Question

You are considering a new product launch. The project will cost $982,000, have a four-year life, and have no salvage value; depreciation is straight-line zero. Sales are projected at 300 units per year; price per unit will be $92,200, variable cost per unit will be $15,700, and fixed costs will be $328,000 per year. The required return on the project is 12%, and the relevant tax rate is 40%.

Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within + or - 10%.

What are the best-case and worst-case values for each of the projections (partially filled out below)? Fill in chart below for (A), (B), and (C).

Scenario Units Price/Unit Cost/Unit Fixed Cost

Best (+10%)   (A) $19,200 $14,130 (C)

Base 300 $19,200 $15,700 $328,000

Worst (-10%) 270 $19,200 (B) (C)

What are the best case and worst case OCF's and NPVs (D), (E), (F), and (G) with these projections?

OCF NPV

Best Case (D) (E)

Base Case $531,400 $632,047.44

Worst Case (F) (G)

Answer 1

Before attempting this question, please understand that:

1. There are only three variables specific to the scenario: unit sales, variable cost, and fixed cost
2. In the best case scenario, units sold a will have Base case value + 10% while Variable cost / unit and fixed cost will have Base case values - 10%. Parameters on sale side will be favorably up and those on the cost sides will be favorably down. That's why this is the best case.
3. In the worst case scenario, units sold a will have Base case value - 10% while Variable cost / unit and fixed cost will have Base case values + 10%. Parameters on sale side will be unfavorably down and those on the cost sides will be unfavorably up. That's why this is the best case.

Once you have understood please see the table below for your answers:

All financials below are in $

Scenario	Units	Price / unit	Cost / unit	Fixed cost
Best (+10%)	330 (=330 x 1.1)	19,200	14,130 (=15,700 x 0.9)	295,200 (=328,000 x 0.9)
Base	300	19,200	15,700	328,000
Worst (-10%)	270 (=300 x 0.9)	19,200	17,270 (=15,700 x 1.1)	360,800 (=328,000 x 1.1)

Calculations have been provided in the parenthesis so that you understand how each value has been calculated. The entire table is provide. Please check your figures and also you can locate your missing figures.

OCF = (Revenue - Variable cost - Fixed cost - Annual depreciation) x (1 - Tax rate) + Annual Depreciation

Initial investment = C₀ = 982,000; Life = N = 4 years

Annual Depreciation = Initial investment / Life = C₀ / N = 982,000 / 4 =  245,500

Required return on project, R = 12%, Life of the project = 4 years, no salvage value

Hence, NPV = -Initial investment + PV of OCF as annuities = - C₀ + OCF / R x [1 - (1 + R)^-N] = -982,000 + OCF / 12% x [1 - (1 + 12%)^-4] = -982,000 + 3.037349347 x OCF

OCF is scenario specific. Hence scenario specific NPVs:

Please see the table below for OCF and NPV

Parameter	Linkage	Best Case	Base Case	Worst Case
Unit sales	V	330	300	270
Sale Price	P	19,200	19,200	19,200
Variable cost / unit	VC	14,130	15,700	17,270
Revenue	P x V	6,336,000	5,760,000	5,184,000
[-] Variable cost	VC x V	4,662,900	4,710,000	4,662,900
[-] Fixed cost	FC	295,200	328,000	360,800
[-] Annual Depreciation		245,500	245500	245500
EBIT		1,132,400	476,500	(85,200)
[-] Taxes	40% x EBIT	452,960	190,600	(34,080)
NOPAT		679,440	285,900	(51,120)
[+] Annual Depreciation		245,500	245,500	245,500
OCF	NOPAT + Depreciation	924,940	531,400	194,380
NPV	-982,000 + 3.037349347 x OCF	1,827,366	632,047	(391,600)

Hence the answers in your tabular format will be:

Scenario	OCF	NPV
Best Case	924,940.00	1,827,365.90
Base Case	531,400.00	632,047.44
Worst Case	194,380.00	(391,600.03)

Please check your answers and pick up the missing answers. Figures in parenthesis are negative values.