A question on Calculating present Value

Question

a) The ideal management is considering between two projects A and B. Project A will require an initial

outlay of Sh. 4 million and will generate Sh. 3.5 million per annum for the 8 years of its useful life.

This project does not have a residual value at the end of the 8 years. While Project B will generate

Sh.2.7 Million per annum in perpetuity. The company has a cost of capital of 16%.

Required:

i) Determine the net present value (NPV) of each project (4 Marks)

ii) Based on your calculations above, advice management of Ideal Manufacturing Company the

project to undertake.

Answer 1

You can use Excel's NPV formula for Project A:

=NPV(.16,-4000000,3500000,3500000,3500000,3500000,3500000,3500000,3500000,3500000)

Formula syntax:

=NPV(rate, value1, value2, value3...value9)

rate = 16%, or the cost of capital. value1 is the outlay at the beginning of the project at year 0. value2 through value9 is the cash flow generated annually (year 1 through year 8). The last year's cash flow includes the residual value of zero at the end of the project.

Net present value Project A = Sh. 9,657,386.

Project B:

The net present value of a perpetuity is the annual cash flow divided by the interest rate (cost of capital for the example). The present value of the outlay is -4,000,000, paid at the beginning of the project. So the NPV of Project B is:

=(2700000/0.16)-4000000

Net present value Project B = Sh. 12,875,000.

NPV Project B: Sh. 12,875,000

NPV Project A: Sh. 9,657,386

Project B is a better deal for the company if the outlay is the same for both projects (Sh. 4,000,000).

You can play with different numbers in the formulas to see how it impacts the NPV of each project.

Note: Instead of manually entering annual cash flows in the NPV formula, you can point to the values in your excel spreadsheet. For example: =NPV(0.16,F5:F13).