# Relevant Cash Flows

Investment decisions, like all other decisions, should be analysed in terms of the cash flows that can be directly attributable to them. These cash flows should include the incremental cash flows that will occur in the future following acceptance of the investment. The cash flows will include cash inflows and outflows, or the inflows may be represented by savings in cash outflows. For example, a decision to purchase new machinery may generate cash savings in the form of reduced out-of-pocket operating costs. For all practical purposes such cost savings are equivalent to cash receipts. It is important to note that depreciation is not included in the cash flow estimates for capital investment decisions, since it is a non-cash expense. This is because the capital investment cost of the asset to be depreciated is included as a cash outflow at the start of the project, and depreciation is merely a financial accounting method for allocating past
capital costs to future accounting periods. Any inclusion of depreciation will lead to double counting.

## Timing of cash flows

To simplify the presentation our calculations have been based on the assumption that any cash flows in future years will occur in one lump sum at the year-end. Obviously, this is an unrealistic assumption, since cash f lows are likely to occur at various times throughout the year, and a more realistic assumption is to assume that cash flows occur at the end of each month and use monthly discount rates. Typically, discount and interest rates are quoted as rates per annum using the term annual percentage rate (APR). If you wish to use monthly discount rates it is necessary to convert annual discount rates to monthly rates. An approximation of the monthly discount rate can be obtained by dividing the annual rate by 12.

However this simplified calculation ignores the compounding effect whereby each monthly interest payment is reinvested to earn more interest each month.
To convert the annual discount rate to a monthly discount rate that takes into account the compounding effect we must use the following formula:

Monthly Discount Rate = (¹²√ 1 + APR) – 1    (formula 6.6)

Assume that the annual percentage discount rate is 12.68 per cent. Applying formula 6.6 gives a monthly discount rate of:

(¹²√1.1268) – 1 = 1.01 – 1 = 0.01 (i e. 1 % per month)

Therefore the monthly cash flows would be discounted at 1 per cent, In other words, 1 per cent compounded monthly is equivalent to 12.68 per cent compounded annually Note that the monthly discount rates can also be converted to annual percentage rates using the formula:

(1 + k)¹² – 1 (where k = the monthly discount rate) (Formula 6.7)
Assuming a monthly rate of 1% the annual rate is (1 01;”-1 =0.1268(i e. 12 68% per annul) instead of using formula (6.6) and (6.7) you can divide the annual percentage rate by 12 to obtain an approximation of the monthly discount rate or multiply the monthly discount rate by 12 to approximate the annual percentage rate.