Discounted Payback Time
Given I, r, and CF, find n. This calculated n is a discounted payback time. The
simple payback time (I/CF) is equivalent to a discounted payback time when r =
0 (i.e., with no discounting). Likewise, if we calculate IRR for, say, n = 20 and then
we set r = IRR, we will just back-calculate n = 20. Therefore, for 0 < r < IRR, the
calculated payback time will be (I/CF) < n <20. Likewise, if r > IRR, then n >20.
If the cash flows, CF, are uniform, we can solve for n as follows:
n ¼
ln
CF
CF À Ir
ln 1 þ r
ð
Þ
:
(6)
Sales Price Required to Obtain a Given Discounted
Cash Flow Rate or Return
Given I, n, and a desired rate of return, r, we can calculate the required cash flow, CF,
according to formula (b). This cash flow can be used in the economic analysis to
calculate the product sales price that will be necessary to generate this cash flow. If this
cash flow is obtained, then we have the desired discounted cash flow rate of return, r.
This calculated sales price is a function of both r and n.
For the calculation of the cash flow, CF, the appropriate computer function, if
available, is
@pmt I, r, n
ð
Þ
where r must be used in the decimal form for the corresponding period.
Appendix 1: Refinery Plant Inadequacies Report:
Example Work Sheet
See Fig. 12.
Appendix 2: Example of a Crude Oil Inventory Schedule
See Fig. 13.
Appendix 3: Example of a Product Inventory and Schedule
See Fig. 14.
Appendix 4: An Outline Operating Schedule
See Fig. 15.
760
D.S.J. Jones and P.R. Pujado ´