7  An example

This section of the paper applies the weighted average cost of capital to determine the appropriate social opportunity cost discount rate to apply to the long term cost recovery situation where the costs to be incurred are known with a high degree of certainty. This example also assumes that the costs will be recovered prior to any expenditure being incurred. This covers any circumstance where there is an ability of the Government to set the price to ensure cost recovery and there is no cross subsidisation between the users of the services and other taxpayers. The costs and benefits are occurring over a number of years. The example below estimates a real discount rate.

7.1  Weighted Average Cost of Capital

The weights for the debt and equity components should follow the particular circumstances of the situation. This may depend on the type of agency within government that is undertaking the activity. For example, if the government is undertaking something directly through taxation or a subsidy, versus through a department or SOE. In addition, it depends on the type of market the agency is operating within.

The application of the WACC uses the results from applying CAPM. This full cost recovery situation example is, however, a special case. This is because it is assumes there is certain that the Government will fully cost recover and the Government is not trying to cross subsidise between users. This situation would not have general taxpayers subsidising the users of the service. In this case, it looks very much like a debt smoothing or financing operation rather than an investment situation. Under this view, there would be 100% bond financing and no equity financing.

The WACC calculation would then become one of 100% times the return on debt. This is a rather simpler calculation. Later subsection 7.3 covers the determination of the return on debt.

A hypothetical situation would have the optimal level of debt and equity determined by the asset beta so that the equity beta is 1 and moves exactly in line with the market. For example if the asset beta has a value of 0.6, the level of equity would be 60%, giving a unity equity beta so the stock value would move in line with the market. In this situation, the amount of borrowings should be inversely proportional to the asset beta. The use of equity and debt financing could be seen as using general tax revenues as well as any fees or charges to smooth the expenditure flows.

Overall, the alternative approach in this case is not superior to the 100% debt situation of debt smoothing so the example in section 7.3 will use a 100% debt weighting in the weighted average cost of capital formula.

If this were not a special case, then the proportion of equity and debt would need to be determined. The optimal debt equity level given the asset beta is one approach. Debt funding can be seen as financial smoothing for user charging. Equity funding can be though of as first order tax funding of the proposal. If the proposal is to be funded by an increase in general taxation then 100% equity may be appropriate.

As an aside, the weighted average will not always be the same as the 50% debt/ 50% equity used in the departmental capital charge formula. For example, if a new project is particularly risky and does not reflect the existing business then there is no reason why the same discount rate should be used.

7.2  Capital Asset Pricing Model

There are several components to the return calculated using CAPM. The key components are the risk-free rate including inflation if a nominal rate is required, beta or the adjustment for risk, and market risk premium

This cost recovery-focused situation is often very long-term in nature so the term of the risk-free rate should match this. Therefore, the appropriate government bond rate is a long term one. In this situation the 10-year bond rate is therefore the most appropriate rate as it is the longest rate available for which there are forecasts or robust data.

The Treasury’s long-term fiscal model assumes that the interest rate forecast to occur in the last period of the forecasts continues on for the timeframe of the long-term fiscal model. In the 2002 Budget Economic and Fiscal Update the nominal 10-year government bond rate in the long-term fiscal model was 6.2%.

The other alternative is to use the longest government stock currently available, that there is sufficient market information on. This is a government bond maturing April 2013 with an interest rate of 6.35% on 5 August 2002.[10]

This example uses the 10-year nominal interest rate from the long-term fiscal model as this rate reflect the long term nature of the example and takes a neutral position on the output gap. This rate is therefore effectively a steady state rate.

The Reserve Bank Act sets a band within which the Reserve Bank Governor needs to maintain the inflation rate. The band for the inflation rate was 0-3%. The long-term fiscal model used by the Treasury in the 2002 Budget assumed that the inflation rate would be 1.5% or in the middle of the inflation rate band.

In the short term, the Treasury forecasts the inflation rate explicitly. This can be used to derive real short-term interest rates if required. As this case is long-term in nature, if an inflation rate is required for converting rates from real to nominal or vice versa, 1.5% will be used to match the timeframe of the project in this example.

The market risk premium used should be consistent with the market risk premium used elsewhere in the Treasury. The market risk premium used in the departmental capital charge formula is 9%. This is not required in this case. The government is guaranteed to receive the revenue in this example so the correlation of the return with the market is zero. This means that the market related term drops out. This example then reverts to a 100% debt related situation so the return on equity does not have to be considered further.

The nominal rate of return on the forecast 10 year government bond rate is:

(10)    nominal 10 year government bond rate + debt premium= nominal return

(11)    k_b = 0.062 + 0.010 = 0.072

7.3  Numerical Results

Using the formula in equation 4 above:

(12)    WACC = k_b D/(D+E) + K_e E/(D+E)

This formula uses K_e as the tax adjusted return on equity and is defined in equation 5 above. However, in this case there is a 100% debt situation so the equation becomes:

(13)     WACC = k_b D/(D)

So:

(14)     WACC = k_b = 0.072

After converting this back to a real WACC figure using equation 8 above the real discount rate under the 100% debt/bond scenario is: 0.056 or 5.6%.

The above leads to a 5.6% real discount rate for this example of a cost recovery situation. This is based on a scenario of receiving revenue in advance of incurring costs making a 100% debt-financing situation appropriate. The result depends on the assumptions used in the long-term fiscal model, a 1% debt premium to reflect the opportunity cost of capital, and the application of the capital asset pricing model and the weighted average cost of capital formula when there is 100% debt financing. A different interest or inflation rate would give a different real discount rate.

When undertaking calculations using the estimated discount rate, it is important to undertake sensitivity analysis. This analysis could be done by repeating the net present value calculations with different discount rates. If small changes in the discount rate impact markedly on the result then the results should be used with caution.

The discount rate for other investment decisions would vary, depending on the market-related factors associated with the particular investment.