Question

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

Unit price: $ 80

Variable cost: $ 60

Fixed cost: $ 440,000

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 5% higher or 5% lower than the initial estimate. The project will last for 10 years and requires an initial investment of $1.1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 21% and the required rate of return is 14%.

(For all the requirements, 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?

Answer 1

In the worst case scenario the unit price and expected sales will be 5% lower and variable cost and fixed cost will be 5% higher.

Annual depreciation = $1.1 million/10 years = $0.11 million per year

Then the cash flows will be:

Sales = 40,000 units * (1-0.05) * $80 unit price * (1-0.05)

= 38,000 units * $76

= $2,888,000

Variable cost = 38,000 units * $60 * (1+0.05) = $2,166,000

Fixed costs = $440,000*(1+0.05) = $462,000

Now operating cash flow = EBIT + Depreciation - Tax

a	b	c	d	e	f	g = c - d - e - f	h	I = g + f - h
Year	Initial investment	Sales	Variable costs	Fixed costs	Depreciation	EBIT	Tax = 21% of EBIT	Operating cash flow
0	- 1,100,000
1		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
2		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
3		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
4		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
5		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
6		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
7		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
8		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
9		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500
10		2,888,000	2,166,000	462,000	110,000	150,000	31,500	228,500

Using the operating cash flow we can compute the NPV:

Year (t)	Initial investment	Operating cash flow	1+r	PV = operating cash flow/(1+r)^t
0	- 1,100,000		1.14	- 1,100,000.00
1		228,500.00		200,438.60
2		228,500.00		175,823.33
3		228,500.00		154,230.99
4		228,500.00		135,290.34
5		228,500.00		118,675.74
6		228,500.00		104,101.53
7		228,500.00		91,317.13
8		228,500.00		80,102.74
9		228,500.00		70,265.56
10		228,500.00		61,636.46
			NPV	91,882.43

Thus NPV = $91,882.43 in the worst case scenario.