##### Abstract

Corporate taxes are associated with depreciation deductions in the future. The tax deduction, which is a future cash flow if we rule out Brown taxation (pure cash flow tax), has to be accounted for by the firm when it comes to project valuation. But in order to include this factor in the valuation of a project the cash flow has to be properly valuated, i.e. all factors that affect the value of the future cash flow have to be included. One factor is the risk associated with the cash flow. There are three types of risk that can be said influence the valuation of depreciation allowances. The first is related to the risk of the company being in tax position. Will the firm be able to pay taxes such that it will be eligible to collect the tax deduction in the future? A second type of risk associated with the tax deduction is a possible change in the tax system by the tax authorities. For example the tax rate might be changed after the project has been initiated. A third type of risk is the risk of inflation uncertainty. Economists always assume that economic agents only care about real rates of return and not nominal. Correspondingly the firm will only care about the real value of future cash flows. But since the inflation rate is uncertain, even though the nominal value of the cash flow might be known, the real value will be uncertain. This uncertainty might have a big impact on the valuation of the future cash flow in question.

Using a survey-method Summers (1986) finds that firms generally use a too high discount rate when it comes to valuating depreciation allowances. His main argument is that the risk associated with inflation is non-existing or negligible, such that the discount rate applied should be given by the after-tax coupon payments on a safe bond.

In the paper “Taxation, Uncertainty, and the Cost of Equity” by Lund (2002) professor Lund looks at how the valuation of the net cash flow of a company is affected by the presence of tax shields. With basis in the CAPM one of the main findings is that beta value of equity is lower when there are depreciation schedules, and that the value is decreasing in the tax rate. Lund (2002) also touches indirectly upon the question about whether Summers (1986) was right to assume that the risk of depreciation allowances could be ignored when it comes to valuation of these cash flows. He concentrates mostly on the risk associated with the firm’s tax position.

The aim of this thesis is to see if the risk of inflation uncertainty has an effect on the valuation of a nominally risk free cash flow. Basically I assumed as case 1 in Lund (2002) that the firm

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is in tax position with certainty and thus that there is a nominally risk free claim one period ahead. As a first case I look at a representative Norwegian company with a possible investment project in Norway. I set up a real CAPM, additionally assuming that there exists a risk free rate. Further on I deduce the expression for the beta value of a nominally risk free claim of 1 NOK. In order to estimate the beta value I use a sample of Norwegian data in the period 1988-2006 and estimate each part in the expression by using empirical moments. The statistical program used is STATA 9.2, although other packages like Microsoft Excel could have been utilized just as well.

As a second case I look at multinational company (American) with an investment project in Norway. The assumptions are the same as in the first case but the major difference is that now the exchange rate plays a part. A similar expression for the beta value is presented, but to be precise it is not the beta value of a nominally risk free claim in terms of USD since the exchange rate is uncertain one period ahead. But the claim is nominally risk free in terms of NOK. The method used for estimation is analogous to the one in case 1 but the period is different. Because I had difficulties finding data for TIPS (Treasury Inflation-Protected Securities) prior to January 2003 I used data from the period January 2003-January 2009.

In the first case I found a beta value of the nominally risk free cash flow close to zero. This means that in the period in question, 1988-2006, the risk of inflation uncertainty did not affect the valuation of equity of the firm. Based on this one can argue that Summers (1986) was right to assume that depreciation allowances are “nearly” risk free. But of course, this is just one period. The result might not have been the same if we looked at another time period with different economic conditions.

In the second case, with an American multinational investing in Norway, I found a negative beta value of the nominally NOK-risk-free claim. In CAPM-terms this means that the return on the market portfolio and the return on the claim are negatively correlated. I argued that the origin of uncertainty came from the close relationship of the oil price and the value of the Norwegian currency. It is reasonable to assume, since Norway is a major oil-exporting country, that the value of NOK will be high when the oil price is high. Further on, the oil price will of course depend on the supply- and demand forces in the market. It is argued that in periods where the oil price variations are dominated by changes on the supply side the beta value of the oil price will be negative in the U.S., i.e. the return on the S&P 500 is low when the oil price is high and vice versa. The reason is that changes in the oil price that are supply

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side- dominated are associated with factors that have a negative influence on the world economy, like political unrest, wars and strained relationships among OPEC-countries. Naturally, new technologies in the energy sector and newly discovered oilfields will also affect the supply side. These factors can be related to the period 2003-2009, and therefore explain the negative beta value found.