Saturday, January 30, 2010


Advantages of Payback

Payback is a popular investment criterion in practice. It is considered to have certain virtues.
  • Simplicity. The most significant merit of payback is that it is simple to understand and easy to calculate. The business executives consider the simplicity of method as a virtue. This is evident from their heavy reliance on it for appraising investment proposals in practice.
  • Cost effective. Payback method costs less than most of the sophisticated techniques that require a lot of the analysts’ time and the use of computers.
  • Short term effect. An investor can have more favorable short term effects on earnings per share by setting up a shorter standard payback period. It should, however, be remembered that this may not be a wise long term policy as the investor may have to sacrifice its future growth for current earnings.
  • Risk shield. The risk of the project can be talked by having a shorter standard payback period as it may ensure guarantee against loss. An investor has to invest in many projects where the cash inflows are and life expectancies are highly uncertain. Under such circumstances, payback may become important, not as much as a measure of profitability but as a means of establishing an upper bound on the acceptable degree of risk.
  • Liquidity. The emphasis in payback is on the early recovery of the investment. Thus, it gives an insight into the liquidity of the project. The funds so released can be put to other uses.

Friday, January 29, 2010


Payback Period Method

Payback is the number of years required to recover the original cash flow outlay investment in a project.

The payback is one of the most popular and widely recognized traditional methods of evaluating investment proposals.

If the project generates consistent annual cash inflows, the payback period can be computed by dividing cash outlay by the annual cash inflow. That is:

Payback = Initial investment / Annual Cash inflow

Acceptance Rule

Many firms use the payback period as an investment evaluation criterion and method of ranking projects. They compare the project’s payback with a predetermined, standard payback. The project would be accepted if its payback period is less than the maximum or standard payback period set by management. As a ranking method, it gives highest ranking to the project, which has the shortest payback period and lowest ranking to the project with highest payback period. Thus, if the firm has to choose between two mutually exclusive projects, the project with shorter payback period will be selected.

Wednesday, January 27, 2010


Profitability Index

Profitability index is the ration of the present value of cash inflows, at the required rate of return, to the initial cash outflow of the investment. Profitability index is another time adjusted method of evaluating the investment proposals is the benefit-cost (B/C) ratio or profitability index (PI).

PI = Present value of cash inflows/ Initial cash outflow

Acceptance Rule

The following are the profitability index (PI) acceptance rules:
  • Accept the project when profitability index is grater than one
  • Rejected the project when profitability index is less than one
  • May accept the project when profitability index equal one

The project with positive net present value will have profitability index grater than one. Profitability index less than one means that the project’s net present value is negative
Evaluation of profitability index (PI) method

Profitability index (PI) is a conceptually sound method of appraising investment projects. It is a variation of the net present value (NPV) method, and requires the same computations as the net present value (NPV) method.

  • Time value. It recognizes the time value of money.
  • Value maximization. It is consistent with the shareholder value maximization principle. A project with profitability index grater than one will have positive net present value (NPV) and if accepted, it will increase shareholders wealth.
  • Relative profitability. In the profitability index (PI) method, since the present value of cash inflows is divided by the initial cash outflow, it is a relative measure of a project’s profitability.

Like the net present value (NPV) method, this criterion also requires calculation of cash flows and estimate of the discount rate. In practice, estimation of cash flows and discount rate pose problems.

Monday, January 25, 2010


Evaluation of Internal Rate of Return Method

Internal rate of return (IRR) method is like the net present value (NPV). It is a popular investment criterion since it measures profitability as a percentage and can be easily compared with the opportunity cost of capital. Internal rate of return (IRR) method has following merits:
  • Time value. The internal rate of return (IRR) method recognizes the time value of money.
  • Profitability measure. It considers all cash flows occurring over the entire life of the project to calculate its rate or return.
  • Acceptance rule. It generally gives the same acceptance rule as the net present value (NPV) method.
  • Shareholder value. It is consistent with the shareholders wealth maximization objective. Whenever a project’s internal rate of return (IRR) is grater than the opportunity cost of capital, the shareholders wealth will be enhance.

Here is the briefly mention the problems that internal rate of return (IRR) method may suffer from.

  • Multiple rates. A project may have multiple rates, or it may not have a unique rate of return. These problems arise because of the mathematics of internal rate of return (IRR) computation.
  • Mutually exclusive projects. It may also fail to indicate a correct choice between mutually exclusive projects under certain situations.
  • Value additively. Unlike in the case of the net present value (NPV) method, the value additively principle does not hold when the internal rate of return (IRR) method is used internal rate of returns (IRRs) of projects do not add. Thus, for projects A and B, IRR (A) + IRR (B) need not be equal to IRR (A+B).

Sunday, January 24, 2010


Internal Rate of Return (IRR)

The internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implied that the rate of return is the discount rate which makes net present value (NPV) =0. There is no satisfactory way of defining the true rate of return of a long term asset. Internal rate of return (IRR) is the best available concept. We shall see that although it is very frequently used concept in finance, yet at times it can be a misleading measure of investment worth.

The internal rate of return (IRR) method is another discounted cash flow method for investment appraisal, which takes account of the magnitude and timing of cash flows. Other terms used to describe the internal rate of return (IRR) method are yield on an investment, marginally efficiency of capital, rate of return over cost, time adjusted rate of internal return and so on.

Friday, January 22, 2010


Limitations of Net Present Value

The net present value (NPV) method is a theoretically sound method. In practice, it may pose some computation problems.
  • Cash flow estimation. The net present value (NPV) method is easy to use if fore casted cash flows are known. In practice, it is quite difficult to obtain the estimates of cash flows due to uncertainty.
  • Discount rate. It is also difficult in practice to precisely measure the discount rate.
  • Mutually exclusive projects. Further, caution needs to be applied in using the net present value (NPV) method when alternative projects with unequal lives, or under funds constraint are evaluated. The net present value (NPV) rule may not give unambiguous results in these situations.
    • Ranking of projects. It should be noted that the ranking of investment projects as per the net present value (NPV) rule is not independent of the discount rates.

Thursday, January 21, 2010


Importance of the Net Present Value (NPV)

Net present value (NPV) is the true measure of an investment’s profitability. It provides the most acceptable investment rule for the following reasons:
  • Time value. It recognizes the time value of money-a $ received today is worth more than a $ received tomorrow.
  • Measure of true profitability. It uses all cash flows occurring over the entire life of the project in calculating its worth. Hence, it is a measure of the project’s true profitability. The net present value method relies on estimated cash flows and the discount rate rather than any arbitrary assumptions, or subjective considerations.
  • Value additively. The discounting process facilitates measuring cash flows in terms of present values that is in terms of equivalent, current $. Therefore, the net present values of projects can be added. For example, NPV (A+B) =NPV (A) +NPV (B). This is called the value additively principle. It implies that if we know the net present values (NPV) of individual projects, the value of the firm will increases by the sum of their net present values (NPVs). We can also say that if we know values of individual assets, the firm’s value can simply be found by adding their values. The value additively is an important property of an investment criterion because it means that each project can be evaluated, independent of others, on its own merit.
  • Shareholder value. The net present value (NPV) method is always consistent with the objective of the shareholder value maximization. This is the greatest virtue of the method.

Monday, January 18, 2010


Net Present Value Method (NPV)

The net present value (NPV) method is the classic economic method of evaluating the investment proposals. It is discounted cash flow technique that explicitly recognizes the tine value of money. It correctly postulates that cash flows arising at different time periods differ in value and are comparable only when their equivalents present values are found out. The following steps involved in the calculation net present value (NPV):
  • Cash flows of the investment project should be forecast ed based on realistic assumptions.
  • Appropriate discount rate should be identified to discount the forecast ed cash flows. The appropriate discount rate is the projects opportunity cost of capital, which is equal to the required rate of return expected by investors on investments of equivalent risk.
  • Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate.
  • Net present value (NPV) should be found out by subtracting present value of cash outflows from present value of cash inflows. The project should be accepted if net present value (NPV) is positive.

Project acceptance rule using net present value

It should be clear that the acceptance rule using the net present value (NPV) method is to accept the investment project if its net present value (NPV) is positive and to reject it if the net present value (NPV) is negative. Positive net present value (NPV) contributes to the net wealth of the shareholders, which should result in the increased price of a firm’s share. The positive net present value (NPV) will result only if the project generates cash inflows at a rate higher than the opportunity cost of capital. A project with zero net present value (NPV) may be accepted. A zero net present value (NPV) implies that project generates cash flow at a rate just equal to the opportunity cost of capital.

The net present value (NPV) acceptance rules are:

  • Accept the project net present value (NPV) is positive
  • Reject the project net present value (NPV) is negative
  • May accept the project when net present (NPV) is zero

The net present value (NPV) can be used to select between mutually exclusive projects; the one with the higher net present value (NPV) should be selected. Using the net present value (NPV) method, projects would be ranked in order of net present values; that is, first rank will be given to the project with higher positive net present value (NPV) and so on.

Sunday, January 17, 2010


Investment Appraisal Criteria

A number of investment appraisal criteria or capital budgeting techniques are in use of practice. They may be grouped in the following two categories:
  1. Discounted cash flow criteria
    • Net present value (NPV)
    • Internal rate of return (IRR)
    • Profitability index (PI)
  2. Non discounted cash flow criteria
    Payback period
    • Accounting rate of return
    • Discounted payback period

Discounted payback is a variation of the payback method. It involves discounted cash flows, but it is not a true measure of investment profitability. We will show in our following posts the net present value (NPV) criterion is the most valid technique of evaluating an investment project. It is consistent with the objective of maximizing the shareholders wealth.

Friday, January 15, 2010


Investment Evaluation Criteria

Three steps are involved in the evaluation of an investment:
  • Estimation of cash flows
  • Estimation of the required rate of return (the cast of capital)
  • Application of a decision rule for decision rule for making the choice

Investment decision rule

The investment decision rules may be referred to as capital budgeting techniques, or investment criteria. A sound appraisal technique should be used to measure the economic worth of an investment project. The essential property of a sound technique is that is should maximize the shareholders wealth. The following other characteristics should also be possessed by a sound investment evaluation criterion:

  • It should consider all cash flows to determine the true profitability of then project.
  • It should provide for an objective and unambiguous way of separate good projects from bad projects.
  • It should help ranking of projects according to their true profitability.
  • It should recognize the fact that bigger cash flows are preferable to smaller ones and early cash flows are preferable to later ones.
  • It should help to choose among mutually exclusive projects that project which maximizes the shareholders wealth.
  • It should be a criterion which is applicable to any conceivable investment project independent of others.

These conditions will be clarified as we discuss the features of various investment criteria in the following posts.

Wednesday, January 13, 2010


Types of Investment Decisions (2)

Another useful way of classify investments is as follows
  • Mutually exclusive investment
  • Independent investment
  • Contingent investment

Mutually exclusive investment

Mutually exclusive investments serve the same purpose and compete with each other. If one investment is undertaken, others will have to be excluded. A company may, for example, either use a more labor intensive, semi automatic machine, or employ a more capital intensive, highly automatic machine for production. Choosing the semi-automatic machine precludes the acceptance of the highly automatic machine.

Independent investment

Independent investments serve different purposes and do not compete with each other. For example, a heavy engineering company may be considering expansion of its plant capacity to manufacture additional excavators and addition of new production facilities to manufacture a new product light commercial vehicles. Depending on their profitability and availability of funds, the company can undertake both investments.

Contingent investment

Contingent investments are dependent projects; the choice of one investment necessitates undertaking one or more other investment. For example, if a company decides to build a factory in a remote, backward area, it may have to invest in houses, roads, hospitals, etc. For employees to attract the work force thus, building of factory also requires investment in facilities for employees. The total expenditure will be treated as one single investment.

Monday, January 11, 2010


Types of Investment Decisions

One of the classifications is as follows,
  • Expansion of existing business
  • Expansion of new business
  • Replacement and moderation

Expansion and Diversification

A company may add capacity to its existing product lines to expand existing operation. For example, the Company Y may increase its plant capacity to manufacture more “X”. It is an example of related diversification. A firm may expand its activities in a new business. Expansion of a new business requires investment in new products and a new kind of production activity within the firm. If a packing manufacturing company invest in a new plant and machinery to produce ball bearings, which the firm has not manufacture before, this represents expansion of new business or unrelated diversification. Sometimes a company acquires existing firms to expand its business. In either case, the firm makes investment in the expectation of additional revenue. Investment in existing or new products may also be called as revenue expansion investment.

Replacement and Modernization

The main objective of modernization and replacement is to improve operating efficiency and reduce costs. Cost savings will reflect in the increased profits, but the firm’s revenue may remain unchanged. Assets become outdated and obsolete with technological changes. The firm must decide to replace those assets with new assets that operate more economically. If a Garment company changes from semi automatic washing equipment to fully automatic washing equipment, it is an example of modernization and replacement. Replacement decisions help to introduce more efficient and economical assets and therefore, are also called cost reduction investments. However, replacement decisions that involve substantial modernization and technological improvements expand revenues as well as reduce costs.

Saturday, January 9, 2010


Importance of Investment Decisions

Investment decisions require special attention because of the following reasons:
  • They influence the firm’s growth in the long run
  • They affect the risk of the firm
  • They involve commitment of large amount of funds
  • They are irreversible, or reversible at substantial loss
  • They are among the most difficult decisions to make


The effects of investment decisions extend into the future and have to be endured for a longer period than the consequences of the current operating expenditure. A firm’s decision to invest in long term assets has decisive influence on the rate and direction of its growth. A wrong decision can prove disastrous for the continued survival of the firm; unwanted or unprofitable expansion of assets will result in heavy operating costs to the firm. On the other hand inadequate investment in assets would make it difficult for the firm to compete successfully and maintain its market share.


A long-term commitment of funds may also change the risk complexity of the firm. If the adoption of an investment increases average gain but causes frequent fluctuations in its earnings, the firm will become more risky. Thus, investment decisions shape the basic character of a firm.


Investment decisions generally involve large amount of funds, which make it imperative for the firm to plan its investment programmers very carefully and make an advance arrangement for procuring finances internally or externally.


Most Investment decisions are irreversible. It is difficult to find a market for such capital items once they have been acquired. The firm will incur heavy losses if such assets are scrapped.


Investment decisions are among the firm’s most difficult decisions. They are an assessment of future events, which are difficult to predict. It is really a complex problem to correctly estimate the future cash flows of an investment. Economic, political, social and technological forces cause the uncertainty in cash flow estimation.

Thursday, January 7, 2010


Nature and Introduction of Investment Decisions

An efficient allocation of capital is the most important finance function in the modern items. It involves decisions to commit the firm’s funds to the long term assets. Capital budgeting or investment decisions are of considerable importance to the firm since they tend to determine its value by influencing its growth, profitability and risk.

The investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decisions. A capital budgeting decision may be define as the firm’s decisions to invest its current funds most efficiently in the long term assets in anticipation of an expected flow of benefits over a series of years.

The long term assets are those that affect the firm’s operations beyond the one year period. The firm’s investment decisions would generally include expansion, acquisition, modernization and replacement of the long term asset. Sale of division or business is also as an investment decision. Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programmed have long term implications for the firm’s expenditures and benefits, and therefore, they should also be evaluated as investment decisions.

It is important to note that investment in the long term assets invariably requires large funds to be tied up in the current assets such as inventories and receivables. As such, investment in fixed and current assets is one single activity.

The following are the features of investment decisions,
  • The exchange of current funds for future benefits.
  • The funds are invested in long term assets.
  • The future benefits will occur to the firm over a series of years.

Tuesday, January 5, 2010


Ordinary Share as an Option

One distinguishing feature of ordinary share is that it has limited liability. The limited liability feature provides an opportunity to the shareholders to default on a debt. If a firm has incurred a debt, each time a payment is due, the shareholders can decide to make payment or to default.

If the firm’s value is more than the payment that is due, the shareholders will make payment since they shall be left with a positive value of their equity and keep the firm. If the payment that is due is more than the value of the firm, the shareholders will default and let the debt holders keep the firm. Since the shareholders have a hidden right to default on debt without any liability, the debt contract gives them a call option on the firm.

The debt holders are the sellers of call option to the share holders. The amount of debt to be repaid is the exercise price and the maturity of debt is the time to expiration.

The value of the shareholders equity is the difference between total value of the firm and the value of the debt. The value of equity cannot be negative. If the value of the firm is less than the value of the debt, the shareholders will not exercise the option of owning the firm. Thus, at the time of exercising the option, the value of equity will be either the excess of the total firm’s value over the value of the debt or zero.

There is an alternate way of looking at ordinary share as an option. The shareholders’ option can be interpreted as a put option. The share holders can sell (handover) the firm to the debt holders at zero exercise prices if they do not want to make the payment that is due.

We can use the black-scholes model to value the ordinary share as an option.

Monday, January 4, 2010


Option valuation

Option’s delta or Hedge ratio

We have earlier explained the concept of the option’s delta. The hedge ratio is commonly called the option’s delta. The hedge ratio is a tool that enables us to summarize the overall exposure of portfolios of options with various exercise prices and maturity periods. An option’s hedge ratio is the change in the option price for a 1$ increase in the share price. A call option has a positive hedge ratio and a put option has a negative hedge ratio.

Under the black scholes option formula, the hedge ratio of a call option is N (d1) and the hedge ratio for a put is N (d1)-1. Recall that N (d) stands for the area under the standard normal curve up to d. Therefore, the call option hedge ratio must be positive and the put option hedge ratio is negative and of smaller absolute value than 1.0.

Implied Volatility

The black scholes option valuation assumes that the volatility is given. We can ask a different question. What is the volatility (or standard deviation) for the observed option price to be consistent with the black scholes formula? This is implied volatility of the stock. Implied volatility is the volatility that the option price implies. An investor can compare the actual and implied volatility.

If the actual volatility is higher than the implied volatility, the investor may conclude that the option’s fair price is more than the observed price. Hence, she may consider option as potentially a good investment. You can use the excel spreadsheet to calculate the black scholes option price and implied volatility's.

Dividend paying share option

The share prices go down by an amount reflecting the payment of dividend. As a consequence, the value of a call option will decrease and the value of a put option will increase. The share price is assumed to have a risk less component and a risky component. The black scholes model includes the risky component of the share price. The present value of dividends (from ex-dividend dates to present) can be treated as the risk-less component of the share price.

Thus, for valuing a call option, we should adjust downwards the share price for the present value of the dividend payments during the life of the option, and then use the black scholes model. We also need to adjust the volatility in case of a dividend-paying share since in the black scholes model it is the volatility of the risky part of the share price. This is generally ignored in practice.

Sunday, January 3, 2010


Black and Scholes Model (B-S Model) For Option Valuation

The logic of valuing a call option, as discussed in the previous posts, is quite simple. The framework can, however, be extended beyond two periods. We can also make the time period and the movement in the share price very small. The computation would be quite complex, fortunately, we can use the Black and Scholes (B-S0 model.

Which, under certain assumption, can be used for valuing options as the time period becomes continuous.


The Black and Scholes (B-S) model is based on the following assumptions,
  • The rates of return on a share are log normally distributed.
  • The value of the share (the underlying asset) and the risk free rate of are constant during the life of the option.
  • The market is efficient and there are no transaction costs and taxes.
  • There is no dividend to be paid on the share during the life of the option.

Friday, January 1, 2010


Bi nominal Model for Option Value

In previous posts we have enumerated factors that influence the value of an option. Let us examine the methods of valuing options next.

We shall illustrate only the valuation of stock (share) options. We shall first discuss simple binomial tree approach to option valuation and later the Black schools option valuation model.
Inadequacy of Discounted cash flow analysis

As we discussed that assets are valued using the discounted cash flow approach. The value of an asset equals the discounted value of its cash flows. Is not the value of an option its present value?

The discounted cash flow approach does not work for options because of the difficulty in determining the required rate of return of an option. Options are derivative securities. Their risk is derived from the risk of the underlying security. The market value of a share continuously changes. Consequently, the required rate of return to a stock option is also continuously changing. Therefore, it is not feasible to value options using the discounted cash flow technique.

Options give the holder a right over the favorable outcomes of an asset. These outcomes are, however, highly risky. But a buyer pays much less for an option than the price of the asset. The buyer makes a very small investment in high risk outcomes. Options are more risky than the underlying asset.

A simple binomial approach to option valuation

Suppose you own a share that has a current price of 150$. Its price at the end of one year has two possibilities: either 100$ or 300$. Assume that you buy a call option on the share with an exercise price of 200$. At the end of the year, you will exercise your option if the share price is 300$ and the value of the option you will be 300$-100$ = 100$. You will forgo your call option if the share price is 100$, and the value of option will be zero.


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