Question

We are evaluating a project that costs $520,000, has a six-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 65,000 units per year. Price per unit is $45, variable cost per unit is $30, and fixed costs are $840,000 per year. The tax rate is 35 percent, and we require a return of 10 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.)
a. Best-case $584,621, worst case $ –$285,079 b. Best-case $2,026,176.65, worst case $ –$1,761,593.58 c. Best-case $88,832.77, worst case –$1,510,000 d. None of the above

When I calculated it myself I got :

worst case -$1,761,594.09

best case $2,026,176.14

If you notice it is very close to answer b so I am asking you to calculate it to see if you get a different answer than I did, or am I correct? Thank you

Answer 1

First we calculate the CF for each scenario:

			Base Case	Best Case	Worst Case
Particular	Remark	Year 0	Year 1-6	Year 1-6	Year 1-6
Units	Given		$         65,000.00	$       71,500.00	$         58,500.00
SP	Given		$                 45.00	$                49.50	$                 40.50
Sales	Sp x Units		$   29,25,000.00	$ 35,39,250.00	$   23,69,250.00
VC	Given		$                 30.00	$                27.00	$                 33.00
Total VC	Vc x Units		$   19,50,000.00	$ 19,30,500.00	$   19,30,500.00
Fixed cost	Given		$     8,40,000.00	$    7,56,000.00	$     9,24,000.00
EBITDA	Sale-Total VC-Fixed Cost		$     1,35,000.00	$    8,52,750.00	$    -4,85,250.00
Depreciation	520000/6		$         86,666.67	$       86,666.67	$         86,666.67
EBIT	EBITDA-Depreciation		$         48,333.33	$    7,66,083.33	$    -5,71,916.67
tax	0.35 x EBIT		$         16,916.67	$    2,68,129.17	$    -2,00,170.83
EAT	EBIT-tax		$         31,416.67	$    4,97,954.17	$    -3,71,745.83
Depreciation	Added Back as non cash		$         86,666.67	$       86,666.67	$         86,666.67
OCF	EAT+Depreciation		$     1,18,083.33	$    5,84,620.83	$    -2,85,079.17
Investment	Given	$ -5,20,000.00
CF		$ -5,20,000.00	$ 1,18,083.33	$ 5,84,620.83	$ -2,85,079.17

• Base cases figures are given
• In best case, the Price and quantity will increase by 10% of base case scenario and VC and FC will go down by 10%
• In worst case, the Price and quantity will fall by 10% of base case scenario and VC and FC will go up by 10%

Now we will calculate the NPV of each scenario:

Base case:

Year	CF	Discount Factor		Discounted CF
0	$     -5,20,000.00	1/(1+0.1)^0=	1	1*-520000=	$       -5,20,000.00
1	$       1,18,083.33	1/(1+0.1)^1=	0.909090909	0.909090909090909*118083.333333333=	$        1,07,348.48
1	$       1,18,083.33	1/(1+0.1)^1=	0.909090909	0.909090909090909*118083.333333333=	$        1,07,348.48
3	$       1,18,083.33	1/(1+0.1)^3=	0.751314801	0.751314800901578*118083.333333333=	$            88,717.76
4	$       1,18,083.33	1/(1+0.1)^4=	0.683013455	0.683013455365071*118083.333333333=	$            80,652.51
5	$       1,18,083.33	1/(1+0.1)^5=	0.620921323	0.620921323059155*118083.333333333=	$            73,320.46
6	$       1,18,083.33	1/(1+0.1)^6=	0.56447393	0.564473930053777*118083.333333333=	$            66,654.96
				NPV = Sum of all Discounted CF	$              4,042.65

Best case:

Year	CF	Discount Factor		Discounted CF
0	$     -5,20,000.00	1/(1+0.1)^0=	1	1*-520000=	$       -5,20,000.00
1	$       5,84,620.83	1/(1+0.1)^1=	0.909090909	0.909090909090909*584620.833333334=	$        5,31,473.48
1	$       5,84,620.83	1/(1+0.1)^1=	0.909090909	0.909090909090909*584620.833333334=	$        5,31,473.48
3	$       5,84,620.83	1/(1+0.1)^3=	0.751314801	0.751314800901578*584620.833333334=	$        4,39,234.28
4	$       5,84,620.83	1/(1+0.1)^4=	0.683013455	0.683013455365071*584620.833333334=	$        3,99,303.90
5	$       5,84,620.83	1/(1+0.1)^5=	0.620921323	0.620921323059155*584620.833333334=	$        3,63,003.54
6	$       5,84,620.83	1/(1+0.1)^6=	0.56447393	0.564473930053777*584620.833333334=	$        3,30,003.22
				NPV = Sum of all Discounted CF	$      20,74,491.91

Worst Case:

Year	CF	Discount Factor		Discounted CF
0	$     -5,20,000.00	1/(1+0.1)^0=	1	1*-520000=	$       -5,20,000.00
1	$     -2,85,079.17	1/(1+0.1)^1=	0.909090909	0.909090909090909*-285079.166666667=	$       -2,59,162.88
1	$     -2,85,079.17	1/(1+0.1)^1=	0.909090909	0.909090909090909*-285079.166666667=	$       -2,59,162.88
3	$     -2,85,079.17	1/(1+0.1)^3=	0.751314801	0.751314800901578*-285079.166666667=	$       -2,14,184.20
4	$     -2,85,079.17	1/(1+0.1)^4=	0.683013455	0.683013455365071*-285079.166666667=	$       -1,94,712.91
5	$     -2,85,079.17	1/(1+0.1)^5=	0.620921323	0.620921323059155*-285079.166666667=	$       -1,77,011.73
6	$     -2,85,079.17	1/(1+0.1)^6=	0.56447393	0.564473930053777*-285079.166666667=	$       -1,60,919.76
				NPV = Sum of all Discounted CF	$    -17,85,154.35

So the correct answer is none of the above