3.3 Bond Yield Plus Risk Premium Model
The first method to estimate the capitalization rate was the
method used by the French tax authority. Farming consultants have to keep in
mind that their valuation methods can be used as the base of the calculation
for a capital gain on the sale of a company. The tax authority therefore has
the right to modify the tax base if it considers that the results do not
represent a fair value at the time of the transaction. The most common tax
adjustment in those cases is the hidden donation, when the tax authority
considers that the company or its shares (not publicly tradable in the case of
most farms) are undervalued. This is why it is necessary to include the methods
used by the administration in this study. In reality, this method is based on
the CAPM, as the risk premium is the difference with the total expected return
minus the risk-free return. The actualization rate formula can be presented in
this way:
A: Actualization rate,
Rf: Risk free rate,
â: Beta,
Rp: Risk premium for the French market.
3.3.1
Risk-Free Rate
As presented by Sharpe (1964) it was assumed that everyone can
borrow or lend its funds at a «pure rate of interest». This risk-free
rate is considered by the tax authority as the government bonds rate (Direction
Générale des Impots, 2006), and was assumed in this paper as
equivalent to the French government debt reference rate, given by the French
central bank (a 12 month average of the 10 years bonds monthly average was
used).
3.3.2 Beta and Risk premium
The risk free rate has to be increased by a risk premium,
justified by the necessary supplementary yield that a risky asset needs to
deliver compare to a pure interest rate. The tax authority recommends using the
historical risk premium observed in the French economy, which can be increased
to consider the size of the company studied. For the calculations, the
references of the tax authority were used, and an increase to consider that we
are dealing with micro-capitalization.
The first bias that arises is easy to consider, as stated by
Damodoran (2011), would be to include 2008 stock results in our time-frame: the
major crash observed this year would diminish the results significantly,
leading investors to think that the risk would be lower after the 2008 crisis
than before. However, from a pragmatic point of view, this could be considered
as logical: there is less risk of a major historical crisis after it happens
than before, like there are less risks of a centenary flood after ones
happen.
The Beta is used to consider the risk relative to the company
and the sector in which it operates (Direction Générale des
Impots, 2006). Once again, the tax authority produced some recommendation and
we will base our calculation on it. We will compare this beta with the beta
observed by another author for agriculture in France.
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