Impact of Debt Policy on Capital Budgeting (Ch. 19)
FORMULAS FROM CH 18
VL = VU + D*T’
– PV(COFD), where T’
= 1 – [(1 - Tpe)(1 - Tc)]/(
1 - Tp)]
Cost of debt = Rd (1 –
T’), where Rd is the (before tax)
WACC = (D/V) Rd (1
- T’)+ (E/V) Re = Ra
*(1 – [D/V]* T’)
Re = Ra + (D/E) (Ra - Rd) (1
- T’)
·
The value of debt in all these formulas is the market value.
Whenever we have a debt ratio (debt-to-value or debt-equity), it is a
market value debt ratio (using market values for both debt and equity)
·
The formulas assume that the firm maintains a constant debt
ratio over time. If the value of
the assets increases, the firm will increase its debt; if the value of the
assets falls, the firm will reduce its debt.
·
Theoretically, we can recognize that costs of financial
distress exist. But in practice
there is no reliable way to estimate future COFD or their PV.
We are forced to leave COFD out of our computations.
COMPUTATIONS
FOR A FIRM
·
There are two approaches to computing VL:
o
Adjusted
PV (APV) – compute VU by discounting expected cashflows at Ra,
and make a separate adjustment for PVTS by adding D*T’
o
WACC
– compute VL directly in one step by discounting expected cashflows
at WACC. This implicitly accounts
for the value of interest tax shields through the discount rate.
o
The
book calls Ra the opportunity cost of capital. It is the discount rate we would use for an all-equity firm
or an all-equity project. It
reflects the risk of the cashflows generated by the assets and does not make any
adjustments for the impact of debt financing (i.e. value of tax shields).
When we discount at this rate, we have to separately account for the
value of tax shields.
o
WACC
is called the adjusted cost of capital. It
adjusts for the value of tax shields in the discount rate itself.
No separate adjustment for the impact of debt financing is necessary.
·
Like in Chapter 17, we can compute EL directly
by discounting cashflows to s/h at Re only if we already know EL
or if we know the firm’s debt-equity ratio.
If neither of these values is known, the only way to compute EL
is by going VL - DL.
·
Consider a firm whose assets will generate a perpetuity of $2
million. If the firm remains
unlevered, its required return will be 10%.
The firm has issued perpetual debt with expected interest payments of
$0.5 million each year, and a required return of 6%. Assume that T’ is 20%. Compute WACC, VL, EL.
·
Note that when you’re not given D/E or D/V you can’t
compute WACC till you know VLor EL.
·
We’ll have to first get VU and DL.
Then we can compute everything else
·
DL = 500,000/.06 = 8,333,333.33
·
VU = 2,000,000/.1 = 20,000,000
·
Using APV approach, VL = 20,000,000 +
8,333,333.33*.2 = 21,666,666.67
·
EL = 21,666,666.67 - 8,333,333.33 = 13,333,333.33
=> D/VL = 8,333,333.33/21,666,666.67 =
.3846, and D/E = .625
·
Re
= Ra + (D/E) (Ra
- Rd) (1 - T’) = .10 + .625*(.10 - .06)*.8 = 12%
·
Now there are 2 ways to compute WACC:
WACC = (D/V) Rd (1
- T’)+ (E/V) Re =
.3846*.06*.8 + (1 - .3846)*.12 = 9.2308%
WACC = Ra *(1 – [D/V]*
T’) = .10*(1 – .3846*.2)
= 9.2308%
·
We can now verify both VL and EL:
VL = 2,000,000/.092308 =
21,666,666.67
CF to s/h = 2,000,000 – 500,000 +
interest tax shield = 1,500,000 + 500,000*.2 = 1,600,000
EL = 1,600,000/.12 =
13,333,333.33
· Suppose we now want to know how WACC, VL, EL will change if the firm increases its debt-to-value ratio to 50%. Note that Ra will stay the same (since it doesn’t depend on leverage); Rd, Re and WACC will all change. DL, EL and VL will all change as well.
WACC = Ra *(1 – [D/V]*
T’) = .10*(1 – .5*.2)
= 9%
VL = 2,000,000/.09 =
22,222,222.22
Since D/V = E/V = 0.5, both DL
and EL are 11,111,111.11
We can confirm VL by
going VU + D*T = 20,000,000 + 11,111,111.11*.2 = 22,222,222.22
(Without Rd we can’t
compute Re. Else we could confirm WACC and EL as well.)
COMPUTATIONS FOR A PROJECT
· We use the same approach, except we
also include issue costs:
NPV of debt financed project = NPV if equity financed
+ PVTS – Issue costs
Once
again we are forced to ignore COFD.
Under
the APV approach, we get the NPV under equity financing by discounting the
project’s cashflows at Ra and then we add D*T’.
Under the WACC approach, we discount the project’s
cashflows at WACC to get (NPV if equity financed + PVTS) in one step
· Consider
a project with an investment of $1 million, and expected cashflows of
$108,000 forever. If the project
was all-equity financed, its required return would be 11.2%.
The project will be financed as follows:
a)
30% of the required investment will come from internally
generated funds
b)
25% of the required investment will be new equity.
Equity has issue costs of 5%.
c)
45% of the required investment will be new debt.
Debt has issue costs of 3%.
Assume that T’ is 20%.
Should the project be accepted? What
is the project’s WACC?
o
Base
case NPV = 108,000/.112 – 1,000,000 = -35,714.29
o
Amount
of new equity needed after issue costs = .25*1,000,000 = 250,000
Let X = amount of new equity to be
issued
Then X*(1 - .05) = 250,000
=> X = 263,157.89
Issue costs for equity = 263,157.89
* .05 = 13,157.89
Similarly, if Y = amount of new
debt to be issued, then Y*(1 - .03) = 450,000
=> Y = 463,917.53, and issue
costs for debt = 463,917.53 * .03 = 13,917.53
o
Total
issue costs = 13,157.89 + 13,917.53 = 27,075.42
o
PVTS
= 463,917.53*.2 = 92,783.51
o
Total
NPV of project = -35,714.29 + 92,783.51 - 27,075.42 = 29,993.80
o
In
this example, WACC cannot be computed till we first figure out the project’s
total NPV. The reason is that we
don’t know the market value debt ratio till we know the project’s NPV.
Also, the concept of WACC includes PVTS but not issue costs.
So to compute WACC using the formula Ra
*(1 – [D/V]* T’), we have to leave out issue costs when
computing V.
In other words, V is the value of
the project before issue costs = Investment + base case NPV + PVTS =
1,057,069.22
D/V = 463,917.53/1,057,069.22 =
.4389
WACC = Ra *(1 – [D/V]*
T’) = .112 * (1 - .4389 * .2) = 10.22%
(To verify, discounting the
project’s cashflows at this WACC should give us the project’s value before
issue costs, i.e. 1,057,069.22.
108,000/.1022 does indeed turn out to be 1,057,069.22.)