Untitled-29

Capital Structure Theories^273

the value of firm L (the levered firm) is equal to the value of the unlevered firm plus

the present value of the interest tax shield as shown in Equation below:

Value of levered firm = Value of unlevered firm + PV of tax shield

Vt = vu+ TD

...(13)

We can write Equation (13) in its expanded form as follows:

Vt =

 

 



-+

...(14)

where Vt is the value of the firm with debt, X (I - T) is perpetual operating income

stream of the pure-equity firm, ku is the pure-equity capitalisation rate, kd is the

expected rate of return on debt, D is debt and D is the corporate tax rate.

Equation (13) implies that when the corporate tax rate, T, is positive (T > 0), the value

of the levered firm will increase continuously with debt. Thus, theoretically the

value of the firm will be maximum when it employs 100 per cent debt. This is shown

in Figure 8.

Figure 8: Value of levered firm Figure 9: Cost of capital of the evered firm

Vl=Vu+TD

V
V

V

V

TD

l V

u

l l

(^1) = +
1 =V +
V
u TL
l
(setting D/Vl = L)
V V
l TL
= u
1 -
Thus, for T > 0, Vl will be maximum when L = 1.0.
Under the assumption of the M-M hypothesis with corporate taxes, the levered firmís
cost of capital is given by the following formula:
kl = ku(1ñTL) ...(15)
where k, is the levered firmís cost of capital, ku is the pure-equity capitalisation rate,
Value
Vu Vu
o Leverage D/V
V 1
Cost
kd kd
o Leverage D/V
k 1