Question

Consider a project to supply your church with 55,000 gallons of hand sanitizer annually for church services. You estimate that you will need an initial Gh¢4,200,000 in terms of investment to get the project started. The project will last for 5 years.
The project will bring in annual cash flows of Gh¢1,375,000. It also estimates a salvage value of Gh¢300,000 after dismantling costs.
Your cost of capital is 13 percent. Assume no taxes or depreciation.
Required:
What is the NPV of the sanitizer project? Should you pursue this project?

b) Suppose you believe that there is a best case scenario where initial investment could be 15% lower with salvage value and revenue being 10% higher, what would be the NPV under this scenario?
c) In the worst case scenario, you expect annual cash inflows to be 10% lower, salvage value to be 12% lower and initial investment to be 10% higher. Calculate the NPV under this worst case scenario. Would you still pursue the project?
d) You just received additional information that suggests that your base case (answer to a), best case (b) and worst case (c) scenarios have probabilities of 0.35, 0.35 and 0.30 respectively. What will be the expected NPV of the sanitizer project. What about the standard deviation of the sanitizer project? Do you think the project is still viable?

Answer 1

a) base case

calculation of NPV:

NPV = present value of cash inflows - present value of cash outflowls

year	cash inflows in Gh¢	preseent value factor @ 13%	present value of cash inflows in Gh¢
0	(4200000)	1	(4200000)
1to 5	1375000	cumulative present value factor @ 13% for 5 years = 3.5172	4836150
5	300000	present value factor for 5th year @ 13% = 0.5427	162810
		NPV	798960

as NPV is positive and this project should be accepted and should pusue this project.

b) best case

initial investment 15% lower new initial investment will be (Gh¢ 4200000-15%) = Gh¢ 3570000

same salvage value as earlier = Gh¢ 300000

earlier depreciation = (4200000-300000)/5 =780000

there is no tax so no effect of depreciation on cashinflows

revenue 10% higher will be = 1375000 + 10% =Gh¢ 1512500

calculation of NPV:

NPV = present value of cash inflows - present value of cash outflowls

year	cash inflows in Gh¢	preseent value factor @ 13%	present value of cash inflows in Gh¢
0	(3570000)	1	(3570000)
1to 5	1512500	cumulative present value factor @ 13% for 5 years = 3.5172	5319765
5	300000	present value factor for 5th year @ 13% = 0.5427	162810
		NPV	1912575

c) worst case

annual cash inflow 10% lower = 1375000 - 10% =1237500

salvage value 12% lower = 300000 -12% = 264000

initial investment 10% higher = 4200000 + 10% = 4620000

calculation of NPV:

NPV = present value of cash inflows - present value of cash outflowls

year	cash inflows in Gh¢	preseent value factor @ 13%	present value of cash inflows in Gh¢
0	(4620000)	1	(4620000)
1to 5	1237500	cumulative present value factor @ 13% for 5 years = 3.5172	4352535
5	264000	present value factor for 5th year @ 13% = 0.5427	143272.8
		NPV	(124192.2)

as per this situation NPV is negative so this project should not be pursued.

d)  base case (answer to a), best case (b) and worst case (c) scenarios have probabilities of 0.35, 0.35 and 0.30 respectively :

then first calculation of NPV

case (1)	NPV in Gh¢ (2)	probability (3)	NPV using probability (4=2x3)
base case	798960	0.35	279636
best case	1912575	0.35	669401.25
worst case	(124192.2)	0.30	(37257.66)
		total NPV	911779.59

as per using above probability NPV is positive so we can still accept this projecr and still pusue it.

now calcualtion of standard deviation :

mean = 798960x0.35 + 279636x0.35 + (37257.66)x0.30 = 911779.59

stsndsrd deviation = √[(x1-mean)2x(probality of x1)+(x2-mean)2x(probality of x2)+(x3-mean)2x(probality of x3)+(x4-mean)2x(probality of x4)]

standard deviation = √[(798960-911779.59)2x0.35+(669401.25-911779.59)2x0.35+(-37257.66-911779.59)2x0.30]

= √(-112819.59)2x0.35)+(-242378.34)2x0.35+(-949037.25)2x0.30

= √295217942421

= 543339.62

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