Net Present Value and Profitability Index

Net Present Value (NPV)

• an indicator of how much value an investment could contribute to the firm
• takes into account the concept of time value of money
• the Present Value Interest Factor (PVIF) Table can be used to calculate present value
• the criteria below should be considered before accepting for rejecting a project or an investment:

NPV > 0  

The investment would add value to the firm.

The project should be accepted.

NPV < 0

The investment would subtract value from the firm, that means the project reduces shareholder wealth.

The project should be rejected.

NPV = 0

The investment would neither gain nor lose value for the firm.

We would be indifferent in the decision whether to accept or reject the project.  This project adds no monetary value.  Decision should be made based on OTHER CRITERIA.

Total Present Value = sum of the discounted value of all future cash flows.

NPV =  Total Present Value - Total Investment.

Probability Index 

The project is not profitable when its profitability index (PI) is less than 1.00

PI = Total Present Value / Total Investment

Flexibility: The inclusion of flexibility into the analysis is generally more relevant in the valuation of individual businesses and projects.

Net present values (NPVs) calculated from single cash flow projections may be inadequate because they do not take into account the ability to expand or scale back.



Here is a simple example.  

A firm can scale back by eliminating a negative cash flow project after the first period.

There is a 60% probability of $20 per year forever or 40% probability of -$6 per year forever.

The discount rate is 10%.


Without an option to cancel

If the initial cost today is $100, then without an option to cancel, the NPV would be:

-$100 + 0.6 x ($20/0.10) + 0.4 x (-$6/0.10) = -$4


With an option to cancel after the first year

With the option to abandon after the first year, the NPV would be:

-$100 + 0.6 x ($20/0.10) + 0.4 x (-$6/1.10) = $17.82


The value of the option to cancel the project is the difference, or $21.82



Conclusion:

The inclusion of flexibility into the analysis is generally more relevant in the valuation of individual businesses and projects.

The real-option valuation (ROV) and decision tree analysis (DTA) are the two primary methods of valuation.

• Both depend on forecasting based on contingent states of the world.
• Although ROV is often a better methodology to use than DTA, it is not the right approach in every case.

Dividend Discount Model

Present Value Models

Dividend Discount Model


1.  If a company pays regular dividends

The dividend discount model (DDM) values a share of common stock as the present value of its expected future cash flows (dividends).

When an investor sells a share of common stock, the value that the purchaser will pay equals the present value of the future stream of cash flows (i.e. the remaining dividend stream).

Therefore, the value of the stock at any point in time is still determined by its expected future dividends.

When this value is discounted to the present, we are back at the original dividend discount model.



2.  If a company pays no dividends currently

If a company pays no dividends currently, it does not mean that its stock will be worthless.

There is an expectation that after a certain period of time the firm will start making dividend payments.

Currently, the company is reinvesting all its earnings in its business with the expectation that its earnings and dividends will be larger and will grow faster in the future.



3.  If the company is making losses

If the company does not make positive earnings going forward, there will still be an expectation of a liquidating dividend.  

The amount of this dividend will be discounted at the required rate of return to compute the stock's current price.




Additional notes:

The required rate of return on equity is usually estimated using the CAPM.

Another approach for calculating the required return on equity simply adds a risk premium to the before-tax cost of debt of the company.

Investment Decisions

Some investment decisions are easy to make.

• Perhaps, a government safety regulation makes an item of capital expenditure compulsory.
• Or perhaps, an essential piece of machinery breaks down and just has to be replaced.

Many other investment decisions are not nearly so clear cut and hinge on whether the proposed expenditure will generate sufficient future cash savings to justify itself.

There are many very sophisticated techniques for aiding this decision.  Here are three techniques that are commonly used:

• Payback
• Return on investment
• Discounted cash flow.

Payback

This has the merit of being extremely simple to calculate and understand.  It is a simple measure of the period of time taken for the savings made to equal the capital expenditure.

Return on investment

This takes the average of the money saved over the life of the asset and expresses it as a percentage of the original sum invested.

Discounted cash flow.

This technique takes account of the fact that money paid or received in the future is not as valuable as money paid or received now.  For this reason, it is considered superior to payback and to return on investment.  However, it is not as simple to calculate and understand.  Discounted cash flow involves bringing the future values back to its Net Present Value.

Business value cannot be precisely determined. Make use of ranges of values.

Business value cannot be precisely determined. 

Not only do a number of assumptions go into a business valuation, but relevant macro and micro economic factors are constantly changing, making a precise valuation impossible. 

Although anyone with a calculator or a spreadsheet can calculate a net present value of future cash flows, the precise values calculated are only as accurate as the underlying assumptions.

Investors should instead make use of ranges of values, and in some cases, of applying a base value. 

Ben Graham wrote:

The essential point is that security analysis does not seek to determine exactly what is the intrinsic value of a given security. It needs only to establish that the value is adequate—e.g., to pro­tect a bond or to justify a stock purchase—or else that the value is considerably higher or considerably lower than the market price. For such purposes an indefinite and approximate measure of the intrinsic value may be sufficient.

There are only three ways to value a business. 

1.   The first method involves finding the net present value by discounting future cash flows. 

Problems with this method involve trying to predict future cash flows, and determining a discount rate. 

Investors should err on the side of conservatism in making assumptions for use in net present value calculations, and even then a margin of safety should be applied.

2.  The second method is Private Market Value using Multiples. 

This is a multiples approach (e.g. P/E, EV/Sales) based on what business people have paid to acquire whole companies of a similar nature. 

The problems with this method are that comparables assume businesses are all equal, which they are not. 

Furthermore, exuberance can cause business people to make silly decisions. 

Therefore, basing your price on a price based on irrationality can lead to disaster. 

This is believed to be the least useful of the three valuation methods.

3.  Finally, liquidation value as a method of valuation. 

A distinction must be made between a company undergoing a fire sale (i.e. it needs to liquidate immediately to pay debts) and one that can liquidate over time. 

Fixed assets can be difficult to value, as some thought must be given to how customised the assets are (e.g. downtown real-estate is easily sold, mining equipment may not be).

When should each method be employed? 

They can all be used simultaneously to triangulate towards a value. 

In some cases, however, one might place more confidence in one method over the others. 

For example, 

• liquidation value would be more useful for a company with losses that trades below book value, while 
• net present value is more useful for a company with stable cash flows.

Using the methods of valuation described, you can search for stocks that are trading at a severe discount; it is possible, their stock price more than doubled soon after.

Beware of these failures

The failures of relying on a company's earnings per share - too easily massaged.

The failure of relying on a company's book value  - not necessarily relevant to today's value.

The failure of relying on a company's dividend yield - incentives of management to make yields appear attractive at the expense of the company's future.

Read also:

• 
  
• Your investments using Mutual Funds or Money Managers
• Trading and portfolio management from a value investing point of view
• Value Investor's Opportunities in Distressed Securities
• Value Investing Opportunities in the Banking Sector
• Look at FUNDAMENTALS and POTENTIAL CATALYSTS when making investment decisions
• Where to look for Investment Opportunities
• Business value cannot be precisely determined. Make use of ranges of values
• Central elements to a Value Investing Philosophy
• The Philosophy of Value Investing and Why It Works
• Philosophy of value investing. Need to have clear strategies too
• How Wall Streets can create investment fads? The Junk Bond Market of mid-1980s
• Understanding these changes in the investment world allows investors to earn superior returns
• What's good for Wall Street is not necessarily good for investors
• Speculators, Investors and Market Fluctuations

Investment Decisions and Fundamentals of Value

Investment Decision Rules:

Accept all investments with Net Present Value greater than Zero.

Accept all investments with Rates of Return greater than their Opportunity Costs of Capital





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An example:

You are considering an investment opportunity that costs $100,000 and promises to return 10%.

A comparable investment in the financial market returns 15%.

A bank offers to lend you $100,000 at 8% with no conditions.


Questions:

1.  Do you invest $100,000 in the investment opportunity?

Answer:  NO

2.  What is the investment's cost of capital?

Answer:  15%.


Reasons:

You should invest the $100,000 in the financial market that returns 15%.

The financial market provides the investing return standards against which other investments are evaluated.

Financing by the bank loan at 8% was irrelevant to the investment decision.

The investment decision and the financing decision are separate and independent decisions.

After you have made the investment decision, thus:

You are considering an investment opportunity that costs $100,000 and promises to return 10%.

A comparable investment in the financial market returns 15%.

Then you make the financing decision, thus:

A bank offers to lend you $100,000 at 8% with no conditions.

What Does Net Present Value - NPV Mean?

What Does Net Present Value - NPV Mean?

The difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of an investment or project.

NPV analysis is sensitive to the reliability of future cash inflows that an investment or project will yield.

Formula:

In addition to the formula, net present value can often be calculated using tables, and spreadsheets such as Microsoft Excel.

Watch: Understanding Net Present Value

Investopedia explains Net Present Value - NPV
NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account. If the NPV of a prospective project is positive, it should be accepted. However, if NPV is negative, the project should probably be rejected because cash flows will also be negative.

For example, if a retail clothing business wants to purchase an existing store, it would first estimate the future cash flows that store would generate, and then discount those cash flows into one lump-sum present value amount, say $565,000. If the owner of the store was willing to sell his business for less than $565,000, the purchasing company would likely accept the offer as it presents a positive NPV investment. Conversely, if the owner would not sell for less than $565,000, the purchaser would not buy the store, as the investment would present a negative NPV at that time and would, therefore, reduce the overall value of the clothing company.

 http://www.investopedia.com/terms/n/npv.asp?partner=basics090211#ixzz1WtS9g5kS

The Time Value of Money

"A bird in hand (today) is worth two in the bush (tomorrow)."

Everyone would rather have a dollar in his or her pocket today than to receive a dollar far into the future.  Today's dollar is worth more - that it has more value - than a dollar received tomorrow.

The three main reasons for this difference in value are:

1.  Inflation.
Inflation does reduce purchasing power (value) over time.  With a 5% per year inflation, a dollar received a year from today will only buy 95c worth of goods.

2.  Risk
There is always the chance that the promise of a dollar in the future will not be met and you will be out of luck.  The risk could be low with a CD at an FDIC insured bank; or the risk could be high if it is your brother-in-law who is promising to repay a personal loan.

3.  Opportunity Cost.
If you loan your dollar to someone else, you have lost the opportunity to use it yourself.  That opportunity has a value to you today that makes today's dollar worth more than tomorrow's.

These three concepts - inflation, risk, and opportunity cost - are the drivers of present value (PV) and future value (FV) calculations used in capital budgeting and investing.

Present value (PV) calculations are used in business to compare cash flows (cash spent and received) at different times in the future.  Converting cash flows into present values puts these different investments and returns onto a common basis and makes capital budgeting analysis more meaningful and useful in decision-making.

Nominal dollars are just the actual amount spent in dollars taken out of your wallet.  Real dollars are adjusted for inflation.  When you take out inflation (i.e. convert from 'nominal dollars' into 'real dollars') the price difference becomes much more comparable and easy to explain.

Capital Budgeting

In capital budgeting, different projects require different investment and will have different returns over time.  In order to compare projects "apples to apples" and "oranges to oranges" on a financial basis, we will need to convert their cash flows into a common and comparable form.  That common form is present value.

Simply put, a little bit of cash that is invested today followed by lots of cash returned in the near future would be a REALLY GOOD financial investment.  

However, lots of cash invested today followed by a little bit of cash returned in a long time would be a REALLY  BAD investment.

Capital budgeting analysis is as simple as that.

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.
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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)