A project gives you a sequence of cash flows Period Cash flows 5 The cash flow i

Question

A project gives you a sequence of cash flows Period Cash flows 5 The cash flow is always received at the end of each period and the interest rate for each period is 10% and constant throughout the entire time horizon. Is the project profitable? What is the maximum investment you are willing to make for this sequence of cash flows? If the cash flow continues forever and will grow in the same pattern as you observe in the first four periods, abstract a general formula for the cash flow in each period. Ex. Cash flow- f) IlI If the cash flow continues forever, what is the maximum investment you are willing to make for this sequence of cash flows?

Explanation / Answer

I. The project is profitable. Every year the cash flows are increasing at a good rate which will help in recovering the initial investment in short span of time.

In trhis case first of all present value of each year cash flow needs to be computed at 10% discount rate

Present value for Year 1= 1

Year 2= 3/0.10= 30

Year 3= 5/(0.10)^2= 50

Year 4= 7(0.10)^3= 700

Total present value of inflow is 1+30+50+700= 781

Hence maximum investment that one will be willing to make will be a point at which inflow is equal to outflow that is $781.

II. Every year there is a increase of 2 units. Cash flow in year 1 was 1, then 3 in year 2 and so on.

So next year cash flow is 2 units more than previous year cashflow

Hence F(n)= F(n-1)+2

III. For perpetual cash flows, the present value is calculated as Cash flow expected in next year/(Disount rate- growth rate).

Cah flow in next year = 9

Dscount rate given is 10%

Say, average growth rate turns out to be 5% in perpetuity

Then maxmimum amount willing to invest= 9/(0.10-0.05)=9/0.05= 180.

Note: This amount can differ with respect to the assumption made for growth rate as average growth rate for perpuity is not given

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