**P****ROJECT
VALUATION**

Comparing Projects
When a company is considering new investments to expand
its earnings, it is frequently considering several projects, and is trying to optimize its choice by selecting
those projects which will produce the highest returns at the lowest risk or cost.

In doing so it will use several criteria, one which will
select that project which produces the highest net discounted present dollars over present cost, called
Net Present Value. This particular criteria, which subtracts the investment from the *present* value
of the cash flow stream, is the gold standard for decisions by the majority of American companies. Its
weakness is that since its a total dollar criteria, it will normally favor *any* investment which
is the larger, and will produce the highest *number of net dollars. Whereas, a standard such as Profitability
Index, which divides the investment into the present value of the cash flow stream will show the return
per dollar of invested capital and will permit projects which require* a smaller investment, but favor
a higher *per dollar* return.

Of the rational remaining criteria used to evaluate and compare
capital projects the *percentage criteria*, called the Internal Rate of Return (IRR), is the most
commonly used. With this standard, the project or projects which produce the *highest rates of return*
are chosen. The process of computing the internal rate of return is done by computer iteration, where
the percentage which discounts the cash flow return from the investment over the investment period is
*the rate which makes the sum of the present value of the cash flow precisely equal to the investment.*
For example, if a company invested $50,000 in a machine and received net after tax cash flows from it
over a 5 year period, of $15,000 each year, the rate which would produce, a present value of exactly $50,000
of five annual $15,000 cash flows is 15.23%. This type of calculation does not have a practical mathematical
formula, and in the absence of a financial mode line calculator or a computer, it must be computed by
trial and error.

Frequently, in comparing the purchase of new equipment a
company will be considering machines with different productive lives, a five year machine vs. a ten year
machine for example.

The business issue is which investment would produce the
highest net present value: buying the five year machine and renewing the purchase for another five years,
or buying the ten year machine in the first instance. This can be resolved mathematically by *annualizing
the net present value*. In other words, the basic criteria of net present value can be determined for
each one, and then compared as an annualized number. This process is done by computing what is called
the present value of the *equivalent annuity*, and with a computer or calculator it is relatively
simple and direct.

For example, lets assume we are comparing and investment
in either of two copy machines: Machine A costs $25,000 and has a five year projected life, and a positive
net present value of $12,500. Machine B, is a more costly $40,000, has an estimated life of ten years,
and a net present value of $18,500. To *annualize the difference* we divide each net present value
by *an annuity of* $1 for the period, discounted at the same appropriate rate we discounted the cash
flows. Assume we discounted the cash flows by 10%, an annuity of $1 at 10% for 5 years is worth $3.79,
which if divided into $12,500= $3298, while for the 10 year machine that same process would produce an
annuity of $6.14, which if divided into $18,500 = $3013. This process clearly shows that the selection
of the *five year machine* would be preferred.