Monday, July 15, 2013

The Time Value of Money, and Techniques for Determining It


In the case of longer-term projects, the time at which profits start accruing
can have a bearing on the worth of future earnings. This is expressed by
an important financial concept called the time value of money. It states
that, in general, money earned now is worth more than money earned at
some time in the future, for two reasons:

1. Additional return could have been obtained if the money had been
invested in the intervening period.
2. Purchasing power is reduced, due to inflation.
The discount rate used is based on the required or desired
rate of return, and may also include the expected rate of inflation over the
life of the project. Applying discounting rates tends to show very clearly
that projects generating a profit early in their life cycle are preferred to
projects that generate profits much later in the future.
Discounted cash flow takes into account the timing at which
expenditure and profits rise, and shows the effective rate of return on the
total investment over the life of the project.
When evaluating the worth of the project, the desired rate of return can be set at some boundary level. If
the initial analysis and evaluation shows that this rate of return cannot
be achieved, then the returns are likely to be too low and the project
will not be worth pursuing. The method of calculating DCF is relatively
straightforward, and can be easily adapted to spreadsheet methods.
An alternative approach is to determine the discount rate that would
generate a zero return over the complete life of the project. This is termed the internal rate of return (IRR). A hurdle rate can be set for the IRR,
and any project that cannot meet or exceed it is deemed to be not worth
pursuing unless there are other important, nonfinancial factors.

When the discounting process is
applied to project cash flow, it produces the net present value (NPV)
of the proposed project at the given discount rate. (A project will have
an NPV of zero at the IRR.) This is a popular method of establishing
the worth of a project investment, with a positive NPV at the hurdle discount
rate identifying a potentially viable project from a financial point
of view.

In addition to the NPV method, the discounted cash flow return
(DCFR) approach can be used. This approach is particularly suitable if
capital is being borrowed to finance the project.

1. NPV = (Cash inflows Cash outflows) Discount rate
where
Discount rate = 1 / (1 + k + r)t
and
k = the inflation rate
r = the required or desired rate of return
t = time period

2. IRR = the discount rate at which NPV is approximately equal to 0.
Example 1
Your project organization has to decide whether or not to invest in a
project opportunity. The following information is available to you:
Initial cash outflow = $200,000 in the current year (year 0), and $100,000
in the next year
Cash inflows = $100,000 in year 1, $150,000 in year 2, $175,000 in year 3,
and $75,000 in year 4
Required rate of return = 12%
Inflation rate = 4%
a. Calculate the NPV for this project.
b. Calculate the IRR for this project.
Solution
The discount factor and NPV for this example is given by
Discount factor = 1 / (1 + k + r)t = 1 / (1 + 0.04 + 0.12)t for t = 0, 1, 2, 3,
and 4
NPV = Net flow Discount factor
a. NPV (Table 6.1)
b. IRR: Steps (Tables 6.2.1, 6.2.2, and 6.2.3)
1. Assuming an inflation rate of 4 percent, try different rates of
returns to calculate the NPV of the cash inflows.
2. Subtract the cash outlay from the total NPV of the inflows.
3. The rate at which the value from step 2 is close to zero is the IRR.



1. Assuming an inflation rate of 4 percent, try different rates of
returns to calculate the NPV of the cash inflows.
2. Subtract the cash outlay from the total NPV of the inflows.
3. The rate at which the value from step 2 is close to zero is the IRR.
There is an important caveat, however, when using net present value to evaluate
projects. The longer the project’s life or projected stream of revenues, the
less precise this approach becomes.
IRR and NPV calculations typically agree (that is, make the same
investment recommendations) only when projects are independent
of each other. If projects are not mutually exclusive, IRR and NPV
may rank them differently. The reason is that NPV employs a
weighted average cost of capital discount rate that reflects potential
reinvestment, while IRR does not. Because of this distinction, NPV
is generally preferred as a more realistic measure of investment
opportunity.
If cash flows are not normal, IRR may arrive at multiple, conflicting
solutions, as is the case when net outflows follow a period of net cash
inflows. For example, if it is necessary to invest in land reclamation or
other incidental but significant expenses following the completion of
plant construction, an IRR calculation may result in multiple return
rates, only one of which is correct.

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