samlet årgang - Økonomisk Institut - Københavns Universitet

TAXATION OF SHAREHOLDER INCOME AND THE COST OF CAPITAL IN AN OPEN ECONOMY 437
3. The distortionary effect of a personal tax on the full return to equity
Suppose the government levies a symmetric residence-based personal tax at the
rate t on all returns to shares (since we focus on shareholder income taxes, we do not
explicitly model other taxes). If rj and re j are the actual and expected pre-tax returns to
shares of type j, and if taxpayers are granted full loss offsets, we then have
Rj =(1–t) rj , Re j =(1 –t)re j , j=1,2,3 (8)
ˆ 2 j E (R j –R e j )2 =(1 –t) 2 2 j
, j =1,2,3 (9)
ˆ ij E (R i –R e i )(R j –Re j =(1 –t) 2 ij , j =1,2 j = 2, 3 (10)
where 2 j and ij are the variances and covariances of the pre-tax rates of return, respectively.
Inserting (8) through (10) into (5) through (7), we find
i
r e 1 = + (1–t) (v121 + v212 + v313 ) (11)
1–t
i
r e 2 = + (1–t) (v222 + v112 + v323 ) (12)
1–t
i
r e 3 = + (1–t) (v323 + v113 + v223 ) (13)
1–t
The interest rate i and the required expected rate of return r e 3 on quoted shares are
exogenously given from the world market and hence unaffected by the shareholder
income tax. 1 To see how the tax affects the required expected returns on unquoted
shares, we solve (13) for (1 – t) and insert the result into (11) and (12) to get
1. Strictly speaking, since i i p (1 – ) is an after-tax interest rate, it is determined by the pre-tax interest
rate i p given from the world capital market and by the domestic personal tax rate on interest income, . If the
latter were always equal to the tax rate t on shareholder income, the terms i / (1 – t) in (14) and (15) would be
replaced by i p , and the shareholder income tax would not distort the cost of corporate finance (although the
corporate income tax would still drive up the required pre-tax return on the company’s real investment).
However, since I wish to study the effect of granting double tax relief at the shareholder level, the focus of
the present paper is on the isolated effect of personal taxes on income from shares, so the personal tax rate
on interest income is taken as given and independent of t.