3.3 Choosing a Discount Rate
The discount rate is effectively a desired return, or the return that an investor would expect to receive on some other typical proposal of equal risk. The discount rate typically includes:
- The “rate of time preference”. Most people prefer consumption undertaken now rather than later. Thus, a dollar available now is more highly valued than one received later.
- Uncertainty/risk. There is necessarily some degree of uncertainty as to whether a future dollar will actually be received. Its value is lessened in proportion to the expected size of this uncertainty/risk factor.
There is no single rate of return that is appropriate for every project. The Treasury uses a 10% real discount rate whenever there is no other agreed sector discount rate for costing policy proposals. Where there is an agreed sector rate, it may be used instead.
For financial analysis at the level of the organisation – not for national analysis of net benefit – the Department Capital Charge rate is used (currently 7.5% for 2006/07). It is an estimate of the government’s average cost of capital, across all departments, revised annually.
For non-departmental projects (Crown Entities and State Owned Enterprises), or in unusual cases where using the standard rate is inappropriate due to an abnormal amount of risk, it may be appropriate to calculate a different rate. A standard approach in the private sector is to use the weighted average cost of capital (WACC). Analysts should consult with their Treasury Vote team when considering the use or calculation of an alternative discount rate.
Whatever the discount rate chosen, care must be taken to remove the effect of inflation if NPV calculations use figures which are all in today's dollars. Note that the 10% figure used by Treasury in the default case already has inflation removed, as does the Departmental Capital Charge Rate. To remove the effect of inflation from other discount rates, use the formula: (1+nominal discount rate) ÷ (1+inflation rate) - 1.
Example 3.4: Choosing a Discount Rate
The Ministry of Information Technology is a government department. It does not believe that the upgrade proposal is any more or less risky than other similar projects undertaken by government. Therefore, it adopts the 10% real discount rate.
In typical cases, choosing a higher discount rate reduces the net present value of a project, and choosing a lower rate increases the net present value, but this is not always the case. Because the discount rate has a significant impact on the net present value, it is important to make clear which rate is used and why. Sensitivity analysis (see section 4.3) on the discount rate should also be undertaken.
3.3.1 Long-lived Projects
For very long-lived proposals, and particularly where a substantial proportion of the benefits occur well into the future, the use of discounting with a standard discount rate is likely to create a bias against project acceptance. For example, with a discount rate of 10% per annum, only five percent of any benefits occurring in the thirtieth year will be added to the NPV.
In a commercial setting, the low weight given to distant cashflows reflects the desire of investors to achieve a return sooner rather than later. However, some sources recommend using a lower discount rate for very long-lived proposals, but only if “appraisal of a proposal depends materially upon the discounting of effects in the very long term”.
It is anticipated that, in New Zealand, lower discount rates would be used only in exceptional circumstances.
3.3.2 Annual versus Monthly
The discount rate will usually be expressed in annual terms (percent per annum). If the expected cashflows are annual, the rate may be used directly. If, however, expected cashflows are monthly, the discount rate needs to be converted to a monthly rate. Dividing the annual discount rate by 12 will give an approximate rate to use in the NPV calculation.
- Adapted from Ministry of Economic Development. (1999). A Guide to Preparing Regulatory Impact Statements. http://www.med.govt.nz/buslt/compliance/risbccs/regimpact/index.html
- See section 2.4.1 for a discussion on the difference between real and nominal values.
- See http://www.treasury.govt.nz/workingpapers/2002/02-21.asp, at page 12.
WACC = D × (Cost of debt) + (1-D) × (Cost of equity)
D is the percentage of debt finance (in market value terms)
Cost of debt = (interest rate payable for the project) × (1 - corporate tax rate)
Cost of equity = [(risk free rate of return) × (1 - tax rate of investor) + (equity beta) × (market risk premium)] ÷ (1 - corporate tax rate)
The interest rate payable by government departments is often approximated by the risk free rate plus a premium of 1%. The tax rate of the investor has been assumed to be 0.28 (28%) in the past. Values for the asset beta may be obtained from observed equity betas for listed companies. Estimates of the market risk premium in New Zealand have commonly ranged between 5% and 9%. See http://www.treasury.govt.nz/merp/default.asp for more information on the market risk premium.
- A more precise monthly discount rate is given by ((1+(annual rate÷100))1÷12 -1) × 100. For example, if the annual rate is 10%, the monthly rate will be ((1+(10÷100)) 1÷12 -1) × 100 = 0.797%.