Question

You have come up with the idea for a new workplace productivity app which you plan to call B1NDER. To develop it, you need to make an immediate investment of $65,000. Given the large number of competing apps in the market, you are worried about how people will respond to your app. You will learn the response in exactly one year. You believe there are three possibilities:

Response to app	Probability	Outcome
Excellent	0.1	Cash flow of $100,000 every year forever (from n=1)
Fair	0.2	Cash flow of $20,000 every year forever (from n=1)
Poor	0.7	Cash flow of 0 every year forever (from n=1)

The opportunity cost of capital is 20%.

What is the NPV of the project?

What is the IRR of the project?

What is the payback period of the project?

Answer 1

Expected CF per anum:

= Sum [ Prob * CF ]

Response	Prob	Cash flow	Exp Cash Flow
Excellent	0.1	$ 100,000.00	$    10,000.00
Fair	0.2	$   20,000.00	$       4,000.00
Poor	0.7	$                 -	$                   -
Expected CF			$    14,000.00

NPV :
NPV is the difference between Present value of Cash Inflows and Present value of cash outflows.

NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.
PV of Cash Inflows = Cash flow / Disc rate

= $ 14000 / 20%

= $ 70000

NPV = PV of Cash Inflows - PV of Cash Outflows

= $ 70000 - $ 65000

= $ 5000

IRR:

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows or Rate of growth is expected from project/ Investment. At IRR, NPV of Project/ Investment will be Zero. It assumes that intermediary Cfs are reinvested at IRR only.
IRR = Cash flow / Initial Investment

= $ 14000 / $ 65000

= 0.2154 I.e 21.54%

Payback period:

Payback period is the period in which initial investment is recovered.

PBP = Initial Investment / Cash flow per anum
If Actual PBP > Expected PBP - Project will be rejected
Actual PBP </= Expected PBP - Project will be accepted

PBP = Initial Investment / Cash flow per anum

= $ 65000 / $ 14000

= 4.64 Years