Taxes and Business Strategies

NHH FIE-441

Dirk Schindler

Spring 2015

Taxes and Business Strategies

Homework 1: Corporate Finance, Taxation and Domestic Firms

Consider the financial policy of a domestic firm for the periods t = 1, 2, 3. Real

investment generates a cash-flow zt in each period t. The firm can raise capital

at the capital market by issuing bonds (i.e., debt) Bt at interest rate ib and by

offering new stocks (i.e., equity) Vtn . The opportunity costs of shareholders are

given by ρ and are constant over time. For any period t, the share of new stocks

in total equity is denoted by ηt = Vtn /Vt .

Only costs of debt (interest expenses and potential agency costs), but not costs

of equity can be deducted from the corporate tax base. The corporate tax rate is

given by τ . The dividend policy is residual and the dividend Dt in each period t

is determined by cash-inflows and cash-outflows.

(a) Show analytically that the value of old stocks in period t = 2 (i.e., the value

of V2o ) is given by

V2o =

1 − η2

[D2 + V3o ] .

1+ρ

Provide an economic interpretation for this finding.

(b) Assume that some of the old shareholders leave and sell their stocks back

to the firm so that Vtn < 0. Explain verbally (no equations required!), why

a repayment of equity to shareholders that return their old shares at the

beginning of period 2 does not affect remaining shareholders’ stock value

V2o and wealth if the repayment is financed by a cut in the dividend D1

(which is paid beginning of period 2) to remaining old shareholders and if

the investment policy remains unchanged.

(c) The condition for firm value in period t = 2 is

0

W2 =

V3 + z3 + B3

+ z2 ,

1 + r2

where r2 = ρ(1 − b2 ) + ib (1 − τ )b2 + C(b2 ) denotes effective capital costs of the

firm, where b2 =

B2

B2 +V2

is the debt-to-asset ratio, and C(b2 ) with C ′ (b2 ) > 0,

C ′′ (b2 ) > 0 are additional costs of debt (i.e., “agency-costs”).

Take for granted that ρ = ib holds in a capital market equilibrium and...