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:
a) What is the NPV of the sanitizer project? Should you pursue this project? ​(8 Marks)



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? ​(6 Marks)
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?​​(6 Marks)
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

Given: Initial Investment Annual Cash Inflows Salvage Value GH 4,200,000 GH 1,375,000 GH 300,000 a. 0 1 2 3 4 5 -42,00,000 13,75,000 13,75,000 13,75,000 13,75,000 Year Investment Annual Cash Inflows Salvage Value Total Cash Flows Discount factor 13% Present Value Net Present Value -42,00,000 1 -42,00,000 7,99,033 13,75,000 0.88496 12,16,820 13,75,000 0.78315 10,76,831 13,75,000 0.69305 9,52,944 13,75,000 0.61332 8,43,315 13,75,000 3,00,000 16,75,000 0.54276 9,09,123 Yes, it should persue this project b. Best case scenario (Revised) Initial Investment EGH 4,200,000*(1 -0.15) Annual Cash Inflows =GH 1,375,000*(1 + 0.10) Salvage Value =GH 300,000*(1 -0.15) GH 3,570,000 GH 1,512,500 GH 255,000 1 2 3 4 5 0 -35,70,000 15,12,500 15,12,500 15,12,500 15,12,500 Year Investment Annual Cash Inflows Salvage Value Total Cash Flows Discount factor 13% Present Value Net Present Value -35,70,000 15,12,500 0.88496 13,38,502 1 15,12,500 0.78315 11,84,514 15,12,500 0.69305 10,48,238 15,12,500 2,55,000 17,67,500 0.54276 9,59,328 15,12,500 0.61332 9,27,647 -35,70,000 18,88,229 4620000 C. Worst case scenario (Revised) Initial Investment =GH 4,200,000*(1 +0.10) Annual Cash Inflows =GH 1,375,000*(1 - 0.10) Salvage Value =GH 300,000*(1 -0.12) GH 4,620,000 GH 1,237,500 GH 264,000 1237500 264000 1 2 3 4 5 0 -46,20,000 12,37,500 12,37,500 12,37,500 12,37,500 Year Investment Annual Cash Inflows Salvage Value Total Cash Flows Discount factor 13% Present Value Net Present Value -46,20,000 1 -46,20,000 -1,24,127 12,37,500 0.88496 10,95,138 12,37,500 0.78315 9,69,148 12,37,500 0.69305 8,57,649 12,37,500 0.61332 7,58,984 12,37,500 2,64,000 15,01,500 0.54276 8,14,954 No, we will not pursue project as NPV is negative d. Expected NPV & Standard Deviaton of the Sanitizer project Expected Net Case Net Cash Flow Probability (p) Cash Flow (ENCF) Base Case 7,99,033 0.35 2,79,662 Best Case 18,88,229 0.35 6,60,880 Worst Case -1,24,127 0.3 -37,238 9,03,304 Net Cash Flow less ENCF 5,19,371 12,27,349 -86,889 16,59,831 (Net Cash Flow less ENCF)^2*p 94,41,11,82,474.35 5,27,23,52,06,473.67 2,26,49,02,197.63 6,23,91,12,91,145.65 Expected NPV of the Sanitizer Project - GH 903,304 Standard Deviation is under root of total of last colum = (Net Cash Flow less ENCF)^2*p SD = 7,80,880.55 (approximately) Yes, project is still viable Note: We have used discount rate factor upto five places in order to calculate NPV, consider that in mind when you cross check answers Let me know, if you have any questions over comments section, rate positive if you are satisfied with the solution