Question

LH Corp is evaluating a project that costs $724,000, has an 8-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life the project. Sales are projected at 75,000 units per year with price per unit is $39. Variable cost per unit is $23. Fixed costs are $850,000 per year. The tax rate is 35%, and the discount rate on this project is 15%. a). Calculate the accounting break-even point.

b). Calculate the base-case cash flow and NPV.

c). What is the sensitivity of NPV to changes in the sales figure? IF Sales dropped by 400 units, what is the corresponding change of NPV?

d). What is the sensitivity of operating cash flow to changes in the variable cost figure? Based on your calculation, how much is the change of operating cash flow if variable costs increased by $2 per unit?

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

Answer 1

	a)	ACCOUNTING BREAKEVEN POINT
	A	Projected annual sales in units	75,000
	B	Price per unit	$39
	C	Variable cost	$23
	D=B-C	Unit contribution	$16	(39-23)
	E=D/B	Contribution margin percentage	41.03%	(16/39)
	F	Annual Fixed costs(without depreciation)	$850,000
	G	Annual depreciation	$              90,500	(724000/8)
	H=F+G	Total annual fixed cost	$940,500	(850000+905000
	I=H/E	Accounting Breakeven point (Sales)	$2,292,469
	J=H/D	Accounting Breakeven Quantity	58781	(58781*39)=	$2,292,469
	b)	Base-case Cash Flow and NPV
	K=A*B	Annualsales in dollars	$        2,925,000
	L=A*C	Annual Variable costs	$        1,725,000
	M=K-L	Annual Contribution	$        1,200,000
	N	Annual Fixed costs	$940,500
	P=M-N	Earning Before tax	$            259,500
	Q=P*0.35	Tax Expenses	$              90,825
	R=P-Q	After Tax earnings	$            168,675
	S	Add:Non Cash expense of depreciation	$              90,500
	T=R+S	Base case annual cash flow	$            259,175
		Number of years of cash flow	8
		Dicount rate	15%
	PV	Present Value of Cash inFlows	$1,163,002	(Using PV function of excel with Rate=15%,Nper=8, Pmt=-259175)
	X	Initial Cash flow	($724,000)
	NPV=PV+X	Net Present Value (NPV)	$439,002
		IF VARIABLE COST IS INCREASED BY $2 PER UNIT
	K=A*B	Annualsales in dollars	$        2,925,000
	L=A*25	Annual Variable costs	$        1,875,000	(75000*25)
	M=K-L	Annual Contribution	$        1,050,000
	N	Annual Fixed costs	$            940,500
	P=M-N	Earning Before tax	$            109,500
	Q=P*0.35	Tax Expenses	$              38,325
	R=P-Q	After Tax earnings	$              71,175
	S	Add:Non Cash expense of depreciation	$              90,500
	T=R+S	Base case annual cash flow	$            161,675
		Number of years of cash flow	$                         8
		Dicount rate	$                         0
	PV	Present Value of Cash inFlows	$            725,488	(Using PV function of excel with Rate=15%,Nper=8, Pmt=-161675)
	X	Initial Cash flow	$         (724,000)
	NPV=PV+X	Net Present Value (NPV)	$                1,488
		BEST CASE SCENARIO
	B	PRICE=39*1.1=	$                42.90
	A	Quantity=75000*1.1=	82500
	C	Variable Cost=23*0.9=	$                20.70
	D	Fixed Cost=850000*0.9=	$            765,000
	K=A*B	Annualsales in dollars	$        3,539,250
	L=A*C	Annual Variable costs	$        1,707,750
	M=K-L	Annual Contribution	$        1,831,500
	N=D+90500	Annual Fixed costs	$            855,500
	P=M-N	Earning Before tax	$            976,000
	Q=P*0.35	Tax Expenses	$            341,600
	R=P-Q	After Tax earnings	$            634,400
	S	Add:Non Cash expense of depreciation	$              90,500
	T=R+S	Base case annual cash flow	$            724,900
		Number of years of cash flow	$                         8
		Dicount rate	15%
	PV	Present Value of Cash inFlows	$        3,252,859	(Using PV function of excel with Rate=15%,Nper=8, Pmt=-724900)
	X	Initial Cash flow	$         (724,000)
	NPV=PV+X	Net Present Value (NPV)	$        2,528,859
		WORST CASE SCENARIO
	B	PRICE=39*0.9=	$                35.10
	A	Quantity=75000*0.9=	67500
	C	Variable Cost=23*1.1=	$                25.30
	D	Fixed Cost=850000*1.1=	$            935,000
	K=A*B	Annualsales in dollars	$        2,369,250
	L=A*C	Annual Variable costs	$        1,707,750
	M=K-L	Annual Contribution	$            661,500
	N=D+90500	Annual Fixed costs	$        1,025,500
	P=M-N	Earning Before tax	$         (364,000)
	Q=P*0.35	Saving in tax expenses	$            127,400
	R=P+Q	After Tax earnings	$         (236,600)
	S	Add:Non Cash expense of depreciation	$              90,500
	T=R+S	Base case annual cash flow	$         (146,100)
		Number of years of cash flow	$                         8
		Dicount rate	15%
	PV	Present Value of Cash inFlows	$         (655,598)	(Using PV function of excel with Rate=15%,Nper=8, Pmt=146100)
	X	Initial Cash flow	$         (724,000)
	NPV=PV+X	Net Present Value (NPV)	$      (1,379,598)