Question

Really short question! Please help me to solve, thank you!

5. The following estimates have been made for an investment project: Initial investment: $450,000 Unit price: $40 Product life: 5 years Sales volumes (in units): ye Unit cost of a commodity: $20 Cost ofcapital: 790 year 2 year 3 year 4 year 5 3000 6000 7000 8000 7000 Calculate the sensitivity (i.e. maximum tolerable unfavorable change as a percentage of the original estimated value) in (a) sales price, (b) unit costs (c) sales volume, (d) initial investment.

Answer 1

CALCULATION OF NPV
YEAR	SALE VOLUME	PROFIT=Volume*($40-$20)	PV@7%	PRESENT VALUE OF INFLOWS
1	3000	60000	0.934	56040
2	6000	120000	0.873	104760
3	7000	140000	0.816	114240
4	8000	160000	0.763	122080
5	7000	140000	0.713	99820
TOTAL VALUE OF INFLOWS				496940
LESS: INITIAL INVESTMENT				450000
NPV				46940
a)CALCULATION OF SENSITIVITY AS TO UNIT PRICE
LET UNIT PRICE BE=X
YEAR	SALE VOLUME	PROFIT=Volume*($X-$20)	PV@7%
1	3000	3000X-60000	0.934
2	6000	6000X-120000	0.873
3	7000	7000X-140000	0.816
4	8000	8000X-160000	0.763
5	7000	7000X-140000	0.713
TOTAL VALUE OF INFLOWS			24847X-496940
HERE X WILL BE TO MAKE NPV 0			24847X-496940-450000=0
			X=(496940+450000)/24847
			38.11083833
	SENSITIVITY		(40-38.11)/40
			0.04725
			4.73%
b)CALCULATION OF SENSITIVITY AS TO UNIT COST
LET UNIT COST BE=Y
YEAR	SALE VOLUME	PROFIT=Volume*($40-$Y)	PV@7%
1	3000	120000-3000Y	0.934
2	6000	240000-6000Y	0.873
3	7000	280000-7000Y	0.816
4	8000	320000-8000Y	0.763
5	7000	280000-7000Y	0.713
TOTAL VALUE OF INFLOWS			993880-24847Y
HERE Y WILL BE TO MAKE NPV 0			993880-24847Y-450000=0
			Y=(993880-450000)/24847
			21.88916167
	SENSITIVITY OF COST PRICE		(21.89-20)/20
			0.0945
			9.45%
c)SENSITIVITY AS TO SALES VOLUME
AS THE SALE IS IN THE RATIO OF 3:6:7:8:7
LET SALE BE		PROFIT=Volume*($X-$20)	PV@7%
1	3X	60X	0.934
2	6X	120X	0.873
3	7X	140X	0.816
4	8X	160X	0.763
5	7X	140X	0.713
TOTAL VALUE OF INFLOWS				496.94X
496.94X-450000=0
X=450000/496.94
905.5419165
YEAR	NEW SALE VOLUME	PRESENT SALE VOLUME		SENSITIVITY AS %
1	2716.62	3000	0.09446	9.45
2	5433.24	6000	0.09446	9.45
3	6338.78	7000	0.09446	9.45
4	7244.32	8000	0.09446	9.45
5	6338.78	7000	0.09446	9.45
c) SENSITIVITY AS TO INITIAL INVESTMENT
YEAR	SALE VOLUME	PROFIT=Volume*($40-$20)	PV@7%	PRESENT VALUE OF INFLOWS
1	3000	60000	0.934	56040
2	6000	120000	0.873	104760
3	7000	140000	0.816	114240
4	8000	160000	0.763	122080
5	7000	140000	0.713	99820
TOTAL VALUE OF INFLOWS				496940
LESS: INITIAL INVESTMENT				450000
NPV				46940
		SENSITIVITY AS TO INITIAL INVESTMENT		0.104311111
				10.43%