Question

Questions:

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:

1. 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
Year	0	1	2	3	4	5
1.Initial Investment	-4200000
2.Net Salvage						300000
3.Annual Cash flows		1375000	1375000	1375000	1375000	1375000
4.Total annual FCFs(1+2+3)	-4200000	1375000	1375000	1375000	1375000	1675000
5.PV F at 13%(1/1.13^yr.n)	1	0.88496	0.78315	0.69305	0.61332	0.54276
6.PV at 13%(4*5)	-4200000	1216814	1076827	952944	843313.3	909122.9
7.NPV (sum of Row 6))	799021

Yes. The project can be pursued as it returns POSITIVE NPV of its cash flows at 13% cost of capital.

b. Best case
Year	0	1	2	3	4	5
1.Initial Investment	-3570000
2.Net Salvage						330000
3.Annual Cash flows		1512500	1512500	1512500	1512500	1512500
4.Total annual FCFs(1+2+3)	-3570000	1512500	1512500	1512500	1512500	1842500
5.PV F at 13%(1/1.13^yr.n)	1	0.88496	0.78315	0.69305	0.61332	0.54276
6.PV at 13%(4*5)	-3570000	1338496	1184509	1048238	927644.6	1000035
7.NPV (sum of Row 6))	1928923

c. Worst case
Year	0	1	2	3	4	5
1.Initial Investment	-4620000
2.Net Salvage						264000
3.Annual Cash flows		1237500	1237500	1237500	1237500	1237500
4.Total annual FCFs(1+2+3)	-4620000	1237500	1237500	1237500	1237500	1501500
5.PV F at 13%(1/1.13^yr.n)	1	0.88496	0.78315	0.69305	0.61332	0.54276
6.PV at 13%(4*5)	-4620000	1095133	969144	857649.6	758981.9	814954
7.NPV (sum of Row 6))	-124138

d..Summary of NPVs
Base case	799021
Best case	1928923
Worst case	-124138

Expected NPV of the sanitizer project

(0.35*799021)+(0.35*1928923)+(30%*-124138)=

917539

Standard deviation of the sanitizer project=

Sq. rt. Of (sum of Variances/No.of scenarios)

ie. (((799021-917539)^2+(1928923-917539)^2+(-124138-917539)^2)/3)^(1/2)=

841038.07

Coefficient of variation=

Standard deviation/Expected NPV

ie. 841038/917539=

0.92

A coefficient of variation less than 1 is acceptable

Hence the project is STILL VIABLE & Can be accepted.