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# Step 5: Discount and compare costs and benefits

140.In all but the simplest proposals, costs and benefits should be identified for each year over the life of the project. In general, it is not appropriate to treat costs and benefits in one period as having the same weight as costs and benefits in other periods. Rather, they need to be discounted to a common point in time. The recommended discount rates change from time to time and can be found on the Treasury website http://www.treasury.govt.nz/publications/guidance/planning/costbenefitanalysis/currentdiscountrates

## Discounting

141.The term discounted means that costs or benefits which occur later are given less weight than costs or benefits which occur sooner, with larger reductions the further into the future the costs or benefits occur. The discounted value of costs or benefits is therefore the relevant assessment measure. The discounted value is also known as the present value.

142.An intuitive justification for discounting is that most people would prefer receiving a dollar today over receiving a dollar in a year’s time. This is referred to as time preference or the time value of money.

Example: Discounting - the rationale

A dollar today can be invested, say in a bank deposit at an interest rate of 5%, so that in a year's time it is worth \$1.05. Receiving \$1.05 in a year's time is therefore equivalent to receiving a dollar now.

143.To value the future receipt in today’s terms, we discount the future receipt by the discount rate, which in the case of the example above is 5%.

144.The number by which we have to multiply the future value to obtain today’s equivalent is called the discount factor, and is equal to

145.Where n is equal to the number of years over which the value is being discounted.

146.A second, related, justification for discounting, and the one which is used in practice to derive the discount rate (r), is that when a person assesses a proposal, they will require a return at least as high as they can obtain from any other investment of equal risk.

147.By discounting, the net benefit or cost over and above the return for other proposals of equal risk can be determined. A net present value (NPV) above zero indicates a higher return than other proposals of equal risk, an NPV of zero indicates an equal return, and a negative NPV indicates a lower return.

Example: Discounting Using the Formula

If the discount rate is 10%, the discounted values of expected costs or benefits are calculated as illustrated in the following table:

Year (n)   0 1 2 3
Discount factor = 1 ÷ (1 + 10%)n      1.000 0.909 0.826 0.751
Forecast costs or benefits   -100 45 45 45
Discounted values (value x discount factor)   -100 40.909 37.188 33.808
Present value (sum of discounted values) 11.906
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