A number of devoted readers to this blog have asked about the concept of duration as an investment appraisal technique.

Duration tells us the average time at which a project will recover the net present value of the project or, alternatively the value of the original investment. It is most commonly encountered in discussion of fixed income securities but it also has a role in the less esoteric areas of capital budgeting. It serves two purposes, it is a measure of the average period to recovery of the value invested which, unlike payback, incorporates time value and does not ignore any of the cash flows in the recovery phase of the project. It also answers a riddle about internal rate of return and the circumstances in which IRR will agree with NPV and when it will not.

The first step in its measurement is to take each year’s cash flow and discount them by the internal rate of return of the project. Alternatively, take each year’s cash flow and discount them by the firm’s cost of capital. In the first case divide each year’s discounted cash flow by the value of the initial investment, in the second case divide by the project’s present value. The sum of the resulting values in either case should equal one. Then, multiply each weighted cash flow by the year to get a weighted average of years. This is the project duration.

How do we interpret the duration? It tells us when the bulk of the cash flows will be received over the life of the project. In this respect it has a similar value to payback in that a firm exposed to significant liquidity risk might prefer the short duration project to one where the bulk of the cash flows arrive at the end of the project’s life.

Duration also helps us solve a problem in finance when using the IRR as a technique for distinguishing between mutually exclusive projects. IRR favours short duration projects and in those cases will contradict NPV. With long duration projects, IRR and NPV will be in agreement. The duration of the project helps reconcile NPV and IRR but more importantly it provides an important timing metric that does not have the faults of payback or discounted payback.

Here is a useful pointer to a reference:

http://www.accessmylibrary.com/article-1G1-137876341/ranking-mutually-exclusive-projects.html

## 7 comments:

thanks prof bob..

hi prof bob, could you clarify whether I am right

The sterling/euro exchange rate is xxx.

'xxx' is a direct or indirect rate or it can be either one?

if it is either one, how should i differentiate it?

thank you very much for your much appreciated clarification

On my exam papers for MBA, MSc etc I normally spell out the nature of the exchange rate i.e., $1.5 per £1 or use the words direct or indirect. It can be confusing especially when the currencies are close to parity. However, in my exams I would not penalise an error by (say) more than one mark. However, good tip learn roughly what the current rates are for the principal currency pairs and you shouln't go wrong.

On my exam papers for MBA, MSc etc I normally spell out the nature of the exchange rate i.e., $1.5 per £1 or use the words direct or indirect. It can be confusing especially when the currencies are close to parity. However, in my exams I would not penalise an error by (say) more than one mark. However, good tip learn roughly what the current rates are for the principal currency pairs and you shouln't go wrong.

thank you prof Bob. I have much better understanding now.

This paper introduces a new measure of cash flow duration, called return duration, and illustrates its mathematical links to Macaulay duration. Return duration provides the conceptual link between a project's internal rate of return and its net present value. Having a single equation relating duration, IRR, and NPV aides in understanding how cash flow timing differences can create ranking conflicts. Using return duration, a project having a higher IRR and a longer duration will necessarily have a higher NPV when compared to a lower-IRR, shorter-duration project. This intuitively appealing result surprisingly does not always hold with Macaulay duration.

Besides introducing the new measure of duration, the paper clarifies duration's role in capital budgeting decisions when projects are being evaluated in less than perfect markets. If capital budgeting always occurred in the idealized textbook word of perfect capital markets, then the presence of ranking conflicts would be of no particular concern to the analyst. When comparing mutually exclusive projects, firms would maximize shareholders' wealth by choosing the project having the highest NPV, while rates of return and duration would be a secondary concern. However, if a firm faces capital constraints that will extend to future years, the firm must consider duration, IRR, and the potential IRR on future projects--in addition to NPV--when making investment decisions. Suggesting that capital markets might be less than perfect, numerous surveys [13, 14, 20] have shown that managers do in fact consider alternative measures--such as IRR, duration, and payback period--along with NPV when making capital budgeting decisions. By describing when and how duration is relevant to the capital budgeting decision, this paper helps reconcile capital budgeting theory to capital budgeting practice.

prof Bob, when looking at set problems saying that UK firm needs to hedge its FX risk from receiving USD 1m in 3months with currency futures in GBP (or currency options in GBP) - does it involve a crosshedging, as the underlying asset for GBP futures is delivery of 62500 GBP but we are expecting USD instead of GBP. Taken that rates can be expressed in two ways (dirrect and indirect), this gives the hedge ratio of -1. I assume that it means that we need to apply the exact opposite of the normal hedging strategy. I.e. for receiving £1m in 3m, you would normally short 16 GBP-futures contracts,but in case of receiving $1m you would long ($1m/Spotrate)/62500 GBP-futures contracts.

In terms of hedging with FX options, a put option to sell USD for GBP at strike K is the same as call option to buy GBP with USD at strike 1/K.

Let me know if I am on the right track.

Thanks,

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