6  Assumptions required

This section works through the general assumptions required before the weighted average cost of capital can be estimated. There are several components required to calculate the return on equity calculated using CAPM. These are the risk-free rate (including inflation if a nominal rate is required), beta or the adjustment for risk and the market risk premium. The risk-free rate and debt premium are required for calculating the return on debt.

6.1  Risk-free rate

The risk-free rate reflects the rate of return that a person can expect on a completely risk less asset. Most people normally use a government bond rate as the risk-free rate. This is because relative to the other investments in the market, the government bond has very little if any risk.[7] The government bond rate can be thought of representing the time value of money. To be consistent with how other people use CAPM, the government bond rate is considered to be the risk free rate.

The time frame of the government bond rate used should be consistent with the project timeframe. So a five-year project would use a five-year government bond rate and a ten-year project would use a ten-year bond rate or the closest approximation.

6.2  Debt premium

In the case of the government the risk-free rate is also its own bond rate. The government guarantee associated with government borrowing means the government does not pay a debt premium for the risk of default relative to other types of borrowers in New Zealand. The debt premium is related to the quality of the debt on issue. The debt risk premiums observed in the New Zealand bond market for high quality debt without a government guarantee are: Transpower (0.9%), Housing New Zealand (1%), Telecom (1%) and Auckland Airport (0.9%)[8]. Based on this data the departmental capital charge formula uses a debt premium of 1% on the risk free rate to determine the bond rate for the WACC formula.

The appropriate rate of return on debt for the WACC formula is a long-term government bond rate with a debt premium and the alternative uses of those funds. This takes into account the impact on the market of the government raising the debt. The relevant debt premium would be 1% based on the evidence above. This is also consistent with the debt premium used elsewhere in the government sector.

The debt premium is not required to calculate the return on equity using CAPM.

6.3  Inflation Adjustment

The historic government bond rates include inflation. Some people forecast the real interest rate while others forecast the nominal interest rate. There should be consistency in the use of nominal and real figures throughout the calculations. In addition, the final discount rate should be real or nominal depending on the flows it is being used to discount.

The relationship between real and nominal data is multiplicative:

(8)    Real rate = [(1+ nominal rate) / (1 + inflation)] – 1

This adjustment is used to convert a nominal capital charge rate into a real capital charge rate. This formula is consistent with the capital charge formula.

When including a debt premium, a real rate needs to be converted to a nominal rate before adding the debt premium. The result would then be converted back to a real figure if the cash flows to be discounted are real. This ensures consistency in the use of a real discount rate to convert the real cash flows to a net present value calculation.

When calculating an equity return a nominal risk free rate is required to be consistent with the use of a nominal market risk premium in the CAPM formula.

To determine what inflation rate should be used, it is important to choose a rate that is consistent with the time frame of the project and the interest rate used as the risk-free rate of return. If using a 10-year nominal risk-free rate of return, this should be adjusted by a 10-year inflation figure for consistency.

6.4  Market Risk Premium

The market risk premium depends on the way the market moves relative to the risk-free asset or R_m – R_f(1-T_c). Where R_m is the market return, R_f is the risk free rate and T_c the corporate tax rate. It reflects the extra return an investor expects for investing in the market over a risk-free asset. It reflects the systematic risk present in a market that cannot be diversified away. The proportion of extra return taken into account reflects the equity beta. This is discussed below.

The market risk premium can be obtained from elsewhere and does not need to be calculated. For example the SOE and CE cost of capital formula uses a tax adjusted market risk premium of 9%, as does the capital charge rate for government departments (Young, 2000). In March 2000 Pricewaterhouse Coopers New Zealand produced a paper on the New Zealand Equity Market Risk Premium gives a tax adjusted market risk premium in the range of 8%-9%. Pricewaterhouse Coopers New Zealand (August 2002) has updated this and now use a 7.5% tax adjusted market risk premium. The conclusion in their March 2000 paper was driven by low rates of return in the late 1920’s and 1930’s when the financial markets were very different from today. There was the depression in the 1930’s and there were fewer financial market instruments available. Their conclusion was also based on overseas expectations that future rates will be lower than historical rates.

This variable is only required when the case you are examining includes an equity component in the weighted average cost of capital. If this is the case then, use 9% as the most reliable estimate and it also provides for consistency with the departmental capital charge formula.

6.5  Beta or adjustment for risk

In CAPM this risk adjustment is for the systematic risk that cannot be diversified away. It is related to how the particular investment varies with the market. As with the market risk premium above, this is only relevant if there is an equity component in the weighted average cost of capital. An equity beta of 1 would mean that a security moves in step with the market as a whole. If the market return is increasing, the return on the security will be increasing. If the market return is decreasing the return on the security is decreasing.

The equity beta is a multiplier on the market premium. A positive value less than 1 means the security moves in the same direct as the market but not with the same magnitude. A value of more than 1 means that the security moves in the same direct as the market but with a greater magnitude. A negative value means that the security moves in the opposite direction to the market.

The equity beta used is dependent on the situation. There is a general equity beta that is used in the departmental capital charge rate and it takes into account the overall nature of government and its (assumed) debt/equity structure. This reflects the general regulated nature of government.

The equity beta to be used can be derived from an asset beta and debt/equity structure or may be obtained from comparator equity betas. Asset betas can be converted to equity betas using the following formula, assuming tax neutrality[9]:

(9)    β _e = β_a [1+(D/E)]

An optimal debt/equity structure ensures that given the asset beta the balance sheet ensures that the equity beta is 1. Using the optimal structure would divorce the situation from reality, as most organisations do not operate with an optimal debt equity structure. It is also debatable about whether moving perfectly in line with the market is optimal from the point of view of the government or the taxpayer.

The beta that applies in a particular case would need to be estimated separately, unless the project has average government risk. In which case the equity beta used in the departmental capital charge formula would be appropriate. The equity beta used in the departmental capital charge formula is 0.6, and the asset beta underlying this is 0.3.

If the project does not have average government risk then the nature of the situation needs to be clearly defined. For example, a service delivery agency is undertaking a major information technology project with leading edge technology. In this case the project would be more risky than its normal business activities.

Potential questions to ask when thinking about choosing a beta include the following: how stable is the sector? how regulated is the sector? is it a monopoly supplier? is it part of their business as usual activities? what aspects are risky? how risky is the technology? how variable are the cash flows? Once the characteristics of the situation are defined, they can then be compared to those of listed companies and particular sectors. Having defined a match, it is a matter of obtaining a suitable beta.