Page 284 - Introduction to Mineral Exploration

11: PROJECT EVALUATION 267

11.5.2 Operating margin to initial than it will be at some future date because it
investment ratio can be put to work over that period. If a dollar
were invested today at an interest rate of
There are several variations on this theme but 15% compounded annually, it would amount
it produces a dimensionless number which to $1.00 × (1 + 0.15) or $1.15 after 1 year and
indicates the amount of cash flow generated $1.00 × (1.15) = $2.01 after 5 years. This is the
5
per dollar invested. It is an indication as to how compound interest formula:
financially safe the investment is and the larger
the number the higher the value of the miner- S = P(1 + i)n
alisation. It is easy to calculate and considers
the whole life of the project compared with where S is the sum of money after n periods of
payback which considers only the first few interest payment, i is the interest rate, and P
years. All factors in the cash flow (such as the initial investment value. In this example
revenue, operating cost, taxes, etc.) are taken we can say that the 5-year future value of the $1
into consideration and all affect the ratio invested today at 15% is $2.01. Reversing this
number. However, as in payback, the time viewpoint from the calculation of future values
value of money is not taken into consideration. to one of value today, what is the value today of
As a simple example consider spending $100 $2.01(S) if this is a single cash flow occurring in
today to receive $300 in 3 years, or spending 5 years’ time at the accepted rate of interest of
$100 today to receive $400 in 10 years. The 15%? The answer is obviously $1.00 and the
increase in the ratio overfavors the latter yet present value (P) is a variation of the compound
most would prefer the former. Using this interest formula above:
approach the projects in Box 11.2 can be ranked
in order of value as C, D, B, and A.
P = + S n = $.201 5 = .( .497 = ) $ .100
20
0
1
+ .15
11.5.3 Techniques using the time value of (1 n) (10 )
money
This expression is the present value discount
These techniques are commonly used in the factor, more usually termed the discount fac-
financial evaluation of mineralisation and tor, and tables of calculated factors are readily
mineral projects. The opening theme is that available (Table 11.1). From the formula, and
money has a time value (Wanless 1982). Dis- the table, it is evident that this factor decreases
regarding inflation, money is worth more today with increasing interest rates and number of

TABLE 11.1 A selection of present value discount factors.
Years

1 2 3 4 5 10 15
Discount rate 5% 0.952 0.907 0.864 0.823 0.784 0.614 0.481
10% 0.909 0.826 0.751 0.683 0.621 0.386 0.240
15% 0.870 0.756 0.658 0.572 0.498 0.247 0.123
20% 0.833 0.644 0.579 0.482 0.402 0.162 0.065
For explanation see text.
The table demonstrates the decrease in the magnitude of the discount factors with increasing years and increasing discount
rate, governed by the basic formula:
1
discount factor =
(1 − i)n
where i = interest or discount rate (as a fraction) and n = number of years.