We are evaluating a project that costs $1,160,000, has a five-year life, and has

Question

We are evaluating a project that costs $1,160,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 87,700 units per year. Price per unit is $34.60, variable cost per unit is $20.85, and fixed costs are $757,000 per year. The tax rate is 30 percent, and we require a return of 10 percent on this project.

Required: Suppose the projections given for price, quantity, variable costs, and fixed costs are all accurate to within ±10 percent. Calculate the best-case and worst-case NPV figures. (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).)

BEST CASE?

WORST CASE?

Explanation / Answer

NPV is the difference between the present value of cash inflows and cash outflows. The formula for calculating NPV is given below:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3 + Cash Flow Year 4/(1+Discount Rate)^4 + Cash Flow Year 5/(1+Discount Rate)^5

__________

Step 1: Determine Cash Flow Under Each Scenario

Best Case:

In case of best case scenario, price and quantity will increase by 10%, while variable costs and fixed costs will decrease by 10%.

_______

Worst Case:

In case of worst case scenario, price and quantity will decrease by 10%, while variable costs and fixed costs will increase by 10%.

__________

Step 2: Determine NPV Under Each Scenario

Best Case:

NPV = -1,160,000 + 895,662.055/(1+10%)^1 + 895,662.055/(1+10%)^2 + 895,662.055/(1+10%)^3 + 895,662.055/(1+10%)^4 + 895,662.055/(1+10%)^5 = $2,235,263.87

_______

Worst Case:

NPV = -1,160,000 -59,955.545/(1+10%)^1 - 59,955.545/(1+10%)^2 - 59,955.545/(1+10%)^3 -59,955.545/(1+10%)^4 - 59,955.545/(1+10%)^5 = -$1,387,278.69

Cash Flow Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Initial Investment -1,160,000 Sales (87,700*(1+10%)*34.60*(1+10%)) 3,671,648.20 3,671,648.20 3,671,648.20 3,671,648.20 3,671,648.20 Less Variable Costs (87,700*(1+10%)*20.85*(1-10%)) 1,810,259.55 1,810,259.55 1,810,259.55 1,810,259.55 1,810,259.55 Fixed Costs (757,000*(1-10%)) 681,300 681,300 681,300 681,300 681,300 Depreciation (1,160,000/5) 232,000 232,000 232,000 232,000 232,000 Earnings Before Tax 948,088.65 948,088.65 948,088.65 948,088.65 948,088.65 Tax 284,426.595 284,426.595 284,426.595 284,426.595 284,426.595 Earning After Tax 663,662.055 663,662.055 663,662.055 663,662.055 663,662.055 Add Depreciation 232,000 232,000 232,000 232,000 232,000 Operating Cash Flow -$1,160,000 $895,662.055 $895,662.055 $895,662.055 $895,662.055 $895,662.055

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