Question

We are evaluating a project that costs $744,000, has a six-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 45,000 units per year. Price per unit is $60, variable cost per unit is $20, and fixed costs are $744,000 per year. The tax rate is 35 percent, and we require a return of 18 percent on this project.

Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Calculate the base-case cash flow and NPV. (Do not round intermediate calculations and round your NPV answer to 2 decimal places, e.g., 32.16.)

What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) ΔNPV/ΔQ $

Calculate the change in NPV if sales were to drop by 500 units. (Enter your answer as a positive number. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV would (INCREASE/DECREASE) by $

What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) ΔOCF/ΔVC $

Answer 1

Formula	Initial investment	7,44,000
	Life of project	6
SL over 6 yrs	Depreciation (D)	1,24,000
	Unit sales (u)	45,000
	Price/unit (p)	60
	Variable cost/unit (vc)	20
	Fixed costs (FC)	7,44,000
	Tax rate (T)	35%
	Required return ('r)	18%
(u*p)	Total sales (S)	27,00,000
(u*vc)	Total Variable cost (VC)	9,00,000

a). Accounting break-even point = 21,700

Formula	Accounting breakeven point:
FC+D	Fixed costs + Depreciation	8,68,000
(p-vc)	Contribution margin	40
(FC+D)/(p-vc)	Break-even point	21,700

b). Base-case cash flow = 729,800.00; NPV = 1,808,550.35

Formula	OCF calculation:
(S-VC-FC-D)	EBIT	9,32,000.00
35%*EBIT	Tax on EBIT	3,26,200.00
(EBIT-Tax)	Net income (NI)	6,05,800.00
	Add: depreciation (D)	1,24,000.00
(NI+D)	OCF	7,29,800.00

NPV of OCF:
PMT	7,29,800.00
N	6
I	18%
PV	25,52,550.35

NPV = initial investment + NPV of OCF = -744,000+2,552,550.35 = 1,808,550.35

c). Sensitivity of NPV to change in sales figure:

Change sales (in units) to 44,000

NPV becomes 1,717,612.68

Change in NPV/change in units = (1,717,612.68-1,808,550.35)/(44,000-45,000) = 90.938

d). NPV if sales drops by 500 units to 45,000 - 500 = 44,500 units is 1,763,081.52

Decrease in NPV due to sales drop = 1,808,550.35-1,763,081.52 = 45,468.83

Formula	OCF calculation:
(S-VC-FC-D)	EBIT	9,12,000.00
35%*EBIT	Tax on EBIT	3,19,200.00
(EBIT-Tax)	Net income (NI)	5,92,800.00
	Add: depreciation (D)	1,24,000.00
(NI+D)	OCF	7,16,800.00
	NPV of OCF:
	PMT	7,16,800.00
	N	6
	I	18%
	PV	25,07,081.52

NPV of the project:
Initial investment	-7,44,000.00
NPV of OCF	25,07,081.52
NPV	17,63,081.52

e). Change variable cost/unit to $30

Then OCF = 437,300

Change in OCF/Change in variable cost per unit = (437,300-729,800)/(30-20) = -29,250