NPV for cash flow in perpetuity investment, discount, positive, expected, generate

JustasS

Came across an example question and I'm confused how this is calculated

Question:
Cutter Inc. is considering the purchase of a new material handling system for a cost of 15 million. The system is expected to generate a positive cash flow of 1.8 million per year in perpetuity. What is the NPV of the proposed investment if the discount rate is 10.5%

The answer states
NPV = PV(cash inflows) - CF0
= (1.8 million /.105) - 15 million = 2,142,857

Is this possible to calculate using the NPV function on the BA II, I'm confused how they determined this if the cash flow is indefinate. Can someone help explain?

ajpheif16

Well, I don't have my books with me, but I think it's pretty straightforward.

The PV of a perpetuity is Annuity/Rate. To take the cost of the machine into consideration, you have to subtract it from the PV of the cash flow stream.

As for using the BA II, if you're familiar with calculating the NPV of an ordinary annuity with the cash flow mode, I'd assume you could get pretty close by doing the following:

CF0 = -15 million
CF1 = 1.8 million
F1 = ~9999999999
[NPV]
I = 10.5
[Calculate]

evolsteevol

got it,

Thanks!