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: 100,000 units per year

Unit price: $190

Variable cost: $114

Fixed cost: $4,080,000

The project will last for 10 years and requires an initial investment of $11.28 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 $180. The good news is that fixed costs could be as low as $2,720,000, and variable costs would decline in proportion to sales.

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

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

Answer 1

a ) If all variables remains are as expected than NPV is

Particulars	1	2	3	4	5	6	7	8	9	10	Total
Selling price per unit	190	190	190	190	190	190	190	190	190	190
Less: Variable cost per unit	114	114	114	114	114	114	114	114	114	114
Contribution per unit	76	76	76	76	76	76	76	76	76	76
Units sold	100000	100000	100000	100000	100000	100000	100000	100000	100000	100000
Total Contribution	7600000	7600000	7600000	7600000	7600000	7600000	7600000	7600000	7600000	7600000
Less:
Fixed Cost	4080000	4080000	4080000	4080000	4080000	4080000	4080000	4080000	4080000	4080000
Depreciation	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000
PBT	2392000	2392000	2392000	2392000	2392000	2392000	2392000	2392000	2392000	2392000
Tax @ 30%	717600	717600	717600	717600	717600	717600	717600	717600	717600	717600
PAT	1674400	1674400	1674400	1674400	1674400	1674400	1674400	1674400	1674400	1674400
Add: Depreciation	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000
Annual cash flow	2802400	2802400	2802400	2802400	2802400	2802400	2802400	2802400	2802400	2802400
PVIF @ 12%	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066	0.4523	0.4039	0.3606	0.3220
Present Value	2502143	2234056	1994693	1780976	1590157	1419783	1267663	1131842	1010574	902298	15834185
Less : Initial Investment											11280000
NPV											4554185

b)Statement showing worst case NPV

Particulars	1	2	3	4	5	6	7	8	9	10	Total
Selling price per unit	180	180	180	180	180	180	180	180	180	180
Less: Variable cost per unt (Note 1)	108	108	108	108	108	108	108	108	108	108
Contribution per unit	72	72	72	72	72	72	72	72	72	72
Units sold	70000	70000	70000	70000	70000	70000	70000	70000	70000	70000
Total Contribution	5040000	5040000	5040000	5040000	5040000	5040000	5040000	5040000	5040000	5040000
Less:
Fixed Cost	2720000	2720000	2720000	2720000	2720000	2720000	2720000	2720000	2720000	2720000
Depreciation	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000
PBT	1192000	1192000	1192000	1192000	1192000	1192000	1192000	1192000	1192000	1192000
Tax @ 30%	357600	357600	357600	357600	357600	357600	357600	357600	357600	357600
PAT	834400	834400	834400	834400	834400	834400	834400	834400	834400	834400
Add: Depreciation	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000	1128000
Annual cash flow	1962400	1962400	1962400	1962400	1962400	1962400	1962400	1962400	1962400	1962400
PVIF @ 12%	0.8929	0.7972	0.7118	0.6355	0.5674	0.5066	0.4523	0.4039	0.3606	0.3220
Present Value	1752143	1564413	1396798	1247141	1113518	994213	887690	792580	707661	631840	11087998
Less : Initial Investment											11280000
NPV											-192002

Note 1)
Decrease in Sales = (190-180)/190
=10/190
=5.2632%
Variable cost = 114-5.2632%(114)
=108