Sampa Video, Inc.
• A small video chain is deciding whether to engage in
a new line of delivery business and is conducting an
economic analysis of the valuation impacts of this
decision.
• This is a case basically regarding how to measure
the benefits of financial leverage via different
valuation approaches.
Firm valuation (discount cash
flow) and cost of capital
• When you use the after-tax cost of capital to be
the discount rate, you basically take in the
effect of the financing.
• If you discount the project cash flows (without
financing) by the after-tax cost of capital, you
will get the exact net present value as you use
it to discount the total cash flows (project cash
flows plus the financing cash flows).
• That is, when you use the after-tax cost of
capital to discount financing related cash flows,
the net present value would be zero.
（t=0）
（t=1）
（t=2）
（t=3）
（t=4）
6,000,000
6,000,000
6,000,000
6,000,000
(2,000,000)
(2,000,000)
(2,000,000)
(2,000,000)
Deprec.
2,000,000
2,000,000
2,000,000
2,000,000
OP CF
3,500,000
3,500,000
3,500,000
3,500,000
Initial invest.
(total cost)
(8,000,000)
Inc. rev.
Inc. cost
NOP CF
3,000,000
Project CF
(8,000,000)
Financing
8,000,000
Interest (AT)
3,500,000
3,500,000
3,500,000
6,500,000
(360,000)
(360,000)
(360,000)
(360,000)
Repay.
Fin. Rel. CF
Total CF
(8,000,000)
8,000,000
(360,000)
(360,000)
(360,000)
(8,360,000)
0
3,140,000
3,140,000
3,140,000
(1,860,000)
Assuming that financing totally comes from debt, and the before-tax
cost of capital is 6%, tax rate 25%, so the after-tax cost of capital 4.5%.
（t=0）
（t=1）
（t=2）
（t=3）
（t=4）
Project CF
(8,000,000)
3,500,000
3,500,000
3,500,000
6,500,000
NPV (at 4.5%)
7,072,024
（t=1）
（t=2）
（t=3）
（t=4）
3,140,000
3,140,000
3,140,000
(1,860,000)
(t=3）
（t=4）
（t=0）
Total CF
0
NPV (at 4.5%)
Fin. Rel. CF
NPV (at 4.5%)
7,072,024
（t=0）
（t=1）
（t=2）
8,000,000
(360,000)
(360,000)
0
(360,000)
(8,360,000)
Valuation Methods
• Adjusted Present Value (APV) Approach
EBIT(1  t ) tk D D
VL 

 Vu  tD
k su
kD
• WACC approach
– VL = CFL / WACC
where WACC = KSU[1-twd]
• Capital cash flows approach
– VL = (CFL+KDD) / KSU
Adjusted Present Value (APV)
Approach
• APV = PV of asset flows + PV of side
effects associated with the financing
program.
EBIT(1  t ) tk D D
VL 

 Vu  tD
k su
kD
Adjusted Present Value (APV) Approach
• 1. Calculate PV of project (or enterprise)
assuming it is all equity financed (i.e. no
interest expense)
• 2. Calculate value of tax shield. Compare tax
payments with vs. without debt. The difference
equals the tax savings available from the
interest deduction (tax shield). Discount tax
savings at pre-tax rate of return on debt
• 3. Total firm value = value of the all equity firm +
side effects of financing.
All Equity Valuation of the Project
• Free Cash Flow to the Firm = EBIT (1 - tax rate) – (Capital
Expenditures - Depreciation) – Change in Non-cash
Working Capital
If depreciation is straight line, the initial capital expenditure
appears to be depreciated over 7.5 years ($200,000; or
$1,500,000/7.5). The annual capital expenditures of $300,000
seems to be depreciated over 12 years. ($25,000; or 300,000/12)
All Equity Valuation – Cost of Capital
(unlevered equity)
•
•
•
•
Asset Beta
Risk free rate
Market risk premium
Asset Return
[A] from Exhibit 2
[B] from Exhibit 2
[C] from Exhibit 2
[D] = [B] + [A] * [C]
1.50
5.0%
7.2%
15.8%
All Equity Valuation of the Project
2002E
2003E
•
•
•
•
Free CF
-112.0
Discount Rate 15.8%
Discount Factor 0.864
Present Value
-96.7
•
TV=495(1+5%)/(15.8%-5%) = 4812.5
•
•
•
Total PV of FCF
Less: Initial Investment
Net Present Value
6.0
15.8%
0.746
4.5
2004E
2005E
2006E
TV
151.0
15.8%
0.644
97.2
314.0
15.8%
0.556
174.6
495.0
15.8%
0.480
237.7
4812.5
2728.5
1500.0
1228.5
0.480
2311.1
The Value of the Levered Firm: The NPV
of the Project with a Fixed Level of Debt
• To calculate the net present value of the
firm assuming it borrows $750,000 in
perpetuity to fund this project.
• Use APV approach.
Calculate the value of tax shield
• The present value of the expected interest tax
shields equals the expected interest tax shields
discounted at the appropriate cost of capital.
• The cost of debt is 6.8% in Exhibit 3, which is
consistent with the debt beta of .25 from Exhibit
3. Because the debt will be in place forever, the
value of the perpetual shield is equal to:
• V (Tax Shield) = $750,000 * .40 * 6.8% / 6.8% =
$300,000.
The Adjusted Present Value calculation
• The value of the unlevered firm is
$1,228,500,
• The value of the levered firm is equal to
the value of the unlevered firm plus the
present value of tax shields, $300,000,
or $1,528,500
The Value of the Levered Firm: The NPV of the
Project with a Fixed Proportion (25%) Debt
• To calculate the value of the project if the
firm maintains a policy of maintaining
debt-to-value at 25% in each period.
• To use the Weighted Average Cost of
Capital (WACC) method.
• To use the WACC to discount the free
cash flows, which is already calculated .
• VL = CFL / WACC
Calculation of cost of capital –
D
S







levered firm
SD
SD
a
•
•
•
•
•
•
•
•
•
•
•
d
s
Debt beta
[E] from Exhibit 2
0.25
Debt percentage
[F] from questions
25%
Debt Return
[G] = [B] + [F] * [C]
6.8%
Debt beta contribution [H] = [E] * [F]
0.06
Equity beta
[I] = ([A] - [H]) / [J]
1.92
Equity percentage
[J] = 1 - [F]
75%
Equity Return
[K] = [B] + [I] * [C]
18.8%
Equity beta contribution [L] = [I] * [J]
1.44
Asset beta
[M] = [H] + [L] = [A]
1.50
Tax Rate
[N] from Exhibit 2
40%
WACC
[O] = (1-[N]) * [F] * [G] + [J] * [K]
15.1%
Weighted Average Cost of Capital Valuation
with a target debt-to-value ratio of 25%
2002E
2003E
•
•
•
•
Free CF
-112.0
Discount Rate 15.1%
Discount Factor 0.869
Present Value
-96.7
•
TV=495(1+5%)/(15.1%-5%) =5135.9
•
•
•
Total PV of FCF
Less: Initial Investment
Net Present Value
6.0
15.1%
0.755
4.5
2004E
2005E
2006E
TV
151.0
15.1%
0.655
97.2
314.0
15.1%
0.569
174.6
495.0
15.1%
0.495
237.7
5135.9
2970.0
1500.0
1470.0
0.495
2311.1
Capital Cash Flow Valuation with a
target debt-to-value ratio of 25%
Capital Cash Flow Valuation with a
target debt-to-value ratio of 25%
Capital Cash Flow Valuation with
a target debt-to-value ratio of 25%
• To calculate the end-of-year debt balances
implied by the 25% target debt-to-value ratio.
• The capital cash flows are calculated by adding
expected interest tax shield to the free cash
flows.
• The terminal value is calculated using the
capital cash flow for year 5.
• The value of the project using the Capital Cash
Flow approach is $1,470,000, which is the same
as the value using a tax adjusted discount rate
Weighted Average Cost of Capital Valuation
with a target debt-to-value ratio of 25%
•
•
•
•
•
PV of Future FCF
Debt at 25% of Value
Debt Rate
Tax Rate
Interest tax shield
2002E
2970.0
742.5
6.80%
40%
20.2
2003E
3531.0
882.8
6.80%
40%
24.0
•
•
•
Free CF
Interest tax shield
Capital Cash Flow
-112.0
20.2
-91.8
6.0
24.0
30.0
•
•
•
Discount Rate
Discount Factor
Present Value
15.8%
0.864
-79.3
15.8%
0.746
22.4
•
TV=495(1+5%)/(15.1%-5%) =5135.9
•
•
•
Total PV of FCF
2970.0
Less: Initial Investment 1500.0
Net Present Value
1470.0
2004E
4058.9
1014.7
6.80%
40%
27.6
151.0
27.6
178.6
15.8%
0.644
115.0
2005E
4521.6
1130.4
6.80%
40%
30.7
2006E
4891.3
1222.8
6.80%
40%
33.3
314.0
30.7
344.7
495.0
33.3
528.3
15.8%
0.556
191.7
15.8%
0.480
253.7
TV
5135.9
5135.9
0.480
2466.4
Comparison between the WACC
and CCF approaches
• Both the WACC and CCF approaches make the
same assumption that debt is proportional to
value, and because the approaches make the
same assumption, they provide the same values.
• WACC and CCF are special valuation rules,
when debt is assumed to be a fixed proportion
of firm value, and therefore, it is appropriate to
discount interest tax shields at the same rate as
unlevered firm.
The Payoff: Reconciling the valuations
• Value of the project with no debt
$1,228,500
• Value of project with $750,000 debt forever $1,528,500
• Value of project with 25% D/V forever
$1,470,000
Why are the present values of the interest tax
shield greater for the firm with $750,000 in debt
that with the 25% debt-to-value ratio?
• The level of debt with the fixed debt policy is
fixed and thus the interest tax shields have the
same risk as the debt. The discount rate for
interest tax shields with the fixed debt policy
therefore is the debt rate of 6.8%.
• With the 25% debt-to-value policy, the amount of
debt varies with the value of the firm so the
expected interest tax shields also vary with the
value of the firm. These tax shields therefore
should be discounted at the expected asset
return 15.8%, which is higher than the debt rate.