Question

Blinkeria is considering introducing a new line of hand scanners that can be used to copy material and then download it into a personal computer. These scanners are expected to sell for an average price of $104 each, and the company analysts performing the analysis expect that the firm can sell 108,000 units per year at this price for a period of five​ years, after which time they expect demand for the product to end as a result of new technology. In​ addition, variable costs are expected to be $20 per unit and fixed​ costs, not including​ depreciation, are forecast to be $1,010,000 per year. To manufacture this​ product, Blinkeria will need to buy a computerized production machine for $10.9 million that has no residual or salvage​ value, and will have an expected life of five years. In​ addition, the firm expects it will have to invest an additional $302,000 in working capital to support the new business. Other pertinent information concerning the business venture is provided​ here:

Initial cost of the machine	​$10,900,000
Expected life	5 years
Salvage value of the machine	​$0
Working capital requirement	​$302,000
Depreciation method	straight line
Depreciation expense	​$2,180,000 per year
Cash fixed costslong dash—excluding depreciation	​$1,010,000 per year
Variable costs per unit	​$20
Required rate of return or cost of capital	9.2​%
Tax rate	34​%

a. Calculate the​ project's NPV.

b.  Determine the sensitivity of the​ project's NPV to​ a(n) 9 percent decrease in the number of units sold.

c. Determine the sensitivity of the​ project's NPV to​ a(n) 9 percent decrease in the price per unit.

d. Determine the sensitivity of the​ project's NPV to​ a(n) 9 percent increase in the variable cost per unit.

e. Determine the sensitivity of the​ project's NPV to​ a(n) 9 percent increase in the annual fixed operating costs.

Answer 1

	a)	CALCULATION OF PROJECT NPV
	A	Unit sales	108000
	B	Unit Sales Price	$104
	C=A*B	Annual Sales Revenue	$11,232,000
	D	Variable Cost Per unit	$20
	E=A*D	Total Variable Costs	$2,160,000
	F=C-E	Contribution Margin	$9,072,000
	G	Annual Depreciation	$2,180,000
	H	Annual Fixed Cost(excluding Depreciation)	$1,010,000
	I=F-G-H	Income Before Taxes	$5,882,000
	J	Tax Rate	34%
	K=I*J	Tax Expenses	$1,999,880
	L=I-K	Net Operating Income	$3,882,120
	M	Add: Depreciation (non cash expense)	$2,180,000
	N=L+M	Annual Operating Cash Flow	$6,062,120
		DISCOUNT FACTOR:
	Rate	Discount Rate =Required Return	9.2%
	Nper	Number of Years	5
	PV	Present Value of annuity of $1	3.8696	(Using PV function of excel with Rate=9.2%,Nper=5, Pmt=-1)
	DF	DISCOUNT FACTOR=	3.8696
	P=N*DF	Present Value of Annual Cash inflow	$23,457,677
	PW	Present Value of Working Capital Released in year 5	$196,279	(302000/(1.09^5)
	PV=P+PW	Total Present Value of Positive Cash Flows	$23,653,956
	IC	Initial Cost of machine	$10,900,000
	IW	Initial Working Capital	$302,000
	I=IC+IW	Total Initial Cash Outflow	$11,202,000
	NPV=PV-I	Net Present Value (NPV)	$12,451,956
	b)	NPV with 9% DECREASE in number of units sold
	A	Unit sales	98280	(108000*(1-0.09)
	B	Unit Sales Price	$104
	C=A*B	Annual Sales Revenue	$10,221,120
	D	Variable Cost Per unit	$20
	E=A*D	Total Variable Costs	$1,965,600
	F=C-E	Contribution Margin	$8,255,520
	G	Annual Depreciation	$2,180,000
	H	Annual Fixed Cost(excluding Depreciation)	$1,010,000
	I=F-G-H	Income Before Taxes	$5,065,520
	J	Tax Rate	34%
	K=I*J	Tax Expenses	$1,722,277
	L=I-K	Net Operating Income	$3,343,243
	M	Add: Depreciation (non cash expense)	$2,180,000
	N=L+M	Annual Operating Cash Flow	$5,523,243
		DISCOUNT FACTOR:
	Rate	Discount Rate =Required Return	9.2%
	Nper	Number of Years	5
	PV	Present Value of annuity of $1	3.8696
	DF	DISCOUNT FACTOR=	3.8696
	P=N*DF	Present Value of Annual Cash inflow	$21,372,466
	PW	Present Value of Working Capital Released in year 5	$196,279
	PV=P+PW	Total Present Value of Positive Cash Flows	$21,568,745
	IC	Initial Cost of machine	$10,900,000
	IW	Initial Working Capital	$302,000
	I=IC+IW	Total Initial Cash Outflow	$11,202,000
	NPV=PV-I	Net Present Value (NPV)	$10,366,745
				H28 X f C D E =PV(H26,H27,-1) F Annual Depreciation Annual Fixed Cost(excluding Depreciation) I=F-G-H Income Before Taxes Tax Rate K=I*) Tax Expenses L=I-K Net Operating Income Add: Depreciation (non cash expense) N=L+M Annual Operating Cash Flow DISCOUNT FACTOR: Rate Discount Rate =Required Return Nper Number of Years PV Present Value of annuity of $1 $2,180,000 $1,010,000 $5,882,000 34% $1,999,880 $3,882,120 $2,180,000 $6,062,120 M 9.2% 1 3 .8696 (Using PV function of excel with Rate=9.2%,Nper=5, Pm
				C=A*B E=A*D FEC-E 108000 $94.64 (104*(1-0.09) $10,221,120 $20 $2,160,000 $8,061,120 $2,180,000 $1,010,000 $4,871,120 34% $1,656,181 $3,214,939 $2,180,000 $5,394,939 I=F-G-H NPV with 9% decrease in PRICE per unit Unit sales Unit Sales Price Annual Sales Revenue Variable Cost Per unit Total Variable Costs Contribution Margin Annual Depreciation Annual Fixed Cost(excluding Depreciation) Income Before Taxes Tax Rate Tax Expenses Net Operating Income Add: Depreciation (non cash expense) Annual Operating Cash Flow DISCOUNT FACTOR: Discount Rate =Required Return Number of Years Present Value of annuity of $1 DISCOUNT FACTOR= Present Value of Annual Cash inflow Present Value of Working Capital Released in year 5 Total Present Value of Positive Cash Flows Initial Cost of machine Initial Working Capital Total Initial Cash Outflow Net Present Value (NPV) K=I*J LEI-K M N=L+M 9.2% Rate Nper PV PEN*DF PW PV=P+PW IC IW I=IC+IW NPV=PV- 3.8696 3.8696 $20,875,987 $196,279 $21,072,267 $10,900,000 $302,000 $11,202,000 $9,870,267 d) C=A*B E=A*D FEC-E G 108000 $104 $11,232,000 $21.80 (20*1.09) $2,354,400 $8,877,600 $2,180,000 $1,010,000 $5,687,600 34% $1,933,784 $3,753,816 $2,180,000 $5,933,816 I=F-G-H NPV with 9% INCREASE in Variable cost per unit Unit sales Unit Sales Price Annual Sales Revenue Variable Cost Per unit Total Variable Costs Contribution Margin Annual Depreciation Annual Fixed Cost(excluding Depreciation) Income Before Taxes Tax Rate Tax Expenses Net Operating Income Add: Depreciation (non cash expense) Annual Operating Cash Flow DISCOUNT FACTOR: Discount Rate =Required Return Number of Years Present Value of annuity of $1 DISCOUNT FACTOR= Present Value of Annual Cash inflow Present Value of Working Capital Released in year 5 Total Present Value of Positive Cash Flows Initial Cost of machine Initial Working Capital Total Initial Cash Outflow Net Present Value (NPV) K=I* LEI-K M N=L+M 9.2% Rate Nper PV DF PEN*DF PW PV=P+PW 3.8696 3.8696 $22,961,198 $ 196,279 $23,157,477 $10,900,000 $302,000 $11,202,000 $11,955,477 IW I=IC+IW NPV=PV-1 C=A*B E=A*D FEC-E I=F-G-H K=1*] L=I-K M NPV with 9% INCREASE in Annual Fixed Operating costs Unit sales 108000 Unit Sales Price $104 Annual Sales Revenue $11,232,000 Variable Cost Per unit $20 Total Variable Costs $2,160,000 Contribution Margin $9,072,000 Annual Depreciation $2,180,000 Annual Fixed Cost(excluding Depreciation) $1,100,900 (1010000*1.09) Income Before Taxes $5,791,100 Tax Rate 34% Tax Expenses $1,968,974 Net Operating Income $3,822,126 Add: Depreciation (non cash expense) $2,180,000 Annual Operating Cash Flow $6,002,126 DISCOUNT FACTOR: Discount Rate =Required Return 9.2% Number of Years 5 Present Value of annuity of $1 3.8696 DISCOUNT FACTOR= 3.8696 Present Value of Annual Cash inflow $23,225,527 Present Value of Working Capital Released in year 5 $196,279 Total Present Value of Positive Cash Flows $23,421,806 Initial Cost of machine $10,900,000 Initial Working Capital $302,000 Total Initial Cash Outflow $11,202,000 Net Present Value (NPV) $12,219,806 N=L+M Rate Nper PV PW PV=P+PW IW I=IC+IW NPV=PV-