales (Units)	129,870
Selling Price	39
Total Sales	5,045,450
VC per unit	22
Total VC	2,889,608
Fixed Cost	880,651
Depreciation	81,000
EBIT	1,194,191
Tax	262,722
Net Income	931,469

Sales quantity = 117,000 (1+11%) = 129,870units

Price = 35 (1+11%) = $38.85 /unit

Variable cost per unit = 25(1-11%) = $22.25/unit

Fixed cost = 989,496 (1-11%) = $880,651

Operating Cash profit = EBIT + Depreciatio - tax = 1,194,191 + 81,000 – 262,722= $1,012,469

Year   Cash Flow (a)   PV factor (b)       Present Value (a/b)
0   -972,000.00   1.21^0 =    1.0000   -972,000
1   1,012,469.00   1.21^1 =   1.2100   836,751
2   1,012,469.00   1.21^2 =   1.4641   691,530
3   1,012,469.00   1.21^3 =   1.7716   571,512
4   1,012,469.00   1.21^4=   2.1436   472,324
5   1,012,469.00   1.21^5 =   2.5937   390,351
6   1,012,469.00   1.21^6 =   3.1384   322,604
7   1,012,469.00   1.21^7 =   3.7975   266,615
8   1,012,469.00   1.21^8 =   4.5950   220,343
9   1,012,469.00   1.21^9 =   5.5599   182,101
10   1,012,469.00   1.21^10 = 6.7275   150,497
11   1,012,469.00   1.21^11 = 8.1403   124,378
12   1,012,469.00   1.21^12 = 9.8497   102,792

NPV = Cash outflow - PV of cash inflow = $ 3,359,798

b) Worst case NPV

Preparing a proforma Income statement using details available

Particulars	Worst Case
Sales (Units)	104,130
Selling Price	31
Total Sales	3,243,650
VC per unit	28
Total VC	2,889,608
Fixed Cost	1,098,341
Depreciation	81,000
EBIT	-825,299
Tax	-181,566
Net Income	-643,733

Sales quantity = 117,000 (1-11%) = 104,130 units

Price = 35 (1-11%) = $31 /unit

Variable cost per unit = 25(1+11%) = $28/unit

Fixed cost = 989,496 (1+11%) = $1,098,341

Year   Cash Flow (a)   PV factor (b)       Present Value (a/b)
0   -972,000.00   1.21^0 =    1.0000   -972,000
1   -562,733.00   1.21^1 =   1.2100   -465,069
2   -562,733.00   1.21^2 =   1.4641   -384,354
3   -562,733.00   1.21^3 =   1.7716   -317,648
4   -562,733.00   1.21^4=   2.1436   -262,519
5   -562,733.00   1.21^5 =   2.5937   -216,958
6   -562,733.00   1.21^6 =   3.1384   -179,304
7   -562,733.00   1.21^7 =   3.7975   -148,185
8   -562,733.00   1.21^8 =   4.5950   -122,467
9   -562,733.00   1.21^9 =   5.5599   -101,212
10   -562,733.00  1.21^10 =  6.7275   -83,647
11   -562,733.00  1.21^11 =  8.1403   -69,129
12   -562,733.00  1.21^12 =  9.8497   -57,132

NPV = Cash outflow - PV of cash inflow = $ (3,379,625)

Best Case NPV = $ 3,359,798

Worst Case NPV = $ (3,379,625)