Question

You are considering a proposal to produce and market a new sluffing machine. The most likely outcomes for the project are as follows:

Expected sales: 115,000 units per year

Unit price: $220

Variable cost: $132

Fixed cost: $4,890,000

The project will last for 10 years and requires an initial investment of $16.70 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 30%, and the required rate of return is 12%.

However, you recognize that some of these estimates are subject to error. Sales could fall 30% below expectations for the life of the project and, if that happens, the unit price would probably be only $210. The good news is that fixed costs could be as low as $3,260,000, and variable costs would decline in proportion to sales.

a. What is project NPV if all variables are as expected?

NPV =

b. What is NPV in the worst-case scenario?

NPV =

Answer 1

Part a:
Calculation of Net Present value of the project if all variables are as expected
Particulars	0	1	2	3	4	5	6	7	8	9	10
Initial Investment
Investment (A)	-16700000
Operating Cash Flows
Sales Revenue (115,000 * $220)		25300000	25300000	25300000	25300000	25300000	25300000	25300000	25300000	25300000	25300000
Less: Variable Costs (115,000 * $132)		-15180000	-15180000	-15180000	-15180000	-15180000	-15180000	-15180000	-15180000	-15180000	-15180000
Less: Fixed Costs		-4890000	-4890000	-4890000	-4890000	-4890000	-4890000	-4890000	-4890000	-4890000	-4890000
Less: Depreciation ($16700000/10 years)		-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000
Profit Before Tax		3560000	3560000	3560000	3560000	3560000	3560000	3560000	3560000	3560000	3560000
Less: Tax@30%		-1068000	-1068000	-1068000	-1068000	-1068000	-1068000	-1068000	-1068000	-1068000	-1068000
Profit After Tax		2492000	2492000	2492000	2492000	2492000	2492000	2492000	2492000	2492000	2492000
Add back Depreciation		1670000	1670000	1670000	1670000	1670000	1670000	1670000	1670000	1670000	1670000
Net Operating Cash Flows (B)		4162000	4162000	4162000	4162000	4162000	4162000	4162000	4162000	4162000	4162000
Total Cash Flows (C = A+B)	-16700000	4162000	4162000	4162000	4162000	4162000	4162000	4162000	4162000	4162000	4162000
Discount Factor @12% (D) 1/(1+12%)^n n=0,1,2,3,4,5,6,7,8,9,10	1	0.89285714	0.79719388	0.71178025	0.63551808	0.56742686	0.50663112	0.45234922	0.40388323	0.36061002	0.32197324
Discounted Cash Flows (E = C*D)	-16700000	3716071.43	3317920.92	2962429.39	2645026.24	2361630.57	2108598.73	1882677.43	1680961.99	1500858.92	1340052.61
Net Present value	6816228.24
Net Present value of the project if all variables are as expected is $6,816,228.24
Part b:
Sale Units = 115000 units - Reduction in Units (30%) = 80,500 units
Calculation of Net Present value of Worst Case Scenario
Particulars	0	1	2	3	4	5	6	7	8	9	10
Initial Investment
Investment (A)	-16700000
Operating Cash Flows
Sales Revenue (80,500 * $210)		16905000	16905000	16905000	16905000	16905000	16905000	16905000	16905000	16905000	16905000
Less: Variable Costs (80,500 * $132)		-10626000	-10626000	-10626000	-10626000	-10626000	-10626000	-10626000	-10626000	-10626000	-10626000
Less: Fixed Costs		-3260000	-3260000	-3260000	-3260000	-3260000	-3260000	-3260000	-3260000	-3260000	-3260000
Less: Depreciation ($16700000/10 years)		-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000	-1670000
Profit Before Tax		1349000	1349000	1349000	1349000	1349000	1349000	1349000	1349000	1349000	1349000
Less: Tax@30%		-404700	-404700	-404700	-404700	-404700	-404700	-404700	-404700	-404700	-404700
Profit After Tax		944300	944300	944300	944300	944300	944300	944300	944300	944300	944300
Add back Depreciation		1670000	1670000	1670000	1670000	1670000	1670000	1670000	1670000	1670000	1670000
Net Operating Cash Flows (B)		2614300	2614300	2614300	2614300	2614300	2614300	2614300	2614300	2614300	2614300
Total Cash Flows (C = A+B)	-16700000	2614300	2614300	2614300	2614300	2614300	2614300	2614300	2614300	2614300	2614300
Discount Factor @12% (D) 1/(1+12%)^n n=0,1,2,3,4,5,6,7,8,9,10	1	0.89285714	0.79719388	0.71178025	0.63551808	0.56742686	0.50663112	0.45234922	0.40388323	0.36061002	0.32197324
Discounted Cash Flows (E = C*D)	-16700000	2334196.43	2084103.95	1860807.1	1661434.91	1483424.03	1324485.74	1182576.55	1055871.92	942742.788	841734.632
Net Present value	-1928621.9
Net Present value of the worst case scenario of the project is ($1,928,621.9)