Strategic financial management
Les 1: 27/09
Practicalities
Lecture 8-10: financial modelling
- = the act of building financial models in excels
- Make a virtual version of a company and see what it will look like in the future
- Often used in fin decisionmaking
- You get grades in return for being there and participating actively in the lectures
Examination
- Everything on Toledo
- Study material
o Slides op Toledo, maar ingevulde slides pas achteraf na de les op Toledo
o Academic papers
o Book chapters -> kun je gaan kopiëren in de bib
- 15% of the grade, you get just by participating in the last three lectures
- 85% on written examination (14th of January)
o Mostly multiple choice -> verhoogde seizuur
o But at least one open question (zie voorbeeldvraag op Toledo)
No recordings of the lectures
LES 1: Capital Structure
What comes to mind when you hear the word capital structure
- Which type of funding we use to finance our company
- Distribution between debt and equity in a firm
How should we think about capital structure?
The intuition behind Modigliani & Miller (1958)
Suppose that you buy an asset (a house) today
- The price you pay today: 100.000
- You plan to sell it next year
- Mortgage rate, if you take a mortgage = 5%
o You can choose: not taking mortgage, taking 50% mortgage, taking 90% mortgage
- House price can: drop next year, increase next year, boom in the housing market next year
(alles 1/3 kans)
1
, = the realized returns
= the expected returns
Where does this 55% come from?
- If you sell the house after one year, you get 130.000
- You took a mortgage of 50% -> that means: we borrowed 50.000
o We have to repay the 50.000
o We have to repay the interest of 5% = 2500
- (Return – payback to the bank) / the investment, equity that we put in it
- (130.000 – (50.000 + 2500)) / 50.000 = 55%
Does the value of the house depend on the size of the mortgage?
- No
On what does it depend?
- On the state of the economy: house price drops, raises or booms
What does change with the size of the mortgage?
- Obviously
o The interest that you have to may, the more I borrow, the more interest I will have to
pay
o You become more leveraged
- The expected return on investment
o The more leverage you take, the higher ROI, but the more risk you get
- The risk of your investment
o You can see this in the standard deviation
o If the standard deviation goes op, the risk also goes up
o The more leverage you take, the more risk you get
M&M Proposition I
Proposition: In a perfect capital market, the total value of a firm is equal to the market value of its
current and future cash flows generated by its asset and is not affected by its choice of capital
structure.
- Perfect capital markets = strong assumption
- Value only depending on the present value of the current and future cashflows that the firm
will generate.
o Vb. investment in house: the value of the house depends only on if it is going to be
an expected bad market or good market (not on the mortgage that you take). The
potential market is influencing the value of the house, not whether I buy the house
with equity or debt
- The size of the pie is the same, it does not matter the way of financing
- Value of a firm V = value of its equity (E) + value of its debt (D)
Exercise 1
- Firm that is fully funded trough equity. Project: invest 800
- Tomorrow: 1400 in strong economy, 900 in a weak economy (probability both 50%)
- Risk free rate = 5% = Rrisk free
- Project risk premium = 10% = Rproject - Rrisk free
- 1. NPV of this project?
- 2. For how much can we sell this project, what is the value that we can raise?
2
, - 3. What are the returns that shareholders will get form this project? In the good state, in the
bad state, in expectation?
Solution 1
- 1. NPV = ((0,5*1400+0,5*900) / 1,15) – 800 = 200
- Where does the 1,15 come from? We need to discount the future cash flows with the total
risk of the project Rproject (10% = Rproject - 5%)
- 2. Equity that we can raise = ((0,5*1400 + 0,5*900) / 1,15 = 1000
- 3. Returns in the good state = 40% (1000 + 40% van 1000 = 1400
o They put in 1000 -> was het geen 800 -> neen je moet kijken naar de equity that we
can raise = 1000
- 3. Return in the bad state = -10% (1000 -10% van 1000 = 900)
- 3. Expected return = 0,5*40% + 0,5*-10% = 15%
o The shareholders get a reward that is equal to Rproject
o This is not a coincidence, see further
Exercise 2
- Now suppose the firm borrows $500, in addition to selling equity
o So first borrowing 500, raise the rest with equity
- Note: Project Cash Flows > Debt Owed in each state!
o Debt is risk-free ➔ Rdebt = Rrisk free = 5%
- Payoffs to Debt and Equity
o D -> in strong or weak economy, you have to pay the bank 500 + 5%
o E is different in strong and weak economy because debtors are paid out first
- 1. What is the value of equity now = how much are people going to be willing to pay to
purchase this equity?
- 2. Why is the value of debt not 457
Solution 2
- 1. Value of equity = (0,5*875 + 0,5*375)/1,15 = 543
o The expected payoff is higher
o ! if you don’t discount, you het the expected cash flow -> not the same as the value
of the equity
o ‘but you say that you are only willing to pay 500 for this. Why is that? Because you
believe in the M&Mt theorem, that tells you that it should only be worth 500, that
the value of the firm is unchanged.’ => the value of the equity in the M&M world has
to stay 500, people are only willing to pay 500 for the investment => SO second
question
- Why is the value of the equity 500 and not not 543?
o The risk increases, because the leverage (vreemd vermogen) brengt risk met zich
mee
o So in the formula, we have to use another discount rate because Rproject (the risk of
the project) is higher -> 25% in stead of 15%
- We are pre-promising a piece of the pie to the bank. And the investors in equity take the
residual claim so they increase their risk
3
, - 2. Why is the value of debt not 457
o If I would discount 525/1,15 = 457
o But the value of debt is not 457, but the value is 500 => reason: you have to discount
525/1,05
o 1,05 because that is the return that they will ask, because they are risk free (the bank
is fully risk free)
▪ How can you see that the bank is fully risk free in this model?
They always get the same price / amount, no matter what
Even if the economy goes bad, the opbrengst is still high enough to payback
the bank (900 is more than enough to pay back the bank)
Because of that, the shareholders can sell a piece of the pie to the bank, with
certainty that they can repay the bank.
- SO the ADH have a higher project risk (25%) and the bank had a risk free rate (5%)
Levered equity carries a higher risk premium than unlevered equity
- We therefore need to discount it with a larger discount rate
- In this particular case -> risk premium is no longer 15% but 25%
Exercise 3
Calculate the expected returns in the economy for each of the actors
Bank heeft volledige return 5% 5% 5%
Strong: 375 winst, weak 125 verlies 75% -25% 25%
In dit lijntje overall 0,5*return D + 0,5*return E -> 40% -10% 15%
Takeways from this box
- 1. Leved equity -> higher risk -> higher return (good state 75%, bad state – 25%; previously
good state +40%, bad state -10%) => in expectation, they earned 25% => this is equal to the
risk they take (Rproject = 0,25)
- 2. The reason why the shareholders need a higher discount rate, is not because the risk of
the business changed (the business is exactly the same as it was before). Where do we see
that?
o Good state, still 1400 (+40% return), bad state, still 900 (-10% return) -> in
expectation these two have a risk of 15% -> this is still unchanged (in het rijtje van de
firm is de expected return nog steeds 15%
o The reason that the equity now carries a higher risk premium is simply because the
fin ris, that is been introduced due to the leverage
- 3. The additional risk that the firm took, is not the same as default risk, the firm does not
default in any of these scenarios, because there is always money to fully repay the bank
o Zelfs in een weak economy is er genoeg geld verdiend om de bank helemaal terug te
betalen, de ADH hebben gewoon minder
4
, o Default = the firm can no longer repay the SE, that the value of the assets is not
sufficient to or is less than the claim that the creditors have on the firm
o => Debt is fully risk-free
M&M Proposition II
In a perfect capital market, the WACC of the firm is equal to the risk of the business, the risk of the
firms current and future cash flows and is not affected by its choice of capital structure. It depends
only to the riskiness of the project
- Wacc = weighted average cost of capital
- How can we see this in the previous example:
- The shareholders now require 25% to compensate them for the risk
o They own half of the firm
- But the debtholders only require 5%
o They also own half of the firm
- So the weighted average of the two, given that both of them have the same share, is the
simple average of 5 and 25 = 15 = the wacc = = the risk of the firm the risk of the project
Formula:
But this implies, if we rewrite the terms:
- The cost of equity depends on the riskiness of the firm (risk of the assets) (Ra) + a term that is
proportional (given the D/E level) to the risk of the project
- The more leverage I take, the more my equity will compensate
- The larger the share of the pie that I repackage and sell risk-free (risk of debt), the larger the
risk will be on the package that is left over (risk of equity).
- If I slice my pie in half and sell it risk free to the bank/bondholders, they get that amount in
each state of the economy (SE krijgen sowieso hun geld), ADH get the rest of the pie, so more
of risk of the pie comes to only one half of the pie
o If I sell ¾ of the pie risk-free, the quarter left has to bear all the risk
5
, o The more of the pie I am selling risk free, the more return the ADH ask to
compensate for that risk, because the total risk remains the same
Exercise
Buying a house and selling it one year later
- M&M: for an unlevered firm, the return of the equity = the return on the asset; Ra = Re
-
- Expected return on the house: Ra = 10%
o Gemiddelde van -10, 10 en 30
- If I take no mortgage at all, the required return for the equity: Re = 10%
o The same as the expected return on the house (Ra = Re) because unlevered (no
mortgage)
- If I take a mortgage of 50%, the required return for the equity: Re = 15%
o Ra = 10%, D/E = 1 = 50.000/50.000, Rd = 5%
o Re = 10% + 1*(10%-5%) = 15%
- If I take a mortgate of 90%, the required return for the equity: Re = 55%
o Ra = 10%, D/E = 9 = 90.000/10.000, Rd = 5%
o Re = 10% + 9*(10%-5%) = 55%
o I am taking a larger piece of my pie and selling it as a risk free part, so the rest of the
pie (the equity that is remaining) requires a higher return due to the financial risk
that comes from here. Repackaging the risk.
- ! theoretical mistake in this matrix that we will discuss later
Now we will visualize this:
Cost of capital Re
wacc
Rd
D/(D+E)
How do I show the WACC on this figure?
- It is a constant line: the WACC depends on only one thing: the risk of the current and future
cash flow, the risk of the firm, and NOT the capital structure
- Green line, 15%
How do I show the cost of equity on this figure
- 15% when no debt, 25% when half of it is debt, 55% when 90% of it is debt
- The cost of capital increases when the debt increases
6
, - Exponential red line
How do I show the cost of debt
- Constant line at 5%, but at the end goes up, yellow line
- But obviously we cannot sell the entire pie and pretend that it is risk free, the cash flow have
their own risk
o Bad economy, the return is 900
o Total size of the pie, is determined by the firm value = the present value of the future
cash flows = 1000
o At some point, the bank will pay 1000 for the pie, but in a bac economy can only get
900, so at some point, it is not risk free anymore for the bank;
▪ This point comes at 860, because you still need to pay interest, so then you
come at 900 that is fully repayable
o The bank must ask a return of 15% at the end, otherwise it looses money
Fallacy
A misconception that people that invest tend to have in mind, but it is wrong:
- Leverage can increase stock prices, because I you borrow more, you have less shares and
whatever profits you have, can go to the fewer shareholders. So if you have less shares, there
are higher earnings per share, you split the profit with less shareholders and therefor you
would have higher stock prices.
This is not the case
- Leverage can increase stock prices via its effect on EPS (earnings per share)?
Stel: company X, no debt, EBIT 10, 10 shares, share price 7,5 dollar/share
- => company is worth 75
- Can this company create extra value for the (remaining) shareholders by borrowing 15 from
the bank, that would allow the firm to buy back 2 shares (2*7,5 per share)
o Of course if I borrow, I must pay interest
Before repurchase After repurchase
EBIT 10 10
Interest payments 0 (no debt) 8%*15 = 1,2
Earnings 10 10 -1,2 = 8,8
Number of shares 10 8
EPS 10/10 = 1 8,8/8 = 1,1
So here we would say that we did create more value for the remaining shareholders
o But this is the ‘good case’, what happens in ‘the bad case’ (zie hieronder)
Stel: company X, everything the same, EBIT of 4 million
Before repurchase After repurchase
EBIT 4 4
Interest payments 0 (no debt) 8%*15 = 1,2
Earnings 4 4 -1,2 = 2,8
Number of shares 10 8
EPS 4/10 = 0,4 2,8/8 = 0,35
Fallacy error: it ignores the impact of leverage on risk!
o You increase the risk if I repurchase my shares
o The remaining shareholders pay price of the risk in bad times
- So higher earnings per share in the good times, but lower earnings per share in the bad times
o When are firms buying back shares -> in the good times, when it has more cash flow
than it sees opportunities
7
,Business risk vs. financial risk
Business risk: the risk that comes from the firm
- What affect the business risk: operations, the cash cycle, the general state of the economy
Financial risk: The risk that comes to the firm as a result of leverage (debt in the firm)
- Depends on the amount of leverage
What are the other assumptions behind M&M
M&M assumes
- Perfect capital markets
- Neutral taxes, towards debt and equity
- No bankruptcy costs
- No agency costs/benefits -> people with different interest
- No information asymmetry
- No transaction costs
What is the point of M&M
- If capital structure will matter, capital structure can either avoid or take advantage of the
frictions that M&M don’t think exist (assumptions of M&M)
- Soms frictions will arise when you put debt in the company (negative influence of debt),
some frictions will go away with debt (positive influence of debt)
When is capital structure relevant
M&M is not reality, because we are not in a perfect capital market
- Some firms work with high leverage, and some with lower, people think about it
- In reality, capital structure does matter
When is capital structure relevant? DEBT and TAXES
- Corporation pay taxes on their profits
- EBIT is the same, but one company is leveraged and other company not
- Income before tax is different, net income is different
- What company has the most value: the company with leveraged even tough the net income
is lower than the net income of the company without leverage
- The company with leverage has a value of 952, other company 812
- Difference of 140 million in value
o = tax shield
o Interest payment*tax rate = 400*0,35
o Present value of the annal interest tax shield (perpetual debt)
8
, ▪ = (tax rate*interest) / Rd
▪ = a huge amount
- Reason: interest payment on debt are tax deductible, you pay your interests before the taxes
are calculated = the non neutrality of taxes
o I can only reward the ADH after the taxes
o I can reward the debtholders before the taxes
In our world, the total pie is not changed, but the government takes a slice of the pie
- We want to minimize the slice for the government
- We can do this by financing with debt
-
Firm value increase by vale of tax shield
- Value levered firm = value unlevered firm + present value of interest tax shield
- The more leverage I take, the larger the PV of the interest tax shield becomes
We can present this graphically again (like before)
cost of
capital
15%---
10% __
D/(D+E)
1
9
, - What do I do with the WACC (green)
o The wacc decreases as D/E increases
o
o Wacc captures the risk of the firm/cash flows
o In M&M it was constant, now it goes down linearly -> the more I borrow, the
cheaper that my business is being funded, because I have more tax shiel
▪ It should go down by?
▪ If I fully finance with equity -> 15%
▪ If I fully finance with debt -> the benefit of the tax shield = (1-0,35)*15% =
ongeveer 10%
- What do I do with the Re (cost of equity) (red)
o Start at 15% because if I don’t borrow, there is no tax shield, so it is the same as
previous
o As my tax shield goes up, I am adding risk, so exponential going up
- What do I do with Rd (cost of debt) (yellow)
o Start at 3%
o As soon as I take a little bit of debt, it goes up all the way to the wacc
What is the optimal strategy to do?
- It is possible that the interest expense comes lager than the tax shield?
- Is it possible than the tax shield becomes lager than the interest payment?
o The tax shield is a function of the interest payments ->
▪ tax shield = interest payment*(1-tax rate)
▪ So the larger the interest payments, the larger the tax shield
▪ But it can never cross, one is always 35% of the other
- if you fully finance with debt, it gives you the lowest wacc
But in reality, do we see firms that are fully debt funded? No
- That brings us to the trade off theory
10
Les 1: 27/09
Practicalities
Lecture 8-10: financial modelling
- = the act of building financial models in excels
- Make a virtual version of a company and see what it will look like in the future
- Often used in fin decisionmaking
- You get grades in return for being there and participating actively in the lectures
Examination
- Everything on Toledo
- Study material
o Slides op Toledo, maar ingevulde slides pas achteraf na de les op Toledo
o Academic papers
o Book chapters -> kun je gaan kopiëren in de bib
- 15% of the grade, you get just by participating in the last three lectures
- 85% on written examination (14th of January)
o Mostly multiple choice -> verhoogde seizuur
o But at least one open question (zie voorbeeldvraag op Toledo)
No recordings of the lectures
LES 1: Capital Structure
What comes to mind when you hear the word capital structure
- Which type of funding we use to finance our company
- Distribution between debt and equity in a firm
How should we think about capital structure?
The intuition behind Modigliani & Miller (1958)
Suppose that you buy an asset (a house) today
- The price you pay today: 100.000
- You plan to sell it next year
- Mortgage rate, if you take a mortgage = 5%
o You can choose: not taking mortgage, taking 50% mortgage, taking 90% mortgage
- House price can: drop next year, increase next year, boom in the housing market next year
(alles 1/3 kans)
1
, = the realized returns
= the expected returns
Where does this 55% come from?
- If you sell the house after one year, you get 130.000
- You took a mortgage of 50% -> that means: we borrowed 50.000
o We have to repay the 50.000
o We have to repay the interest of 5% = 2500
- (Return – payback to the bank) / the investment, equity that we put in it
- (130.000 – (50.000 + 2500)) / 50.000 = 55%
Does the value of the house depend on the size of the mortgage?
- No
On what does it depend?
- On the state of the economy: house price drops, raises or booms
What does change with the size of the mortgage?
- Obviously
o The interest that you have to may, the more I borrow, the more interest I will have to
pay
o You become more leveraged
- The expected return on investment
o The more leverage you take, the higher ROI, but the more risk you get
- The risk of your investment
o You can see this in the standard deviation
o If the standard deviation goes op, the risk also goes up
o The more leverage you take, the more risk you get
M&M Proposition I
Proposition: In a perfect capital market, the total value of a firm is equal to the market value of its
current and future cash flows generated by its asset and is not affected by its choice of capital
structure.
- Perfect capital markets = strong assumption
- Value only depending on the present value of the current and future cashflows that the firm
will generate.
o Vb. investment in house: the value of the house depends only on if it is going to be
an expected bad market or good market (not on the mortgage that you take). The
potential market is influencing the value of the house, not whether I buy the house
with equity or debt
- The size of the pie is the same, it does not matter the way of financing
- Value of a firm V = value of its equity (E) + value of its debt (D)
Exercise 1
- Firm that is fully funded trough equity. Project: invest 800
- Tomorrow: 1400 in strong economy, 900 in a weak economy (probability both 50%)
- Risk free rate = 5% = Rrisk free
- Project risk premium = 10% = Rproject - Rrisk free
- 1. NPV of this project?
- 2. For how much can we sell this project, what is the value that we can raise?
2
, - 3. What are the returns that shareholders will get form this project? In the good state, in the
bad state, in expectation?
Solution 1
- 1. NPV = ((0,5*1400+0,5*900) / 1,15) – 800 = 200
- Where does the 1,15 come from? We need to discount the future cash flows with the total
risk of the project Rproject (10% = Rproject - 5%)
- 2. Equity that we can raise = ((0,5*1400 + 0,5*900) / 1,15 = 1000
- 3. Returns in the good state = 40% (1000 + 40% van 1000 = 1400
o They put in 1000 -> was het geen 800 -> neen je moet kijken naar de equity that we
can raise = 1000
- 3. Return in the bad state = -10% (1000 -10% van 1000 = 900)
- 3. Expected return = 0,5*40% + 0,5*-10% = 15%
o The shareholders get a reward that is equal to Rproject
o This is not a coincidence, see further
Exercise 2
- Now suppose the firm borrows $500, in addition to selling equity
o So first borrowing 500, raise the rest with equity
- Note: Project Cash Flows > Debt Owed in each state!
o Debt is risk-free ➔ Rdebt = Rrisk free = 5%
- Payoffs to Debt and Equity
o D -> in strong or weak economy, you have to pay the bank 500 + 5%
o E is different in strong and weak economy because debtors are paid out first
- 1. What is the value of equity now = how much are people going to be willing to pay to
purchase this equity?
- 2. Why is the value of debt not 457
Solution 2
- 1. Value of equity = (0,5*875 + 0,5*375)/1,15 = 543
o The expected payoff is higher
o ! if you don’t discount, you het the expected cash flow -> not the same as the value
of the equity
o ‘but you say that you are only willing to pay 500 for this. Why is that? Because you
believe in the M&Mt theorem, that tells you that it should only be worth 500, that
the value of the firm is unchanged.’ => the value of the equity in the M&M world has
to stay 500, people are only willing to pay 500 for the investment => SO second
question
- Why is the value of the equity 500 and not not 543?
o The risk increases, because the leverage (vreemd vermogen) brengt risk met zich
mee
o So in the formula, we have to use another discount rate because Rproject (the risk of
the project) is higher -> 25% in stead of 15%
- We are pre-promising a piece of the pie to the bank. And the investors in equity take the
residual claim so they increase their risk
3
, - 2. Why is the value of debt not 457
o If I would discount 525/1,15 = 457
o But the value of debt is not 457, but the value is 500 => reason: you have to discount
525/1,05
o 1,05 because that is the return that they will ask, because they are risk free (the bank
is fully risk free)
▪ How can you see that the bank is fully risk free in this model?
They always get the same price / amount, no matter what
Even if the economy goes bad, the opbrengst is still high enough to payback
the bank (900 is more than enough to pay back the bank)
Because of that, the shareholders can sell a piece of the pie to the bank, with
certainty that they can repay the bank.
- SO the ADH have a higher project risk (25%) and the bank had a risk free rate (5%)
Levered equity carries a higher risk premium than unlevered equity
- We therefore need to discount it with a larger discount rate
- In this particular case -> risk premium is no longer 15% but 25%
Exercise 3
Calculate the expected returns in the economy for each of the actors
Bank heeft volledige return 5% 5% 5%
Strong: 375 winst, weak 125 verlies 75% -25% 25%
In dit lijntje overall 0,5*return D + 0,5*return E -> 40% -10% 15%
Takeways from this box
- 1. Leved equity -> higher risk -> higher return (good state 75%, bad state – 25%; previously
good state +40%, bad state -10%) => in expectation, they earned 25% => this is equal to the
risk they take (Rproject = 0,25)
- 2. The reason why the shareholders need a higher discount rate, is not because the risk of
the business changed (the business is exactly the same as it was before). Where do we see
that?
o Good state, still 1400 (+40% return), bad state, still 900 (-10% return) -> in
expectation these two have a risk of 15% -> this is still unchanged (in het rijtje van de
firm is de expected return nog steeds 15%
o The reason that the equity now carries a higher risk premium is simply because the
fin ris, that is been introduced due to the leverage
- 3. The additional risk that the firm took, is not the same as default risk, the firm does not
default in any of these scenarios, because there is always money to fully repay the bank
o Zelfs in een weak economy is er genoeg geld verdiend om de bank helemaal terug te
betalen, de ADH hebben gewoon minder
4
, o Default = the firm can no longer repay the SE, that the value of the assets is not
sufficient to or is less than the claim that the creditors have on the firm
o => Debt is fully risk-free
M&M Proposition II
In a perfect capital market, the WACC of the firm is equal to the risk of the business, the risk of the
firms current and future cash flows and is not affected by its choice of capital structure. It depends
only to the riskiness of the project
- Wacc = weighted average cost of capital
- How can we see this in the previous example:
- The shareholders now require 25% to compensate them for the risk
o They own half of the firm
- But the debtholders only require 5%
o They also own half of the firm
- So the weighted average of the two, given that both of them have the same share, is the
simple average of 5 and 25 = 15 = the wacc = = the risk of the firm the risk of the project
Formula:
But this implies, if we rewrite the terms:
- The cost of equity depends on the riskiness of the firm (risk of the assets) (Ra) + a term that is
proportional (given the D/E level) to the risk of the project
- The more leverage I take, the more my equity will compensate
- The larger the share of the pie that I repackage and sell risk-free (risk of debt), the larger the
risk will be on the package that is left over (risk of equity).
- If I slice my pie in half and sell it risk free to the bank/bondholders, they get that amount in
each state of the economy (SE krijgen sowieso hun geld), ADH get the rest of the pie, so more
of risk of the pie comes to only one half of the pie
o If I sell ¾ of the pie risk-free, the quarter left has to bear all the risk
5
, o The more of the pie I am selling risk free, the more return the ADH ask to
compensate for that risk, because the total risk remains the same
Exercise
Buying a house and selling it one year later
- M&M: for an unlevered firm, the return of the equity = the return on the asset; Ra = Re
-
- Expected return on the house: Ra = 10%
o Gemiddelde van -10, 10 en 30
- If I take no mortgage at all, the required return for the equity: Re = 10%
o The same as the expected return on the house (Ra = Re) because unlevered (no
mortgage)
- If I take a mortgage of 50%, the required return for the equity: Re = 15%
o Ra = 10%, D/E = 1 = 50.000/50.000, Rd = 5%
o Re = 10% + 1*(10%-5%) = 15%
- If I take a mortgate of 90%, the required return for the equity: Re = 55%
o Ra = 10%, D/E = 9 = 90.000/10.000, Rd = 5%
o Re = 10% + 9*(10%-5%) = 55%
o I am taking a larger piece of my pie and selling it as a risk free part, so the rest of the
pie (the equity that is remaining) requires a higher return due to the financial risk
that comes from here. Repackaging the risk.
- ! theoretical mistake in this matrix that we will discuss later
Now we will visualize this:
Cost of capital Re
wacc
Rd
D/(D+E)
How do I show the WACC on this figure?
- It is a constant line: the WACC depends on only one thing: the risk of the current and future
cash flow, the risk of the firm, and NOT the capital structure
- Green line, 15%
How do I show the cost of equity on this figure
- 15% when no debt, 25% when half of it is debt, 55% when 90% of it is debt
- The cost of capital increases when the debt increases
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, - Exponential red line
How do I show the cost of debt
- Constant line at 5%, but at the end goes up, yellow line
- But obviously we cannot sell the entire pie and pretend that it is risk free, the cash flow have
their own risk
o Bad economy, the return is 900
o Total size of the pie, is determined by the firm value = the present value of the future
cash flows = 1000
o At some point, the bank will pay 1000 for the pie, but in a bac economy can only get
900, so at some point, it is not risk free anymore for the bank;
▪ This point comes at 860, because you still need to pay interest, so then you
come at 900 that is fully repayable
o The bank must ask a return of 15% at the end, otherwise it looses money
Fallacy
A misconception that people that invest tend to have in mind, but it is wrong:
- Leverage can increase stock prices, because I you borrow more, you have less shares and
whatever profits you have, can go to the fewer shareholders. So if you have less shares, there
are higher earnings per share, you split the profit with less shareholders and therefor you
would have higher stock prices.
This is not the case
- Leverage can increase stock prices via its effect on EPS (earnings per share)?
Stel: company X, no debt, EBIT 10, 10 shares, share price 7,5 dollar/share
- => company is worth 75
- Can this company create extra value for the (remaining) shareholders by borrowing 15 from
the bank, that would allow the firm to buy back 2 shares (2*7,5 per share)
o Of course if I borrow, I must pay interest
Before repurchase After repurchase
EBIT 10 10
Interest payments 0 (no debt) 8%*15 = 1,2
Earnings 10 10 -1,2 = 8,8
Number of shares 10 8
EPS 10/10 = 1 8,8/8 = 1,1
So here we would say that we did create more value for the remaining shareholders
o But this is the ‘good case’, what happens in ‘the bad case’ (zie hieronder)
Stel: company X, everything the same, EBIT of 4 million
Before repurchase After repurchase
EBIT 4 4
Interest payments 0 (no debt) 8%*15 = 1,2
Earnings 4 4 -1,2 = 2,8
Number of shares 10 8
EPS 4/10 = 0,4 2,8/8 = 0,35
Fallacy error: it ignores the impact of leverage on risk!
o You increase the risk if I repurchase my shares
o The remaining shareholders pay price of the risk in bad times
- So higher earnings per share in the good times, but lower earnings per share in the bad times
o When are firms buying back shares -> in the good times, when it has more cash flow
than it sees opportunities
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,Business risk vs. financial risk
Business risk: the risk that comes from the firm
- What affect the business risk: operations, the cash cycle, the general state of the economy
Financial risk: The risk that comes to the firm as a result of leverage (debt in the firm)
- Depends on the amount of leverage
What are the other assumptions behind M&M
M&M assumes
- Perfect capital markets
- Neutral taxes, towards debt and equity
- No bankruptcy costs
- No agency costs/benefits -> people with different interest
- No information asymmetry
- No transaction costs
What is the point of M&M
- If capital structure will matter, capital structure can either avoid or take advantage of the
frictions that M&M don’t think exist (assumptions of M&M)
- Soms frictions will arise when you put debt in the company (negative influence of debt),
some frictions will go away with debt (positive influence of debt)
When is capital structure relevant
M&M is not reality, because we are not in a perfect capital market
- Some firms work with high leverage, and some with lower, people think about it
- In reality, capital structure does matter
When is capital structure relevant? DEBT and TAXES
- Corporation pay taxes on their profits
- EBIT is the same, but one company is leveraged and other company not
- Income before tax is different, net income is different
- What company has the most value: the company with leveraged even tough the net income
is lower than the net income of the company without leverage
- The company with leverage has a value of 952, other company 812
- Difference of 140 million in value
o = tax shield
o Interest payment*tax rate = 400*0,35
o Present value of the annal interest tax shield (perpetual debt)
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, ▪ = (tax rate*interest) / Rd
▪ = a huge amount
- Reason: interest payment on debt are tax deductible, you pay your interests before the taxes
are calculated = the non neutrality of taxes
o I can only reward the ADH after the taxes
o I can reward the debtholders before the taxes
In our world, the total pie is not changed, but the government takes a slice of the pie
- We want to minimize the slice for the government
- We can do this by financing with debt
-
Firm value increase by vale of tax shield
- Value levered firm = value unlevered firm + present value of interest tax shield
- The more leverage I take, the larger the PV of the interest tax shield becomes
We can present this graphically again (like before)
cost of
capital
15%---
10% __
D/(D+E)
1
9
, - What do I do with the WACC (green)
o The wacc decreases as D/E increases
o
o Wacc captures the risk of the firm/cash flows
o In M&M it was constant, now it goes down linearly -> the more I borrow, the
cheaper that my business is being funded, because I have more tax shiel
▪ It should go down by?
▪ If I fully finance with equity -> 15%
▪ If I fully finance with debt -> the benefit of the tax shield = (1-0,35)*15% =
ongeveer 10%
- What do I do with the Re (cost of equity) (red)
o Start at 15% because if I don’t borrow, there is no tax shield, so it is the same as
previous
o As my tax shield goes up, I am adding risk, so exponential going up
- What do I do with Rd (cost of debt) (yellow)
o Start at 3%
o As soon as I take a little bit of debt, it goes up all the way to the wacc
What is the optimal strategy to do?
- It is possible that the interest expense comes lager than the tax shield?
- Is it possible than the tax shield becomes lager than the interest payment?
o The tax shield is a function of the interest payments ->
▪ tax shield = interest payment*(1-tax rate)
▪ So the larger the interest payments, the larger the tax shield
▪ But it can never cross, one is always 35% of the other
- if you fully finance with debt, it gives you the lowest wacc
But in reality, do we see firms that are fully debt funded? No
- That brings us to the trade off theory
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