Question

QUESTION 2

–

SENSITIVITY ANALYSIS

(25 POINTS)

Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,600,000 investment in threading equipment to get the project started; the project will last for 6 years. The accounting department estimates that annual fixed costs will be $600,000 and that variable costs should be $250 per ton. Further, the accounting department will depreciate the initial fixed asset investment straight-line to zero over the 6-year project life and estimate a salvage value of $450,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $340 per ton. The engineering department estimates you will need an initial net working capital investment of $560,000. You require a return of 13 percent and face a marginal tax rate of 24 percent on this project.

Suppose you’re confident about your own projections, but you’re a little unsure about Detroit’s actual machine screw requirements.

a. What is the sensitivity of the project OCF to changes in the quantity

supplied?

b. What about the sensitivity of NPV to changes in quantity supplied?

c. Given the sensitivity number you calculated, is there some minimum level

of output below which you wouldn't want to operate?

Answer 1

40000	tons	NPV calculations
Year	0	1	2	3	4	5	6
1.Initial Investment	-5600000
2.Initial NWC	-560000						560000
3.After tax Salvage(450000*(1-24%))							342000
Operating Cash flows:
4.Sales revenue at 340/ton		13600000	13600000	13600000	13600000	13600000	13600000
5. Variable costs at 250/ton		-10000000	-10000000	-10000000	-10000000	-10000000	-10000000
6.Fixed costs		-600000	-600000	-600000	-600000	-600000	-600000
7.EBT(4+5+6)		3000000	3000000	3000000	3000000	3000000	3000000
8. Tax at 24%		-720000	-720000	-720000	-720000	-720000	-720000
9.EAT(7+8)		2280000	2280000	2280000	2280000	2280000	2280000
10.Depn.tax shield(5600000-450000)/6*24%		206000	206000	206000	206000	206000	206000
11.OCF		2486000	2486000	2486000	2486000	2486000	2486000
12. Total annual C/fs(1+2+3+11)	-6160000	2486000	2486000	2486000	2486000	2486000	3388000
13.PV F at 13%(1/1.13^Yr.n)	1	0.88496	0.78315	0.69305	0.61332	0.54276	0.48032
14.PV at 13%(12*13)	-6160000	2200000	1946903	1722923	1524710	1349301	1627319
15. NPV(Sum of Row 14)	4211156

a.. OCF at 40000 tons

((40000*(340-250))-600000)*(1-24%)+206000=

2486000

OCF at 45000 tons

((45000*(340-250))-600000)*(1-24%)+206000=

2828000

Change in OCF for 5000 tons

2828000-2486000=

342000

So, sensitivity of OCF per ton=

342000/5000=

68.4

(for b.) NPV at
45000	tons
Year	0	1	2	3	4	5	6
1.Initial Investment	-5600000
2.Initial NWC	-560000						560000
3.After tax Salvage(450000*(1-24%))							342000
Operating Cash flows:
4.Sales revenue at 340/ton		15300000	15300000	15300000	15300000	15300000	15300000
5.Variable costs at 250/ton		-11250000	-11250000	-11250000	-11250000	-11250000	-11250000
6.Fixed costs		-600000	-600000	-600000	-600000	-600000	-600000
7.EBT(4+5+6)		3450000	3450000	3450000	3450000	3450000	3450000
8. Tax at 24%		-828000	-828000	-828000	-828000	-828000	-828000
9.EAT(7+8)		2622000	2622000	2622000	2622000	2622000	2622000
10. Depn.tax shield(5600000-450000)/6*24%		206000	206000	206000	206000	206000	206000
11.OCF		2828000	2828000	2828000	2828000	2828000	2828000
12. Total annual C/fs(1+2+3+11)	-6160000	2828000	2828000	2828000	2828000	2828000	3730000
13.PV F at 13%(1/1.13^Yr.n)	1	0.88496	0.78315	0.69305	0.61332	0.54276	0.48032
14.PV at 13%(12*13)	-6160000	2502654.9	2214739	1959946	1734465	1534925	1791588
15. NPV(Sum of Row 14)	5578318

b.Sensitivity analysis of NPV:
NPV at 40000 tons	4211156
NPV at 45000 tons	5578318
Change in NPV for 5000 tons	1367162
So, sensitivity of NPV per ton=
1367162/5000=	273.43
	per ton

c.. YES.

c.Minimum level of output below which he will not operate will be at which output level,the NPV becomes 0

That can be found by using "Goal seek" function Excel,

Setting the cell containing the NPV value to 0

by changing the quantity (in tons) value

& the value got is

24598.91 tons

ie. 24599 tons

below which the NPV will be NEGATIVE.