Finance for International Business A Review of Basic Valuation Techniques A good
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Question
Finance for International Business
A Review of Basic Valuation Techniques
A good understanding of valuation methods is essential before we can discuss valuation in an international context. The following exercises are a refresher.
Objective: To illustrate the equivalence of various valuation methods.
Consider a firm as follows: Assume that the firm has no debt. The cashflows are received at the end of each year and are perpetual. Cost of equity capital for an unlevered firm, r0 , is 20%. The first cash-flow will be received one year from today. All calculations for valuation are done today. Firm value is defined as collective value of debt and equity.
Sales $ 500,000
Cash Costs 360,000
________
Operating Income 140,000
Tax @ 34% -47,600
________
Unlevered cash flow (UCF) $ 92,400
Find the firm value, using
a) APV method $__________.
b) FTE method $__________.
c) WACC method $__________.
Now assume that the firm has $126,229.50 of debt. Interest rate on debt is 10%
Find the firm value using
d) APV method $__________.
e) FTE method $__________.
f) WACC method $__________.
________________________________________________________________________
Objective: To illustrate that financing has no impact on firm value if there are no taxes (i.e. financing affects firm value purely because the interest payments generate tax-savings), and to further illustrate the equivalence of various valuation methods.
Assume the the firm has $ 100,000 of debt @ 10% and the tax rate is zero.
Find the firm value using
g) APV method $__________.
h) FTE method $__________.
i) WACC method $__________.
Assume the the firm has $ 200,000 of debt @10% and the tax rate is zero.
Find the firm value using
j) APV method $__________.
k) FTE method $__________.
l) WACC method $__________.
Notes:
1) Depreciation, amortization and capital expenditures were left out for simplicity. These considerations will affect operating income; and will therefore affect value,but the rest of the analysis will be conceptually unchanged.
2) Changes in working capital will occur if there is growth, these will affect UCF (and value). We left these out because we assumed no growth, for simplicity.
3) Our leverage was constant across time; as a result we were able to use a constant WACC. If we change leverage (for example, paying off debt or adding on more) we need to adjust WACC. This is operationally difficult beacuse of the circularity (to find Value we need to know WACC and to find WACC we need to know the Value). This is where the APV method is useful. APV explicitly relies on the fact that firm value depends on financing only to the extent of the tax impact of financing. In any event, all methods -when properly applied- must provide the same answer.
Suggested Reference: Corporate Finance- Ross, Westerfield and Jaffe, 1993, pp 493-502.
Explanation / Answer
Formulas for 3 Methods
WACC Approach
V = St UCFt / (1+rWACC)t
UCF -- expected, after-tax, unlevered cash flow
rWACC = wB rB(1-T)+wS rS
Key assumption -- the weights are constant
Inputs: (1) leverage ratio (weights), (2) component costs of capital, (3) cash flows
APV Approach
V = St UCFt / (1+r0)t + PV(financing effects)
PV(financing effects) = PV(tax shield) + PV(subsidies) - PV(fin. distress/agency costs) – PV (other side-effects)
UCF -- expected, after-tax, unlevered cash flow
r0 -- required return on unlevered equity
Key assumption -- $ amount of debt known
Inputs: (1) financing effects, (2) cost of unlevered equity, (3) cash flows
FTE Approach
S = St LCFt / (1+rS)t
LCF -- expected, after-tax, levered cash flow
rS -- required return on levered equity
Key assumptions -- debt cash flows known, rS constant
Inputs: (1) cost of levered equity, (2) cash flows
Case-1 Valuation under 3 methods (If no Debt)
APV =
Unlevered Cash Flow/ (1+r)
=
92400/(0.2)
=
462000
FTE =
Levered Cash Flow / (1+s)
=
92400/(0.2)
=
462000
Note: Here no debt so ULF=LCF
WACC
UCF / (1+WACC)
=
92400/(0.2)
=
462000
Case – 2 :Now assume that the firm has $126,229.50 of debt. Interest rate on debt is 10%
Sales
500000
Less:
Cash Cost
360000
Operating Income
140000
Less:
Tax @ 34%
47600
UCF
92400
Levered Cash Flow
UCF
92400
Less:
Interest (1-tax)
8331
(12623)(1-0.34)
LCF
84069
APV =
Unlevered Cash Flow/ (1+r) + Tax Shield (Debt)
=
92400/(0.2) + 0.34 126229.5)
=
504918
FTE =
Levered Cash Flow / (1+s)
=
84069/(0.2)
=
420345
Debt =
(10 (1-tax)
ValueWACC=
UCF / (1+WACC)
=
92400/(0.2+0.066)
=
347368
Case – 3 Assume the the firm has $ 100,000 of debt @ 10% and the tax rate is zero.
Sales
500000
Less:
Cash Cost
360000
Operating Income
140000
Less:
Tax
0
UCF
140000
Levered Cash Flow
UCF
140000
Less:
Interest (1-tax)
10000
(12623)(1-0)
LCF
130000
APV =
Unlevered Cash Flow/ (1+r) + Tax Shield (Debt)
=
140000/(0.2) + 0 (100000)
=
700000
FTE =
Levered Cash Flow / (1+s)
=
130000/(0.2)
=
650000
Debt =
(10 (1-tax)
Value WACC
UCF / (1+WACC)
=
140000/(0.2+0.1)
=
466666
Case – 4 Assume the the firm has $ 200,000 of debt @10% and the tax rate is zero.
Sales
500000
Less:
Cash Cost
360000
Operating Income
140000
Less:
Tax
0
UCF
140000
Levered Cash Flow
UCF
140000
Less:
Interest (1-tax)
20000
(12623)(1-0)
LCF
120000
APV =
Unlevered Cash Flow/ (1+r) + Tax Shield (Debt)
=
140000/(0.2) + 0 (200000)
=
700000
FTE =
Levered Cash Flow / (1+s)
=
120000/(0.2)
=
600000
Debt =
(10 (1-tax)
Value WACC
UCF / (1+WACC)
=
140000/(0.2+0.1)
=
466666
APV =
Unlevered Cash Flow/ (1+r)
=
92400/(0.2)
=
462000
FTE =
Levered Cash Flow / (1+s)
=
92400/(0.2)
=
462000
Note: Here no debt so ULF=LCF
WACC
UCF / (1+WACC)
=
92400/(0.2)
=
462000
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