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). Project NPV = sum of present value of cash flows discounted at the cost of capital

= -initial investment + Present Value (PV) of annual cash flows + PV of salvage value

= -4,200,000 + (1,375,000/13%)*(1 - (1+ 13%)^-5) + 300,000/(1+13%)^5 = 799,020.97

The project can be accepted since it has a positive NPV.

b). Best case scenario:

Initial investment = 4,200,000*(1-15%) = 3,570,000

Annual cash flow = 1,375,000*(1+10%) = 1,512,500

Salvage value = 300,000*(1+10%) = 330,000

NPV = -3,570,000 + (1,512,500/13%)*(1 - (1+ 13%)^-5) + 330,000/(1+13%)^5 = 1,928,923.06

c). Worst case scenario:

Initial investment = 4,200,000*(1+10%) = 4,620,000

Annual cash flow = 1,375,000*(1-10%) = 1,237,500

Salvage value = 300,000*(1-12%) = 264,000

NPV = -4,620,000 + (1,237,500/13%)*(1 - (1+ 13%)^-5) + 264,000/(1+13%)^5 = -124,137.69

d). Expected NPV = sum of [probability of each case*NPV of that case]

Standard deviation of the NPV = [sum of [probability*(NPV - expected NPV)^2]^0.5

Expected NPV = 917,539.10

Standard deviation = 829,733.44

The project can still be accepted as expected NPV is positive. Even if expected NPV deviates by 829,733.44, it will still have a positive NPV.