You are considering a new product launch. The project will cost $875,000, have a

Question

You are considering a new product launch. The project will cost $875,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 190 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 35 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 ±10 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).)

NPVbest $

NPVworst $

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

NPVbase $

Requirement 2: What is the sensitivity of the NPV to changes in fixed costs? (Do not round intermediate calculations. Input the amount as a positive value. Round your answer to 2 decimal places (e.g., 32.16).)

For every dollar FC increase, NPV falls by $ .

Explanation / Answer

To calculate the accounting breakeven, we first need to find the depreciation for each year. The depreciation is:

Depreciation = $875,000/4
Depreciation = $218,750 per year

And the accounting breakeven is:

QA = ($345,000 + 218,750)/($19,200 – 15,100)  
QA = 138 units

   We will use the tax shield approach to calculate the OCF. The OCF is:

OCFbase = [(P – v)Q – FC](1 – tc) + tcD
OCFbase = [($19,200 – 15,100)(190) – $345,000](0.65) + 0.35($218,750)  
OCFbase = $358,662.5

Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:

NPVbase = –$875,000 + $358,662.5(PVIFA11%,4)
NPVbase = $237,714.54

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 209 units. The NPV at this sales level is:

OCFnew = [($19200 – 15100)(209) – $345,000](0.65) + 0.35($218,750)  
OCFnew = $409,297.5

And the NPV is:

NPVnew = –$875,000 + $409,297.5(PVIFA11% 4)
NPVnew = $394,804.56

So, the change in NPV for every unit change in sales is:

NPV/S = ($394,804.56 – 237,714.54)/(209 – 190)  NPV/S = +$8267.9 If sales were to drop by 19 units, then NPV would drop by: NPV drop = $8267.9 *(19) = $157,090.

2.     We will use the tax shield approach to calculate the OCF for the best- and worst-case scenarios. For the best-case scenario, the price and quantity increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. The variable and fixed costs both decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. Doing so, we get:

OCFbest = {[($19200)(1.1) – ($15100)(0.9)](190)(1.1) – $345,000(0.9)}(0.65) + 0.35($218,750)  
OCFbest = $897,688

The best-case NPV is:

NPVbest = –$875,000 + $897,688(PVIFA11%,4)
NPVbest = $1,909,987.25

For the worst-case scenario, the price and quantity decrease by 10 percent, so we will multiply the base case numbers by .9, a 10 percent decrease. The variable and fixed costs both increase by 10 percent, so we will multiply the base case numbers by 1.1, a 10 percent increase. Doing so, we get:

OCFworst = {[($19200)(0.9) – ($15100)(1.1)](190)(0.9) – $345,000(1.1)}(0.65) + 0.35($218,750)  
OCFworst = $117,866.04

The worst-case NPV is:

NPVworst = –$875,000 + $117866.04(PVIFA11%,4)
NPVworst = –$509,332.41

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