Question

ou are considering a new product launch. The project will cost $1,950,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 210 units per year; price per unit will be $17,500, variable cost per unit will be $10,600, and fixed costs will be $560,000 per year. The required return on the project is 12 percent, and the relevant tax rate is 21 percent.

a.	Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What is the NPV for the best-case and worst-case scenarios?

b.	Evaluate the sensitivity of your base-case NPV to changes in fixed costs.

c. What is the cash break-even level of output for this project (ignoring taxes)?

d-1 What is the accounting break-even level of output for this project?

d-2 What is the degree of operating leverage at the accounting break-even point?

Answer 1

All financials below are in $.

Part (a)

Base case, upper and lower bounds for these variables:

Parameter	Linkage	Base Case	Upper Bound	Lower bound
		P	Q = P x 1.1	R = P x 0.9
Unit sales	A	210	231	189
Variable cost per unit	B	10,600	11,660	9,540
Variable cost	C = A x B	2,226,000	2,448,600	2,003,400
Fixed costs		560,000	616,000	504,000

Initial investment, C₀ = $1,950,000,

N = 4 year life

Annual depreciation = C₀ / N = 1,950,000 / 4 = 487,500

The required return on the project, R = 12% and the relevant tax rate, T = 21%

Annual operating cash flow, C = [(Sale Price - Variable cost per unit) x Unit sale - Fixed costs - Annual depreciation] x (1 - T) + Annual depreciation

Base case: C = [(17,500 - 10,600) x 210 - 560,000 - 487,500] x (1 - 21%) + 487,500 =  804,685

Hence, NPV = -C₀ + C / R x [1 - (1+R)^-N] = -1,950,000 + 804,685 / 12% x [1 - (1+12%)^-4] =  494,109.46

Best case: C = [(17,500 - 9,540) x 231 - 504,000 - 487,500] x (1 - 21%) + 487,500 =   1,156,835

Hence, NPV = -C₀ + C / R x [1 - (1+R)^-N] = -1,950,000 + 1,156,835 / 12% x [1 - (1+12%)^-4] =   1,563,713.25  

Worst case: C = [(17,500 - 11,660) x 189 - 616,000 - 487,500] x (1 - 21%) + 487,500 =   487,705

Hence, NPV = -C₀ + C / R x [1 - (1+R)^-N] = -1,950,000 + 487,705 / 12% x [1 - (1+12%)^-4] = - 468,668.32

Part (b)

Deviation from base case	-10%	-5%	0%	5%	10%
Fixed costs	504,000	532,000	560,000	588,000	616,000
NPV	628,482	561,296	494,109	426,923	359,737

Please see the table above for sensitivity of NPV with fixed costs:

• NPV decreases with increase in fixed cost
• For 5% increase in fixed cost, NPV decreases by 426,923 / 494,109 - 1 = -13.06%. Hence, for every 1% change in fixed cost NPV changes by 2.61% in other direction.

Part (c)

If Cash break even quantity is Q* then

Revenue = Fixed cost + variable cost

Or, 17,500 x Q* = 560,000 + 10,600 x Q*

Hence, Q* = 560,000 / (17,500 - 10,600) = 81.16 which can be rounded off to 81 or 82 (both are correct answers)

Part (d) - 1

If accounting break even quantity is Q then

Revenue = Fixed cost + variable cost + Depreciation

Or, 17,500 x Q = 560,000 + 10,600 x Q + 487,500

Hence, Q* = (560,000 + 487,500) / (17,500 - 10,600) = 151.81 which can be rounded off to 151 or 152 (both are correct answers)

Part (d) - 2

DOL = Contribution margin / EBIT, Since EBIT = 0 at accounting break even, hence DOL at accounting break even is infinite