Wednesday, June 30, 2010


Replacement of an Existing Asset

We have discussed in our previous posts the method of constant replication or replacement chains to choose between assets with different lives. In those cases we assumed that assets are replaced at the end of their physical lives. In practice, replacement decisions should be governed by the economics and necessity considerations. An equipment or asset should be replaced whenever a more economic alternative is available.

A number of companies follow the practice of approving a new machine only when the existing one can no longer perform its job. These companies follow a simple policy of replacement: replacement is necessary when the machine is beyond repair. They do not decide when to replace, the machine decides for them. This is one of the most expensive wrong policies, which a company could follow. Such a policy erodes the company’s profitability by protecting high operating costs. If the competitors follow cost-reduction policies by following a systematic replacement policy and are able to reduce prices in the future, the high cost company will be squeezed out of the market sooner or later.

Management should follow a replacement policy based on economic considerations and decide when to replace. An economic analysis may indicate to replace machine when it is, say, 5 years old with an improved alternative. If the replacement actually takes place when the machine is, say, 20 years old when it is beyond any repair, the company has been incurring extra costs and losing profits for 15 years.

Tuesday, June 29, 2010


Tree Harvesting Problem in Investment

The optimum investment timing analysis is of direct relevance in the case of tree harvesting problems. Suppose that we own a piece of land and are considering growing a crop of trees, we would like to maximize the net present value (NPV) of investment. The maximization of the investment’s net present value (NPV) would depend on when we harvest trees. The future value of trees increases when harvesting is postponed: but the opportunity cost of capital is incurred by not realizing the value by harvesting the trees. The net present value (NPV) will be maximized when the trees are harvested at the point where the percentage increase in value equals the opportunity cost of capital.

Suppose the net future value obtained over the years from harvesting the trees is At, and if the opportunity cost of capital is K, then the present value (PV) of the net realizable value of trees is given by:

PV = At / (1+K) t = At (1+K)-t

To discussion so far can be put in the formal terms. To determine the optimum harvesting time, which maximizes the net present value (NPV), we set the derivative of the net present value (NPV) with respect to t in equation equal to zero:

NPV = Ate –kt – C

dNPV / dt = -kAte –kt + dAte –kt/ dt = 0

Solving for k, we obtain

K = (dAt / dt) / At

The expression (dAt / dt) At is the rate at which the obtainable net future values changes with time; it is the incremental (marginal) rate of change in value. Thus the NPV will be maximized, when the marginal rate of change in value equals the opportunity cost of capital.

Wednesday, June 23, 2010


Investment Timing and Duration

A firm evaluates a number of investment projects every year. In the absence of a capital constraint, it will undertake all those projects, which have positive net present values (NPVs) and reject those, which have negative net present values (NPVs). Further analysis may, however, indicate that some of the profitable projects may be more valuable (that is, they may have higher NPVs) if undertake in the future. If may also be related that some of the unprofitable projects may yield positive NPVs if they are accepted later on. These categories of investment projects may have different degrees of postponability; some of them may be postponed at the most to one or two periods, while a few may be undertaken any time in future. Those projects, while are postponable, involve two mutually exclusive alternatives: undertake investment now, or later. The firm should determine the optimum timing of investment.

The timing of investment may be a critical factor in case of those investment projects, while occur once in a while and those, while are of strategic importance to the firm. Such projects cannot be deferred for long. Postponability also creates uncertainty. For example, the net present value (NPV) analysis may show that a firm should introduce a new product next year. The firm may still decide to introduce the product this year for two reasons: The firm may have a corporate strategy of remaining market leader in introducing new products. If it anticipates that its competitors will introduce the product this year if it does not, it may come up with the product this year to remain the market leader. Also for the reason of unanticipated competition from unknown quarters the firm may decide to introduce the product now.

Tuesday, June 22, 2010


Projects with Different Lives

The correct way of choosing between mutually exclusive projects with the same lives is to compare their net present values (NPVs), and choose the project with a higher net present value (NPV). The two mutually exclusive projects being compared, however, may have different lives. The use of the net present value (NPV) rule without accounting for the difference in the projects’ lives may fail to indicate correct choice. In analyzing such projects, we should answer the question: what would the firm do after the expiry of the short-lived project if it were acquired instead of the long-lived project?

Annual equivalent value method

Assume we are going to choose one machine from two alternative machines called X and Y. In a choice between machines with different lives, we assume that each machine replaced in the last year of its life. For the purpose of analysis, the replacement chains of the machines can be assumed to extend to the periods of time equal to the least common multiple of the lives of the machines.

The method for handling the choice of the mutually exclusive projects with different lives, as discussed above, can become quite cumbersome if the projects’ lives are very long. The problem fortunately can be handled by a simper method. We can calculate the annual equivalent value (AEV) of cash flows of each project. We shall select the project that has lower annual equivalent cost.

AEV = NPV / Annuity factor

Saturday, June 19, 2010


Complex Investment Decisions

The simple accept or reject investment decisions with conventional cash flows may not be quite common in practice. Generally, a firm faces complex investment situations and has to choose among alternatives. The use of the net present value (NPV) rule can be extended to handle complicated investment decisions.

The choice between mutually exclusive projects is a simple example of project interaction. Project interactions occur in numerous other ways.

The following are some of the complex investment problems, which we shall discuss in our next posts.
  • How shall choice be made between investments with different lives?
  • Should a firm make investment now, or should it wait and invest later?
  • When should an existing asset be replaced?
  • How shall choice be made between investments under capital rationing?

Thursday, June 17, 2010


Important Points about Cash Flow Calculation
  • Free cash flows and the discount rate

Free cash flows are available to service both the shareholders and the debt holders. Therefore, debt flows (interest charges and repayment of principle) are not considered in the computation of free cash flows. The financing effect is captured by the firm’s weighted cost of debt and equity, which is used to discount the project’s cash flows. This approach is based on two assumptions:

  1. The project’s risk is the same as the firm’s risk
  2. The firm’s debt ratio is consistent and the project’s debt capacity is the same as the firm’s.
  • Terminal cash flows

Terminal cash are those, which occur in the projects last year in addition to annual cash flows. They would consist of the after tax salvage value of the project and working capital released (if any). In case of replacement decision, the foregone salvage value of old asset should also be taken into account.

  • Terminal value of new product

Terminal value of new product may depend on the cash flows, which could be generated much beyond the assumed analysis or horizon period. The firm may make reasonable assumption regarding the cash flow growth rate after the horizon period.

  • Incremental cash flows

The term incremental cash flows should be interpreted carefully. The concept should be extended to include the opportunity cost of the existing facilities used by the proposal. Sunk cost and the allocated overheads are irrelevant in computing cash flows. Similarly, a new project may cannibalize sales of the existing products. The project’s cash flows should adjust for the reduction in cash flows on account of the cannibalization.

  • Inflation

The net present value (NPV) rule gives correct answer to choose an investment under inflation if it is treated consistently in cash flows and discount rate. The discount rate is a market determined rate and therefore, includes the expected inflation rate. It is thus generally stated in nominal terms. The cash flows should also be stated in nominal terms to obtain an unbiased net present value (NPV). Alternatively, the real cash flows can be discounted at the real discount rate to calculate unbiased net present value (NPV).

Tuesday, June 15, 2010


Important Points about Cash Flow Calculation

The estimation of cash flows, through difficult, is the most crucial step in investment analysis. Here are some important points about cash flow calculation.
  • Profits vs. cash flows

Cash flows are different from profits. Profit is not necessarily a cash flow; it is the difference between revenue earned and expenses incurred rather than cash received and cash paid. Also, in the calculation of profits, an arbitrary distinction between revenue expenditure is made.

  • Incremental cash flows

Cash flows should be estimated on Incremental basis. Incremental cash flows are found out by comparing alternative investment projects. The comparison may simply be between cash flows with and without the investment proposal under consideration when real alternatives do not exist.

  • Components of cash flows

Three components of cash flows can be identified: (1) initial investment (2) annual cash flows, and (3) terminal cash flows.

  • Initial investment

Initial investment will comprise the original cost (including freight and installation charges) of the project, plus any increase in working capital. In the case of replacement decision, the after-tax salvage value of the old asset should also be adjusted to compute the initial investment.

  • Net cash flow

Annual net cash flow is the difference between cash inflows including taxes. Tax computations are based on accounting profits. Care should be taken in properly adjusting deprecation while computing net cash flows.

  • Depreciation

Depreciation is a non-cash flow through tax shield. The following formula can be used to calculate change in net cash flows from operations

  • Working capital and capital expenditure

In practice, changes in Working capital items – debtors (receivable), creditors (payable) and stock (inventory) – affect cash flows. Also, the firm may be required to incur capital expenditure, during the operation of the investment project.

Thursday, June 10, 2010


Financing Effects in Investment Evaluation

In our discussion so far, we have ignored the question of financing an investment projects in the computation of new cash flows. We have implicitly assume that the firm undertaking the project is a pure-equity financed firm and therefore, the project is sub just only to business risk. The opportunity cost of capital as the discount rate reflects the business risk of the project. Hence the net present value of the project does not include the financing effect.

A firm in practice may finance an investment project either by debt or partly by debt and partly by equity. How should we treat the financing effects in the investment evaluation? Should the proceeds of debt and equity and payments of interest, dividends and principle be considered in the computation of the investment’s net cash flows? According to the conventional capital budgeting approach in which the discount rate is adjusted for financing effects, cash flows should not be adjusted for the financing effects. The firm should not treat the debt and equity proceeds as the investment’s inflows nor should it recognize payment interest, dividends and principle as outflows. Thus, unlike in the computation of the accounting profit, the net cash flows of an investment do not incorporate interest charges and their tax shield. The net cash flows are defined as the free cash flows and calculated as follows:

Delta NCF = Delta EBIT (1 – T) + Delta DEP – Delta NWC – Delta CAPEX

The adjustment for the financing effects is made in the discount rate. The firm’s weighted average cost of capital (WACC) is used as the discount rate. When we discount an investment’s free cash flows by the weighted average cost of debt and equity, we are in fact ensuring that the investment yields enough cash flows to make payments of interest and repayment of principle to creditors and dividends to shareholders. It is important to note that this approach of adjusting for the finance effect is based on the assumptions that:
  • The investment project has the same business risk as the firm.
  • The investment project does not cause any change in the firm’s target capital structure.

These assumptions may be valid for small projects, but not in the case of large projects, which may have different business risk and debt capital.

Tuesday, June 8, 2010


Nominal vs. Real Rates of Returns

How should the rate of inflation be taken into account in the capital budgeting decisions?

We should be consistent in treating inflation. Since the discount rate is market determined, and it is therefore stated in nominal terms; then the cash flows should also be expressed in nominal terms. In other words, cash flows should reflect effect of inflation, when they are discounted by the inflation affect of inflation, when they are discounted by the inflation affected discount rate. We shall elaborate this point in the following section.

Suppose a person-we call him john, deposit 100$ in the HSBC bank for one year at 10% rate of interest. This means that the bank agrees to return 110$ to john after a year, irrespective of how much goods or services this money can buy for him. The sum of 110$ is stated in nominal terms-the impact of inflation not separated. Thus, 10% is a nominal rate of return on john’s investment. Let us assume that the rate of inflation is expected to be 7% next year. What does the rate of inflation imply? It means that prices prevailing today will rise by 7% next year. In other words, a 7% rate of inflation implies that what can be bought for 1$ now can be bought for 1.07$ next year. We can thus say that the purchasing power of 1.07$ next year is the same as that of 1$ today. What is the purchasing power of 110$ received next year? It is $ 110/1.07= $ 102.80; that is, the 110$ received next year can buy goods worth 102.80$ now. The 110$ next year and 102.80$ today are equivalent in terms of the purchasing power if then rate of inflation is 7%. The 110$ is expressed in nominal terms since they have not been adjusted for the effect of inflation. On the other hand, the 102.80$ are in real terms since they have been adjusted for the effect of inflation. Our investor, john, thus earns, 10% nominal rate of return, but only 2.8% rate of return. It should be noted that the rate of inflation is an expected rate; therefore, the real rate of return is also expected. The actual rate of inflation may be different from the expected rate.

The opportunity cost of capital of a firm or project is generally market determined and is based on expected future returns. It is, therefore, usually expressed in nominal terms and reflects the expected rate of inflation. The opportunity cost of capital or the discount rate is a combination of the real rate (say, K) and the expected inflation rate (let us call it, alpha). This relationship, long ago recognized in the economic theory, is called the Fisher’s effect. It may be stated as follows:

Nominal discount rate = (1 + Real discount rate) X (1 + Inflation rate) – 1

K = (1 + K)(1 + Alpha) – 1

Friday, June 4, 2010


Investment Decisions under Inflation

A common problem, which complicates the practical investment decision-making, is inflation. The rule of the game is, as we shall emphasize in the flowing discussions, to be consistent in treating inflation in the cash flows and the discount rate.

Inflation is a fact of life all over the world. A double-digit rate of inflation is a common feature in developing countries. Because the cash flows of an investment project occur over a long period of time, a firm should usually be concerned about impact of inflation on the project’s profitability. The capital budgeting results will be biased if the impact of inflation is not correctly factored in the analysis.

Because executives do recognize that inflation exists but they do not consider it necessary to incorporate inflation in the analysis of capital investment. They generally estimate as cash flows assuming unit costs and selling price prevailing in year zero to remain uncharged. They argue that if there is inflation, prices can be increased to cover increasing costs; therefore, the impact on then projects profitability would be the same if they assume rate of inflation to be zero. This line of argument, although seems to be convincing, is fallacious for two reasons.
  1. The discount rate used for discounting cash flows is generally expressed in nominal terms. It would be inappropriate and inconsistent to use a nominal rate to discount constant cash flows.
  2. Selling prices and costs show different decrease of responsiveness to inflation. In the case of certain products, prices may be controlled by the government, or by restrictive competition, or there may exist a long term contact to supply goods or services at a fixed price.

The drugs and pharmaceutical industry is an example of controlled, slow-rising prices in spite of the rising of the general price level. Costs are usually sensitive to inflation. However, some costs price rise faster than other. For example, wages may increase at rate higher than, say, fuel and power, or even raw material. There are yet examples of certain items, which are not affected by inflation. The depreciation tax shield remains unaffected by inflation since depreciation is allowed on the book value of an asset; irrespective of its replacement are market prices, for tax purposes.