## Numeric Model

1) Payback Period

2) Discounted Cash Flow

3) Internal Rate of Return

4) Profitability Index

### 1) Payback Period

Its the period for initial fixed investment divided by the estimated annual net cash in-flows for/from the project.

This ratio is the number of years required for the project to repay its initial fixed investment.

Example. A project costs 100 K \$ to implement and annual net cash inflow 25 K \$ then payback period is 100 K/ 25 K = 4 Years.

The faster investment is recovered the risk the firm is to exposed and this model ignores any cash inflows beyond the payback period.

### 2) Discounted Cash Flow [Net Present Value ( NPV)]

This determines the net present value of all cash flows by discounting them by the required rate of return known as ‘hurdle rate’ or ‘cutoff rate’.

where,

Ft – The net cash flow in period t

k  – Required rate of return

A0 – Initial cash investment( outflow,will be negative).

To include the impact of inflation/deflation where Pt is predicated rate of inflation during period t, then we have

The project is acceptable if the sum of estimated value of all estimated cash flow over life cycle of project is positive

### 3) Internal Rate of Return

If we have set of expected cash inflows and cash outflows the internal rate of return is the discount rate that is equates the present value of the two set of flows.
If At is outflow for period t and Rt is inflow for period t then Internal rate of return k should satisfy following equation

The value of k is found by trial and error.

### 4) Profitability Index

It is known as benefit cost ratio. It is a net present value of all future expected cash flows divided by the internal cash investment.