NET / DISCOUNT RATE / IRR

In simple terms, it is the current value of the money that you may be spending or earning in the future. Today's Rs. 1.00 can be equivalent to Rs.1.10 one year from now in terms of the standard rate that you can get in the market. If so,

1. The NPV of Rs.1.10 on July 30, 2012 is Rs. 1.00 2. The rate that we took as example above is called the "discount rate".

In order to evaluate a project's worthiness, in terms of the and returns over the next few years, we would apply a standard “discount rate” per market interest rates for the degree of risk we are undertaking on that project. We will then sum up the cash inflows (returns) and cash outflows () for each year of evaluation, and take the resultant amount and apply the discount rate for the number of years we are looking ahead, from today.

We would do that for each year of evaluation (investment, returns considered) similarly and arrive at the actual earnings in today's value for all those future earnings and investments.

If the resultant number is negative, it would mean negative returns on investment with respect to NPV.

If the resultant number is positive, it would mean positive returns on investment with respect to NPV.

If we compare two projects for such NPV, then the higher the NPV the better it is (considering the same amount of initial investments on both projects)

It is also common to consider variable discount rates across years for more realistic evaluation of the project’s value in today’s terms

Formula:

Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms,

where

t - the time of the cash flow i - the discount rate (the that could be earned on an investment in the financial markets with similar risk); the opportunity Rt - the net cash flow (the amount of cash, inflow minus outflow) at time t.

If... It means... Then...

NPV > the investment would the project may be accepted 0 add value to the firm

the investment would NPV < subtract value from the the project should be rejected 0 firm

We should be indifferent in the decision whether to accept or reject the the investment would NPV = project. This project adds no monetary value. Decision should be based neither gain nor lose 0 on other criteria, e.g. strategic positioning or other factors not explicitly value for the firm included in the calculation.

Example of NPV

A corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery, and employee training costs). Other cash outflows for years 1–6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 each for years 1–6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:

Year Cash flow Present value

T=0 -$100,000

T=1 $22,727

T=2 $20,661

T=3 $18,783

T=4 $17,075

T=5 $15,523

T=6 $14,112

The sum of all these present values is the , which equals $8,881.52. Since the NPV is greater than zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if there is no mutually exclusive alternative with a higher NPV.

Note: NPV does not consider Risk or Inflation in the calculation. In other words, we consider a standard rate for inflation across projects, which is OK, but considering the same rate for risk is not. It should be considered in addition to NPV.

IRR – Internal Rate of Return / / Rate of Return

The internal rate of return on an investment or project is the "annualized effective compounded return rate" or discount rate that makes the net present value (NPV) of all cash flows (both positive and negative) from a particular investment equal to zero.

In more specific terms, the IRR of an investment is the discount rate at which the NPV of costs (negative cash flows) of the investment equals the NPV of the benefits (positive cash flows) of the investment.

Internal rates of return are commonly used to evaluate the desirability of investments or projects. The higher a project's internal rate of return, the more desirable it is to undertake the project. Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

A firm should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital.

Formula:

Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return. A rate of return for which this function is zero is an internal rate of return.

Given the (period, cash flow) pairs (n, Cn) where n is a positive integer, the total number of periods N, and the net present value NPV, the internal rate of return is given by r in:

The period is usually given in years.

Example of IRR

If an investment may be given by the sequence of cash flows

Year (n) Cash Flow (Cn) 0 -4000 1 1200 2 1410 3 1875 4 1050

then the IRR r is given by a 0 NPV. Solve the equation.

.

In this case, the answer is 14.3%

Please note that the calculation involved here is mathematical to an extent that will not come in your PMP exam – but the principles and leading indicators would be used in guiding you to the right answer, so be aware of the concept to the extent we have provided here