3e2a1b56-dafb-454d-87ad-86adea3e7b86

Chapter 8 Process technology 225
Discount rate
For example, suppose current interest rates are 10 per cent per annum; then the amount
we would have to invest to receive a1,000 in one year’s time is
1
a1,000 × =a909.10
(1.10)
So the present value of a1,000 in one year’s time, discounted for the fact that we do not have
it immediately, is a909.10. In two years’ time, the amount we would have to invest to receive
a1,000 is:
1 1
1
a1,000 × × =a1,000 × =a826.50
(1.10) (1.10)
(1.10) 2
The rate of interest assumed (10 per cent in our case) is known as the discount rate. More
generally, the present value of ax in n years’ time, at a discount rate of r per cent, is:
x
a
n
(1 + r/100)
Worked example
The warehouse which we have been using as an example has been subjected to a costing
and cost savings exercise. The capital cost of purchasing and installing the new technology
can be spread over three years, and from the first year of its effective operation, overall
operations cost savings will be made. Combining the cash that the company will have to
spend and the savings that it will make, the cash flow year by year is shown in Table 8.4.
Table 8.4 Cash flows for the warehouse process technology
Year 0 1 2 3 4 5 6 7
Cash flow (A000s) −300 30 50 400 400 400 400 0
Present value
(discounted at 10%) −300 27.27 41.3 300.53 273.21 248.37 225.79 0
However, these cash flows have to be discounted in order to assess their ‘present
value’. Here the company is using a discount rate of 10 per cent. This is also shown in
Table 8.4. The effective life of this technology is assumed to be six years:
The total cash flow (sum of all the cash flows) = a1.38 million
However, the net present value (NPV) = a816,500
This is considered to be acceptable by the company.
Calculating discount rates, although perfectly possible, can be cumbersome. As an
alternative, tables are usually used such as the one in Table 8.5.
where
So now the net present value, P = DF × FV
DF = the discount factor from Table 8.5
FV = future value
To use the table, find the vertical column and locate the appropriate discount rate (as
a percentage). Then find the horizontal row corresponding to the number of years it
will take to receive the payment. Where the column and the row intersect is the present
value of a1. You can multiply this value by the expected future value, in order to find its
present value.
➔