Corporate Valuation and Financing
Exercises Session 3
«Valuing levered and companies, the wacc»
Laurent Frisque - laurent.frisque@gmail.com
Steve Plasman – steve.plasman@gmail.com
Q1 Modigliani Miller I
Q1: To value: Freshwater Corp.
• No taxes and perfectly efficient markets.
• Currently the company is not levered all.
• EBIT per year: 500.000 $ and should remain the same perpetually.
• The cost of equity of the company is worth 12% =Re.
In this case what is the value of the company?
Q1 Modigliani Miller I
Q1: In this case what is the value of the company?
• The cost of equity of the company is worth 12% =Re=Ra (no leverage).
Vunlevered
= EBT / Ra
(no Interests)
= 500.000 / 12%
= 4.166.667
Q1 Modigliani Miller I
Q1: To value: Freshwater Corp.
• Issue a perpetual debt for which you pay 30.000$, to buy back shares.
• Interest each year (the borrowing rate of the company is 3%)
What would then be the market value of the company?
Interests =
30.000
Rd
=
3%
D
=
1.000.000
Vu
E
=
=
4.166.667
3.166.667
(E + D = Vu)
Q1 Modigliani Miller I
Q1: And of ra , the wacc, and re?
Ra
= 12%
Unchanged by definition
Re*E
Re
= Ra*Vu - Rd*D
= (Ra*Vu - Rd*D)/ E
= 14,84%
Or Re
= (EBT – I) / E
Wacc
= 12%
(because NO taxes)
Q2 Valuing levered Companies in a world with taxes
Q2: Bobland, not a perfect world: Corporate tax rates: 25% (Tc)
• Same capital structure and revenues as in Tongoland.
What is the value of the levered company? (Vl)
EBIT
=
EBIT (1-Tc) =
Vunlevered
500.000 (Unlevered)
375.000
= EBIT (1-Tc) / Ra = 375.000 / 12% = 3.125.000
Interests = 30.000
Rd = 3%
D = I/Rd = 1.000.000
Tax Shield = Tc*D = 250.000
V levered
= Vu + Tax Shield = 3.375.000
Q2 Valuing levered Companies in a world with taxes
Q2: And of ra, the wacc, and re?
Ra = 12%
Unchanged by definition
Wacc = EBIT * (1-Tc) / VL = 11,11%
Atlernative:
L = D/VL
Wacc = Ra * (1 – Tc*L)
E = VL – D = 2.375.000
Net Earnings = (EBIT-I) * (1-Tc)
Re = Net Earnings / E = 14,84%
Atlernative:
Re = Ra + (Ra – Rd) * (1-Tc)* D/E
Q3 Marginal versus Average Tax RateValuing
Q3: The subsidiary has an EBIT of 250.000$.
The tax structure in Sloland:
•
•
•
the first 100.000$ are tax exempt
the following 100.000$ taxed at 20%
any amount above that is taxed at 30%.
Issue a perpetual debt 75000$ to benefit from the tax shield.
Skeptical with an average tax rate.
Cost of debt (= risk free rate: 4%), he values the tax shield at 10.500$
Hardly interesting in view of the costs associated with a debt issue.
A. Is he right?
B. What would have been the tax shield if the debt had been reimbursed
after two years?
Q3 Marginal versus Average Tax RateValuing
Q3: A. Is he right?
Issue a perpetual debt worth 75000$ to benefit from the tax shield
• Average tax rate = 14%
• D = 75.000
PV Tax Shield = D * Average Tax Rate = 10.500
EBIT = 250.000
Interest payment = 75.000 * 4% = 3.000
Tax saving = 900 (perpetual)
PV Tax saving = 22.500
Q3 Marginal versus Average Tax RateValuing
Q3: B. What would have been the tax shield if the debt had been reimbursed
after two years?
Q4 Leveraging and deleveraging Betas, Company
valuation using the WACC
Q 4: In 2010, Acquisition of Wellstream. Competitors Technip and Prysmian.
Risk Higher: GE’s WACC is not appropriate to value this acquisition.
You get following data:
Comparison
•
•
•
•
•
•
Be
D/E
P/B
D/ Market Cap
Tax rate
1-T
GE
1,16
1,67
2,75
61%
15%
85%
WSM
1,30
1,0
7
14%
25%
75%
Technip
1,35
0
1,85
0%
33%
67%
Prysmian
1,32
0,45
3
15%
30%
70%
Target D/E for Wellstream acquisition: 0.4
Wellstream’s expected real asset cash-flows next year: 50 million $
Growth rate of Wellstream’s cash-flows: 1.5% per year
Marginal corporate tax rate: 20%
Discount rate on debt: 2% (riskless rate)
Expected return of the market portfolio: 7%
Q4 Leveraging and deleveraging Betas, Company
valuation using the WACC
• a) Estimate Wellstream’ beta of operating assets from the peers.
You overheard Technip has also another division, so you may have to
eliminate it.
Q4 Leveraging and deleveraging Betas, Company
valuation using the WACC
• b) Compute the WACC for the Wellstream’s acquisition.
WACC = Re *E/VL + Rd *(1-Tc)*D/VL
• c) Determine the value of this acquisition with the WACC computed in b),
knowing that Wellstreams’s debt is valued at 50 million $.
MARKET VALUE of E !!
Q4 Leveraging and deleveraging Betas, Company
valuation using the WACC
• d) Determine the value of Wellstream with GE’s WACC.
• e) Apply the adjusted present value method to value Welstream’s
acquisition
Q5 APV and wacc
•
•
•
•
•
•
•
•
•
•
Analyse the interest of a new project. The following data are available.
Initial investment of 1 million € in year 0
Additional EBIT of 450.000€ during 5 years (years 1 to 5).
After year 5 there will be no more sales
WCR constant for the whole project.
No depreciation
Target leverage ratio of 50%
Ra 10%
rd= rf= 5%
Marginal corporate tax rate Tc = 30%.
Q5 APV and wacc
A. Should the company launch the project?
• Base Case Vu - I
B. What is the value of the wacc?
Q5 APV and wacc
B. What is the value of the wacc?
• Target leverage ratio L = D/ V constant
• V = PV of remaining after tax cash flow
• wacc Miles-Ezzel = Ra - L*Tc*Rd*(1+Ra)/(1+Rd)
C. How would the value of the project change if the company used a
continuous rebalancing approach?
• Debt rebalanced continously Dt = L *VLt
• wacc Harris Pringle = Ra - Rd*Tc*L
• ! Uncertainty about next Tax shield –
• ! Riskier