Question

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?

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?

Please I need help on this question

Answer 1

Ans a)

Net Present Value = Present Value of Cash Inflow - Present Value of Cash Outflow

NPV = [Ghc1,375,000 * PVAF (13% , 5 years) + Ghc 300,000 * PVF (13% , 5th Year)] - Ghc 4,200,000

NPV = [(Ghc 1,375,000 * 3.517) + (Ghc 300,000 * 0.543)] - Ghc 4,200,000

NPV = Ghc 798,775

Ans b)

Initial Investment = Ghc 3,570,000 [Ghc 4,200,000 * (1 - 0.15)]

Annual Inflow = Ghc 1,512,500 [Ghc 1,375,000 * 1.10}

Salvage Value = Ghc 330,000 [Ghc 300,000 * 1.10]

NPV = [Ghc 1,512,500 * PVAF (13% , 5 years) + Ghc 330,000 * PVF (13% , 5th Year)] - Ghc 3,570,000

NPV = [(Ghc 1,512,500 * 3.517) + (Ghc 330,000 * 0.543)] - Ghc 3,570,000

NPV = Ghc 1,928,653

Ans c)

Initial Investment = Ghc 4,620,000 [Ghc 4,200,000 * (1 + 0.10)]

Annual Inflow = Ghc 1,237,500 [Ghc 1,375,000 * 0.90}

Salvage Value = Ghc 264,000 [Ghc 300,000 * 0.88]

NPV = [Ghc 1,237,500 * PVAF (13% , 5 years) + Ghc 264,000 * PVF (13% , 5th Year)] - Ghc 4,620,000

NPV = [(Ghc 1,237,500 * 3.517) + (Ghc 264,000 * 0.543)] - Ghc 4,620,000

NPV = - Ghc 124,361

Ans d)

Calculation of Expected NPV

= Ghc 798,775 * 0.35 + Ghc 1,928,653 * 0.35 + (- Ghc 124,361 * 0.30)

= Ghc 913,382

Standard Deviation = [(Ghc 798,775 - Ghc 913,382)2 * 0.35 + (Ghc 1,928,653 - Ghc 913,382)2 * 0.35 + (- Ghc 124,361 - Ghc 913,382)2 * 0.30] 1/2

S.D. = Ghc 829,724

As expected NPV of the project is positive, the project is viable.