Question

You are considering a new product launch. The project will cost $857,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 180 units per year; price per unit will be $19,200, variable cost per unit will be $15,100, and fixed costs will be $345,000 per year. The required return on the project is 11 percent, and the relevant tax rate is 34 percent. Requirement 1: Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±5 percent.

(a) What are the best and worst case NPVs with these projections? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places (e.g., 32.16).)

(b) What is the base-case NPV? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Requirement 2: What is the sensitivity of the NPV to changes in fixed costs?

Answer 1

Requirement 1 :

For analyzing the accuracy of project given figures in the question, we have to first analyse the present value of future cash inflows that the project would generate with respect to the required rate of return that is expected with the project.

Given in the question :

Project Cost is $857,000

Life of the project is 4 years

Salvage value is Zero

Projected Sales is 180 units per year

Projected Sales price is $19,200 per unit

Projected Variable cost is $15,100 per unit

Projected Fixed cost is $345,000 per year

Required rate of return is 11%

Relevant Tax rate is 34%

Calculation of Cash Inflows per year

Particulars	Working	Total Amount
Sales	180 units @ $19,200 p.u.	$3,456,000
Less :-
Variable Cost	180 units @ $15,100 p.u.	-$2,718,000
Fixed Cost		-$345,000
Cash Inflows before Tax		$393,000
Less :- Tax	34% on $393,000	-$133,620
Cash Inflows after Tax		$259,380

Note : Cash Inflows are only the cash profits that an entity earns, hence it does not include the Depreciation charge because depreciation is a non cash expense. In case when the depreciation charge is other than that of straight-line then it is first deducted to calculate the correct tax figures and thereafter it will be added back up to find the cash profits.

Computation of Present Value of Cash Inflows

Year(s)	Particulars	Amount (a)	Present Value Factor @ 11% (b)	Present Value Amount x (b)
1 to 4	Cash Inflows after Tax	$259,380	3.1024	$804,700.51

Now, The present value of cash inflows calculated above shall be compared with the project cost of $857,000 to compute the accuracy of the projected sales and cost figures.

Therefore, Cash inflows are approximately 94% of Cash outflows at present day and hence the unit sales, variable costs and fixed cost projections given in the question are not accurate to within +/-5 percent.

Net Present Value can be calculated by subtracting cash outflows from cash inflows and hence the NPV in the given question will be -$52,299.49 that is the base-case NPV.

The best and worst case NPVs can be calculated with the probability of accruing the given cash inflows in the given scenario.

Requirement 2 :

Sensitivity of the NPV to change in a factor of cost can be calculated while considering that we have achieved the required rate of return i.e. NPV comes to zero. In the given case NPV has reached to a negative figure, therefore we have to first assume that NPV is zero for sensitivity analysis.

Change in Fixed Cost = Fixed cost after Tax adjustment

                                    = $345,000 * 66%

                                    = $227,700

Hence Percentage Sensitivity of NPV to Fixed cost = $227,700/$857,000

                                                                                  = 26.57%