Internal Rate of Return

Internal Rate of Return (IRR)

• is the discount rate that generates a zero net present value for a series of future cash flows
• it equates the present value of the future net cash flows from an investment project with the initial cash outflow of the project
• it is calculated by employing trial and error method
• a higher cost of capital lowers the value of NPV and vice versa
• it takes into account the concept of time value of money
• project with IRR more than the required rate of return is considered as acceptable and profitable.

IRR > Required rate of return, accept the project

IRR < Required rate of return, reject the project

IRR = DISCOUNT RATE for positive NPV  + [DISCOUNT RATE DIFFERENCE x (Positive NPV / (Positive NPV - Negative NPV)]



Example:

DISCOUNT RATE @ 18%
Initial Investment 160,000
Cash flows of constant 55,000 for year 1 to year 5.
Given that the discount rate or required rate of return is 18%.
Total Present Value 171,994.41 #
Total Investment  (160,000)

Net Present Value 11,994.41

DISCOUNT RATE @ 24%
IRR is the discount rate that generates zero NPV.
Increasing the discount rate will lower the NPV.
To generate negative NPV, we have to increase the discount rate.
Let this discount rate or cost of capital to be 24%.

Using discount rate of 24%, the values are as follow:

Initial Investment 160,000
Cash flows of constant 55,000 for year 1 to year 5.
Given that the discount rate or required rate of return is 24%
Total Present Value 150,996.15 #
Total Investment  (160,000)

Net Present Value -9,003.85



CALCULATION

IRR

= DISCOUNT RATE for positive NPV  + [DISCOUNT RATE DIFFERENCE x (Positive NPV / (Positive NPV - Negative NPV)]
= [18% + (24% - 18%) {11,994/(11,994-(-9,003.85)}] x 100%
= 18% + 3.4%
= 21.4%

As the cost of capital for this project is 21.4% and the firm will only receive 18% for each dollar invested, the company should not accept this project.




# Note:  The total present value can be calculated thus
CF1/[(1+r)^1]  + CF2/[(1+r)^2] + CF3/[(1+r)^3] + .... CF3/[(1+r)^n]

Project Evaluation

The decisions of where to invest the company's resources have a major impact on the future competitiveness of the company.

Trying to get involved in the right projects is worth an effort, both to

• avoid wasting the company's time and resources in meaningless activities, and 
• to improve the chances of success.

Project evaluation is a process used to determine whether a firm's investments are worth pursuing.

Producing new products, buying a new machine and investing in a new plant are examples of firm's investment.

Investing in those activities involves a major capital expenditure, and management needs to use capital budgeting techniques to determine which projects will yield the most return over an applicable period of time.



Capital Budgeting Factors

Factors involved in capital budgeting are:

1.  Initial Cost
The initial investment or cash capital required to start a project.

2.  Cash In Flow
The estimated cash amount that flows into a business due to operations of the project or business.

3.  Investment Period
The duration of the project and when it is estimated to be completed.

4.  Discount Factor
The value of interest that will be received or charged during the period of the project's execution and it will affect the present value of cash in flows for different years.

5.  Time Value of Money
The idea that a ringgit now is worth more than a ringgit in the future, even after adjusting for inflation, because a ringgit now can earn interest or other appreciation until the time the ringgit  in the future would be received.This theory has its base in the calculation for present value.



Factors influencing investment decision

A firm must make an investment decision to improve or increase the incomes of the company in order to compete in the market.

Investment environments include:

1.  Product development/enhancement
2.  Replacing equipment/machinery
3.  Exploration of new fields or business.



Project Evaluation Methods

Common methods used in evaluating projects, investments or alternatives are:

1.  Payback Period (PBP)
2.  Accounting Rate of Return/Average Rate of Return (ARR)
3.  Net Present Value (NPV)
4.  Profitability Index (PI)
5.  Internal Rate of Return (IRR)


In choosing an investment or project, select the project which generates HIGHER ARR, NPV, PI and IRR; and SHORTER PBP.



APPENDIX:

NPV and IRR - place more importance to the Assumptions than to the Output. "Garbage in, garbage out"

Any attempt to value businesses with precision will yield values that are precisely inaccurate.  The problem is that it is easy to confuse the capability to make precise forecasts with the ability to make accurate ones.

Anyone wi th a simple, hand-held calculator can perform net present va lue (NPV) and internal rate of return (IRR) calculations.  The NPV calculation provides a single-point value of an investment by discounting estimates of future cash flow back to the present.  IRR, using assumptions of future cash flow and price paid, is a calculation of the rate of return on an investment to as many decimal places as desired.

The seeming precision provided by NPV and IRR calculations can give investors a false sense of certainty for they are really as accurate as the cash flow assumptions that were used to derive them.

The advent of the computerized spreadsheet has exacerbated this problem, creating the illusion of extensive and thoughtful analysis, even for the most haphazard of efforts.  Typically, investors place a great deal of importance on the output, even though they pay little attention to the assumptions.  "Garbage in, garbage out" is an apt description of the process.

Net Present Value and Internal Rate of Return Summarize the Returns for a Given Series of Cash Flows

NPV and IRR are wonderful at summarizing, in absolute and percentage terms, respectively, the returns for a given series of cash flows.

When cash flows are contractually determined, as in the case of a bond, and when all payments are received when due, IRR provides the precise rate of return to the investor while NPV describes the value of the investment at a given discount rate.

In the case of a bond, these calculations allow investors to quantify their returns under one set of assumptions, that is, that contractual payments are received when due.

These tools, however, are of no use in determining the likelihood that investors will actually receive all contractual payments and, in fact, achieve the projected returns.

How much should you pay for a business? Valuing a company (6)

Cash flows

When considering purchasing a company, another way to value the business is to examine what cash it will generate over a period of time.

• This can be in straight cash terms not taking into account inflation, price erosion etc. 
• You may also wish to apply discounted cash flow principles to arrive at a net present value (NPV) for the company, or 
• even an internal rate of return (IRR) on the purchase.
• 
  

Perhaps the most useful way to value it is to estimate the economic benefits that the business will generate in the next few years and then apply the NPV process to them. All valuations based on forecast figures are essentially educated guesses, but this analysis is likely to pinpoint the best opportunity for creating value, if the forecasts turn into reality.

Also read:

Valuing a company (1)

Valuing a company using Asset Value (2)

Valuing a company using Multipliers (3)

Valuing a company using Market Capitalisation (4)

Valuing a company using Non-Financial Measures & Balanced Scoreboard (5)

Valuing a company using Cash Flows (6)