Question

3. Consider a project with a 6-year life. The initial cost to set up the project is $1,200,000. This amount is to be linearly depreciated to zero over the life of the project. You expect to sell the equipment for $240,000 after 6 years. The project requires an initial investment in net working capital of $120,000, which will be recouped at the end of the project.

You estimated sales of 57,000 units per year at a price of $167 each. The variable cost per unit is estimated to be $133.6 and fixed costs are $240,000 per year.

You expect unit sales, prices, variable and fixed costs to be within 15% of your estimates.

The required return is 12% and the tax rate is 34%.

You expect unit sales, prices, variable and fixed costs to be within 15% of your estimates.

The required return is 13% and the tax rate is 34%.

1)What is the NPV in the base case?

2) What is the NPV in the pessimistic case?

3)What is the NPV in the optimistic case?

Answer 1

1) At first we calculate Initial outlay of the project

Initial outlay = Cost of the machine + Net working Capital

Hence initial outlay = 1200000 + 120000 = 1320000

Depreciation each year is 1200000/6=200000

Now let's calculate Cash flow after tax = (sales - Cost- Depreciation)*(1-t) + depreciation

= (9519000-7615200-240000-200000)(1-.34) + 200000

=1166108

Now let's calculate terminal cash flow= post tax salvage value + working capital

= 240000*.66+120000=278400

This terminal cash flow will be received at the end of 6 years

Now NPV = Cash inflow/(1+i)^t - initial outlay

i = 12% t= time period

Hence by applying the above formula we get NPV =3615391

2) Pessimistic Case( sales, variable cost and fixed cost be 15% less than the estimate)

Here only cash flow after tax will change, the rest i.e initial investment and terminal cash flow will remain same.

Therefore sales =9519000*.85=8091150

Variable cost =7615200*.85=6472920

Fixed cost = 240000*.85=204000

Cash flow after tax= (8091150-6472920-204000-200000)(1-.34)+200000=1001391

Hence by applying the above formula of NPV taking i= 12% we get NPV =$2938172

3) NPV in optimistic case( sales ,variable cost and fixed cost will be 15% more than the estimate)

Here also only cash flow after tax will change and rest will remail same

Sales =9519000*1.15= 10946850

Variable cost =7615200*1.15= 8757480

Fixed cost = 240000*1.15=276000

Hence cash flow after tax = (10946850-8757480-276000-200000)(1-.34)+200000 = 1330824

Hence by applying the above formula for NPV(taking i= 12%) we get NPV =$4292606