Question

The most likely outcomes for a particular project are estimated as follows:

Unit price: $ 70

Variable cost: $ 50

Fixed cost: $ 300,000

Expected sales: 40,000 units per year

However, you recognize that some of these estimates are subject to error. Suppose that each variable may turn out to be either 10% higher or 10% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $2.2 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%

. a. What is project NPV in the best-case scenario, that is, assuming all variables take on the best possible value? (A negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

b. What is project NPV in the worst-case scenario? (A negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

Answer 1

First lets find out the values of unit sales, sales price, variable cost and Fixed price in best and worst case scenario

		Best case	Worst Case
Sales	40000	44000	36000
Unit price	70	77	63
Variable cost	50	45	55
Fixed Cost	300000	270000	330000

In best case sales price and Unit price will increase by 10% and variable and fix will reduce by 10%

in worst case scenario Sales price and unit price will decrease by 10% and variable and fix will increase by 10%

Present value formula = cash flow/(1+discount rate)^(no of years)

Best case scenario

	Year	0	1	2	3	4	5	6	7	8	9	10
Initial Investment		-2200000
Revenue			3388000	3388000	3388000	3388000	3388000	3388000	3388000	3388000	3388000	3388000
Variable cost			1980000	1980000	1980000	1980000	1980000	1980000	1980000	1980000	1980000	1980000
Fixed Cost			270000	270000	270000	270000	270000	270000	270000	270000	270000	270000
Net income			1138000	1138000	1138000	1138000	1138000	1138000	1138000	1138000	1138000	1138000
Depreciation amount			220000	220000	220000	220000	220000	220000	220000	220000	220000	220000
Taxable Income			918000	918000	918000	918000	918000	918000	918000	918000	918000	918000
after Tax income (0.7*Income after dep.)			642600	642600	642600	642600	642600	642600	642600	642600	642600	642600
Add back dep. (Cash flow)			862600	862600	862600	862600	862600	862600	862600	862600	862600	862600
Present value		-2200000	770178.571	687659.4	613981.6	548197.9	489462.4	437020	390196.4	348389.7	311062.2	277734.1
NPV (Sum of present values)		2673882

Worst case Scenario:

	Year	0	1	2	3	4	5	6	7	8	9	10
Initial Investment		-2200000
Revenue			2268000	2268000	2268000	2268000	2268000	2268000	2268000	2268000	2268000	2268000
Variable cost			1980000	1980000	1980000	1980000	1980000	1980000	1980000	1980000	1980000	1980000
Fixed Cost			330000	330000	330000	330000	330000	330000	330000	330000	330000	330000
Net income			-42000	-42000	-42000	-42000	-42000	-42000	-42000	-42000	-42000	-42000
Depreciation amount			220000	220000	220000	220000	220000	220000	220000	220000	220000	220000
Taxable Income			0	0	0	0	0	0	0	0	0	0
Add back dep. (Cash flow)			178000	178000	178000	178000	178000	178000	178000	178000	178000	178000
Present value		-2200000	158928.571	141900.5	126696.9	113122.2	101002	90180.34	80518.16	71891.21	64188.58	57311.24
NPV (Sum of present values)		-1194260