Question

Question 2: An investor is set to receive cash flows with the following structure: the first cash flow is of size N, and each subsequent cash flow is greater than the previous by a factor of 1 +g. If there are M cash flows in total with a discount rate of r, what is the net present value of all cash flows? What conditions must be satisfied for these cash flows to have finite value if they are received infinitely, and in this case, what is the net present value?

Answer 1

(a) The NPV will be:

NPV = N / (1+r)1 + [(N*(1+g)) / ((1+r)^2)] + [(N*(1+g)^2) / ((1+r)^3)] + ..........+ [(N*(1+g)^(M-1)) / ((1+r)^M)]

(b) This condition is that the discount rate (r) must be greater than growth rate (g).

Since the cash flow is increasing at a constant rate (1+g) for for infinetly the NPV will be

PV = N / r -g

Now we see that if g is greater than r the denominator turns negative which will give negative present value.

This is due to the present value of a growing perpetuity formula being an infinite geometric series