Project Evaluation

Deciding if one should make an investment or undertake a project is one of the most important applications of the time value of money concept.

Net Present Value (NPV)

The sum of the present values of a series of cash flows (for example, all the expected cash flows from a project, including any initial investment) is called its net present value (NPV). It is the key tool in finance to judge if a project is worth investing in or not.

It is customary to do the analysis from the point of view of the investor so that cash flows representing investments are negative. Often the initial cash flow (at time 0) is the investment in the project and is negative even though there may be additional (net) negative cash flows over the years.

Assuming that the discount rate used is appropriate for the risk of the series of cash flows, a positive NPV indicates that over the years the project will generate more cash than will be needed to pay off, with the necessary returns, all the investments the project will require. Therefore, a project with a positive NPV is considered acceptable while one with a negative NPV is not. NPV measures in present value terms the excess cash the project would generate.

Internal Rate of Return (IRR)

The internal rate of return measures the rate of return of a series of cash flows of a project taking into consideration the time value of money. It is the alternate measure used to decide if an investment or project should be accepted. Mathematically speaking, IRR is the rate of return at which the NPV of a project or series of cash flows will equal zero, and it is calculated by iteration from the equation for NPV. If the IRR is greater than the rate of return appropriate for the risk of the project, then the project is considered acceptable (and will have a positive NPV). Otherwise the project should be rejected.

Although many people find the IRR measure intuitively more appealing, it has a few shortcomings, and an alternate measure - modified internal rate of return (MIRR) - has been developed to overcome some of them. In general, though, NPV is the more reliable (and superior) tool for evaluating projects or investments.

“Employees Are Our Most Valuable Asset” (Or Are They?)

You hear it all the time from CEO’s: “Our people are our most valuable assets”. But you see some CEO’s acting as if employees aren’t assets at all. Can you imagine a company downsizing or laying off any other assets – just putting it out on the street in hopes that it will walk away? When CEO’s say they have to cut expenses, what they usually mean is that they are about to let people go.

How to reconcile these two views? From a common-sense perspective, employees are assets. Their knowledge and their work bring value to a company. When one company acquires another, the value of employees is recognised as part of the goodwill.

Otherwise, though, the value of employees doesn’t show up on the balance sheet. There are two reasons:

·       Outside of an acquisition, nobody has any idea how to value employees. What is the value of your knowledge? There isn’t an accountant in the world who wants to tackle that one. And the Financial Accounting Standards Board isn’t about to take it on by amending GAAP.

·       Anyway, companies don’t own employees. So, they can’t be considered assets in accounting terms.

Employees do create expense: payroll, in one form or another, is often one of the biggest items on the income statement. But what those CEO’s are saying has more to do with a company’s culture and attitudes than it does with accounting. Some organisations really do seem to regard employees as assets: they train them, they invest in them, they take good care of them. Others focus on the expense angle, paying people as little as they can and squeezing as much work out of them as possible. Is the former strategy worth it? Many people (including me) believe that treating people right generally leads to higher morale, higher quality, and ultimately higher customer satisfaction. Other things being equal, it boosts the bottom line over the long term and thus increase a business’s value. Of course, many other factors also influence whether a company succeeds or fails. So, there’s rarely a one-to-one correlation between a company’s culture and attitudes (on the one hand) and its financial performance (on the other).

South African Airways and the Sunk-cost fallacy

Sunk costs are like spilled milk: they are past and irreversible. Because they are bygones, they can’t be affected by the decision to approve or reject the new financing being required to recapitalise or ‘save’ SAA.

Those who argue that it is foolish to abandon SAA because of past monies invested are wrong. So are those who argue that because of those past monies on which no satisfactory return has been generated and not likely to be generated, therefore no new investment ought to be made.

Both sides are guilty of the sunk-cost fallacy. Past investments are irrecoverable and are therefore irrelevant. The decision on whether or not to approve new investments ought to be made on the basis of fresh appraisals and whether or not those appraisals indicate potential positive returns. It is as simple as that.

Applied Corporate Finance Series - Time Value of Money

This is one of the basic and foundational concepts in finance. 

 

The essence of the time value of money concept is that a rand today is worth more than a rand in the future. If you have the rand today, you can invest it and earn a return on it so that on any future date you will have more than a rand. This is the future value of the rand. If you have PV₀ rand today and expect to be able to earn a return of r₁ by investing it for one period, then the future value FV₁ of your investment at the end of the period will be:

 

 

If you consider investing it for several more periods and in successive periods expect it to earn returns of r₂, r₃, and so on, then at the end of n periods the future value of your investment will be:

 

 

This process of calculating future value is called compounding because it includes earning returns on returns: in every period, you are earning a return not just on your original investment but also on all returns you have earned until then.

 

So far we have not imposed any requirement that the periods be equal, just that each return be appropriate for the length of the corresponding period. The first period, then, may be a year, in which case r₁ will have to be an annual return, the second period may be a month, in which case r₂ must be a monthly return, and so forth. This is the general formula for calculating future value over time, where the length of each period and the rate of return for it can be different.

 

If we assume that all periods are equal in length (for example, one year) and all the expected returns are the same (r), then we can simplify the equation to:

 

 

Assume that instead of asking what a certain amount of money today will be equal to at some point in the future, we ask what a certain amount of money in the future is equal to today. We then have to reverse the calculations, and the general equation for calculating the present value will be:

 

 

And if we assume that all the periods are equal in length and all the expected returns are the same, then the equation for present value becomes:

 

 

The process of calculating present value is called discounting, which is the inverse of compounding. This also involves earning a return on return, although it is not easy to see it here as it was in the case of compounding.

 

Calculating present and future values can also be viewed as the process of moving an amount of money forward or backward through time. The amounts of money involved are called cash flows because they involve cash as opposed to some accounting measures like earnings. We can write the present value of a cash flow that will occur tperiods from now as:

 

 

It is easy to see that if we are anticipating several cash flows over time, we can calculate the present value of each and then add them together to get the total present value of all cash flows.

 

Here are the key points to keep in mind about calculating present and future values and doing time value of money problems:

 

•   The time value of money concept applies only to cash flows because we can earn returns or have to pay returns only on cash we invest or borrow. We cannot calculate present values or future values for net income, operating income, and so on, because they do not represent cash.

•   Only cash flows taking place at the same point in time can be compared to one another and combined together. If you are dealing with cash flows that take place at different points in time, you have to move them to the same point in time, that is, calculate their present or future values at the same point in time before comparing or combining them. For such calculations, most of the time we either present value all cash flows to today or future value them to the farthest point in time the problem involves. However, if it is more convenient in a specific situation, we can move all cash flows to any other point in time as well. Whenever you calculate a present or future value (especially using Excel function) make sure you know which point in time they relate to.

•   The simpler formulas we derived, as well as most Excel functions, can be used only when all the periods are of equal length and the rate of return is the same for all periods. Otherwise you have to use the longer period-by-period formulas.

•   We use the term compounding when we calculate future values or move earlier cash flows to a later point in time, and the term discounting when we calculate present values or move cash flows to an earlier point in time. However, we often use the term discount rate to refer to the rates of return in both cases.

•   The most important thing to remember about the discount rate you choose to apply to one or a series of cash flows is that it must reflect the risk of the cash flows. It is easy to understand that the discount rate should be higher for more risky cash flows and lower for less risky cash flows. However, estimating the risk of a cash flow and deciding what the appropriate discount rate for it should be is one of the knottiest problems in finance. In the models in this lesson we will assume we know what the appropriate discount rate is.