samlet årgang - Økonomisk Institut - Københavns Universitet

TAXATION OF SHAREHOLDER INCOME AND THE COST OF CAPITAL IN AN OPEN ECONOMY 439
This distortionary effect of taxation will also prevail in the more likely case where
investors are less than perfectly diversified. From (14) and (15) we see that unquoted
shares with different risk characteristics will have different -values, in which case the
personal shareholder income tax t will have a different impact on the cost of capital for
different types of unquoted companies.
4. A personal tax on the equity premium: Neutrality of the Norwegian tax
regime in a world of well-diversified investors
I will now show that this distortion may be eliminated if the shareholder income tax
is levied only on the equity premium, defined as the excess of the rate of return on shares
over the after-tax interest rate on risk-free bonds. Such a tax was proposed in
Sørensen (2005a) and will be introduced in Norway from 2006.
When shareholders are allowed a deduction for their opportunity cost of investment,
given by the risk-free rate of return, the actual and expected after-tax returns on
shares will be
Rj =rj –t(rj –i), Re j =rej –t(rej –i), j= 1, 2, 3 (18)
Note that the tax system in (18) is assumed to be symmetric: if shareholders fail to
obtain a return equal to the risk free rate, they can deduct their »loss« i – r j against
income from other shares (or they can carry their tax loss forward with interest so that
the deduction maintains its present value). Under the tax regime (18) the variances and
covariances of the net rates of return will still be given by (9) and (10), as the reader
may easily verify. Substitution of (9), (10) and (18) into (5) through (7) then yields
r e 1 = i + (1 –t) (v12 1 + v212 + v313 ) (19)
r e 2 = i + (1 –t) (v22 2 + v112 + v323 ) (20)
r e 3 = i + (1 –t) (v323 + v113 + v223 ) (21)
Solving (21) for (1 – t) and substituting the result into (19) and (20), we find that
r e 1 = i + 1 (re 3
r e 2 = i + 2 (re 3
– i) (22)
– i) (23)
where 1 and 2 are defined in (14) and (15). Recall that when portfolios are welldiversified,
we have j → j 3 /2 3 . Thus it follows from (22) and (23) that a shareholder