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]

Simple ways to value stocks and shares

The fundamental basis of value

Stocks and shares confer the right to receive money in the future, and it's this ability to put money in your pocket that gives them their value.  Specifically, the value of a stock is the value of each of those future bits of money all added together.

This is where things start to get a bit tricky, because the value of money you are going to receive in the future depends on three elements:

• how much it is
• when you actually receive it (time value of money) and 
• the return you plan to make in the meantime (internal rate of return or the discount rate).  

For illustration, you plan for your money to make 10% each year.  This is the internal rate of return or the discount rate, depending on which end of the sums you're coming from.  The key point is that a payment of $161.05 in five years' time would have a value today of $100 if you wanted it to deliver a return of 10% a year.

• If you paid more than that then you'd make less than 10%; 
• if you paid less, you'd make more than 10%; and
• if you paid a lot less, you'd make a lot more than 10%.  That's value investing.

When you get a payment that repeats every year, forever, something really handy happens:  the sum of all the individual payments simplifies down to just one payment divided by your discount rate.  

If the payments received are growing - at least if you assume they'll grow at the same rate each year:  you just divided the first payment by the difference between the discount rate and the growth rate (the growth rate effectively offsets part of the discount rate).


The return you plan to make.

For money you plan to commit to the share market, we'd recommend using the long-term return from shares as your discount rate (your "opportunity cost of capital").

• We think 10% is a nice round number to aim for. 
• As long as you choose something in the ballpark of 8 to 12%, though, most of any difference should get lost in the rounding.

Don't confuse value and risk.

Conventional theory says you should finetune your discount rate for different shares, using a higher discount rate for riskier stocks and vice versa, but we think that just confuses the issue.  If something is riskier than something else, it doesn't necessarily mean it has a lower value, it just means that the value is more variable.

How you deal with risk for any particular stock depends on your margin of safety, your diversification and how much risk you're prepared to take.  To understand how these factors all stack up, though, you need to put all stocks on a level playing field in the first place by valuing them on the same basis - which means using the same discount rate.


Related:

• Value Investing is about Buying Stocks for less than they're worth
• Simple ways to value stocks and shares
• Value in the context of Your Overall Portfolio

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)