Chapter 16 – Capital Structure
Steps to Answer Common Questions
MM Propositions
No Tax
𝐸𝐵𝐼𝑇
MMI: 𝑉𝐿 = 𝑉𝑈 = 𝑟
Find the WACC (and Levered Cost of Equity)
0
The value of the levered firm is the same
as the unlevered firm when there is are
no taxes. This is found by taking the PV of
the perpetual EBIT and dividing by the
unlevered cost of equity.
MMII: 𝑟𝑠 = 𝑟𝑜 +
𝐵
(𝑟
𝑆 0
− 𝑟𝐵 )
1. Begin by writing down the formula for WACC:
𝑟𝑊𝐴𝐶𝐶 =
𝑆
𝐵
𝑟 +
∗ 1 − 𝑇𝐶 ∗ 𝑟𝐵
𝐵+𝑆 𝑠
𝐵+𝑆
2. Usually you will have to solve for levered cost of
equity and the weights of debt and equity (as usually
they will give you the debt-equity or target debt-equity
OR they will tell you that X% of the project will be
financed with debt.
Use this to find the levered cost of equity
when there are no taxes.
With Tax
MMI: 𝑉𝐿 = 𝑉𝑈 + 𝑇𝐶 𝐵
Where: 𝑉𝑈 =
(𝐸𝐵𝐼𝑇)∗(1−𝑇𝐶 )
𝑟𝑜
The value of the levered firm in the
presence of taxes is the unlevered firm’s
value (here you discount the after-tax
EBIT at the unlevered cost of equity) plus
the tax shield benefits.
𝐵
MMII: 𝑟𝑠 = 𝑟𝑜 + 𝑆 ∗ (1 − 𝑇𝐶 )(𝑟0 − 𝑟𝐵 )
Use this to find the levered cost of equity
when there are taxes.
Breakeven EBIT
𝐸𝑃𝑆𝐴 = 𝐸𝑃𝑆𝐵
Step 3 is how
to solve for
levered equity!
4. Plug into the
WACC formula as
you now have
everything.
Where EPS is given by:
𝐸𝑃𝑆 =
3. First find the
value of the levered
cost of equity.
a. Find the value of
the levered firm.
Then, plug into V =
B + S the value you
solve for (for V) and
the amount of debt
(for B) and solve for
S.
b. Plug into cost of
equity formula
using these values.
𝐸𝐵𝐼𝑇 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 ∗ (1 − 𝑇𝐶 )
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
Value of a firm
If there are no taxes, then sub 0 in taxes.
If the capital structure is all equity
financed, then sub 0 in for interest.
WACC
Plug into:
𝑉𝐿 = 𝑉𝑈 + 𝑇𝐶 𝐵
Where:
𝑉𝑈 =
𝑟𝑊𝐴𝐶𝐶 = 𝑤𝑆 𝑟𝑠 + 𝑤𝐵 ∗ 1 − 𝑇𝐶 ∗ 𝑟𝐵
𝑆
𝐵
𝑤ℎ𝑒𝑟𝑒 𝑤𝑠 =
𝑎𝑛𝑑 𝑤𝐵 =
𝐵+𝑆
𝐵+𝑆
(𝐸𝐵𝐼𝑇) ∗ (1 − 𝑇𝐶 )
𝑟𝑜
3. First find the
value of the levered
cost of equity.
This is easy here
because you don’t
need to solve for B
and S since B/S in
the MM formula is
just the debt to
equity ratio!
4. Solve for weight
of debt and weight
of equity.
a. Take the target
debt to equity ratio
and solve it for B:
e.g. if the question says
debt to equity ratio is 0.7,
then that means:
𝐵
= 0.7
𝑆
𝑆𝑜𝑙𝑣𝑒𝑠 𝑓𝑜𝑟 𝐵 = 0.7𝑆
Sub this expression
(e.g. B = 0.7S) into
the
weight
of
equity
e.g. if B = 0.7S, go to
𝑆
𝑆
𝑆
𝑤𝑆 =
=
=
𝐵+𝑆
0.7𝑆 + 𝑆 1.7𝑆
1
𝑤𝑆 =
= 0.59, 𝑠𝑜 𝑤𝐵 = 1 − 0.59
1.7
5. Plug into:
𝑟𝑊𝐴𝐶𝐶 = 𝑤𝑆 𝑟𝑠 + 𝑤𝐵 ∗ 1 − 𝑇𝐶 ∗ 𝑟𝐵
Chapter 17 – Financial Distress
Firm Value with Distress Costs
Ex. Iron Maiden Ltd has debt outstanding with a face value of $6 million. The hypothetical unlevered value of the
firm is $12.6 million. There are 260,000 shares outstanding trading at a price of $25 each. The corporate tax rate is
25%. What is the decrease in the firm’s value owing to expected financial distress costs?
Answer: This question gives you everything you need to plug into the value of a levered firm formula:
𝑉𝐿 = 𝑉𝑈 + 𝑇𝐶 𝐵 where Vu is $12.6M and TcB is 0.25 * 6,000,000. Plugging in, you get 14.1M. But the true value of
the firm is given V = B + S, where again B is $6,000,000 and S = shares outstanding * share price, or 260,000 * 25
= $6.5M. The true value is then V = B + S = 6M + 6.5M = 12.5M. The difference between the 14.1M and the 12.5M
is the financial distress costs, and this is 1.6M.
Promised Return to Bondholders
𝑃𝑟𝑜𝑚𝑖𝑠𝑒𝑑 𝐷𝑒𝑏𝑡 𝑅𝑒𝑝𝑎𝑦𝑚𝑒𝑛𝑡 − 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐷𝑒𝑏𝑡
𝑃𝑟𝑜𝑚𝑖𝑠𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛(%) =
−1
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐷𝑒𝑏𝑡
Expected Return to Bondholders
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 =
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑡𝑜 𝐵𝑜𝑛𝑑 𝐻𝑜𝑙𝑑𝑒𝑟𝑠 − 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐷𝑒𝑏𝑡
−1
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐷𝑒𝑏𝑡
Capital Structure Theories
Trade off Theory of Capital Structure: Firms balance the
costs and benefits of debt. They seek the optimal debt
to equity ratio that will simultaneously maximize the
firm value and minimize the WACC
Signalling Theory: Profitable firms will issue more debt
to send a credible signal that they are a healthy company
and can afford interest payments, increasing investor
confidence.
Free Cash Flow Hypothesis: By reducing available cash,
managers are less able to pad their expenses, curtailing
ability to pursue inefficient activities
Pecking Order Hypothesis: Managers prefer internal
financing to external. Start with safer securities (debt)
and issue increasingly riskier securities only as needed.
There is NO target debt-equity ratio. The pecking order
is internal funds, then debt, then equity.
Homemade Leverage
Calculating Cash Flows (Before restructuring)
1. You may be asked to calculate an investors cash flows.
To do this, you will often have to figure out what
the dividend per share is (if it’s given, great!). To find
dividend per share, the formula is:
𝐷𝑖𝑣 =
𝐸𝐵𝐼𝑇 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 ∗ 1 − 𝑇𝐶
𝑆ℎ𝑎𝑟𝑒𝑠 𝑂𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔
∗ 𝑃𝑎𝑦 𝑅𝑎𝑡𝑖𝑜
2. Cash flow is then number of shares owned multiplied
by the value from step 1.
Calculating Cash Flows (After restructuring)
1. As seen in practice problem 5c in chapter 16 of the
booklet, when the firm restructures you will have to
calculate cash flows again, but this isn’t as easy as the
pre-restructuring!
2. While the method is still the same (multiply dividend
by number of shares owned – see above), the issue is
finding the new dividend; You will need to find new
shares outstanding, because they will either be adding
or taking shares away!
3. To do this, find what the firm’s value is. Usually, the
initial capital structure is all equity, and there are never
taxes in these questions, so just find the value of the
unlevered firm, and per MM Prop I (no tax), this is also
the value of the levered firm!
4. Then, based on what is happening to the capital
structure, multiply the addition or subtraction of debt by
the value you get.
Ex 1: If the value is 1M and the firm is adding 20%
debt, do 20% * 1M = 200,000. This means they will use
200,000 to buy shares, so divide 200,000 by the share price
to figure out how any shares they are subtracting.
Ex 2: If the firm is taking debt away, e.g. going from 20%
debt to all equity, take 20% of the firm’s value, then use
this number, divide it by share price to figure out how
many shares are going to be issued/added.
5. From here, calculate dividend using the formula above,
and multiply by shares owned.
Replicating Cash Flows
If the firm adding some debt (which means the firm is
repurchasing shares), then the investor will sell shares
at the same rate the firm added debt to counter this. For
example, if the firm went from all equity to 20% debt, the
investor will sell 20% of their shares and lend the proceeds
at the interest rate. If the firm took away debt, the investor
borrows to buy more shares. E.g. if they reduce debt by 20%
the investor will borrow to buy 20% more shares.
Glossary
MM – Modigliani and Miller
S – Equity
𝐵
= 𝐷𝑒𝑏𝑡 𝑡𝑜 𝐸𝑞𝑢𝑖𝑡𝑦 𝑅𝑎𝑡𝑖𝑜
B – Debt
𝑆
V – Value of Firm
𝑉𝐿 − Value of Levered Firm
𝑉𝑈 − Value of Unlevered Firm
𝑟𝑊𝐴𝐶𝐶 − Weighted Average Cost of Capital
𝑟𝐵 − 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐷𝑒𝑏𝑡
𝑟𝑆 − 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝑒𝑞𝑢𝑖𝑡𝑦
𝑟0 − 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
EBIT – Earnings Before Interest and Tax
EPS – Earnings Per Share
𝑇𝐶 − 𝐶𝑜𝑟𝑝𝑜𝑟𝑎𝑡𝑒 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒
𝑇𝑆 − 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 /𝐸𝑞𝑢𝑖𝑡𝑦 Tax Rate
𝑇𝐵 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑇𝑎𝑥 𝑅𝑎𝑡𝑒
APV – Adjusted Present Value
NPVF – Net Present Value Financing
NPV – Net present Value
FTE – Flow to Equity Approach
Chapter 18 – Capital Budgeting
Security Market Line (CAPM)
𝑟𝑆 = 𝑟𝑓 + 𝛽𝐿𝑒𝑣𝑒𝑟𝑒𝑑 (𝐸 𝑟𝑀 − 𝑟𝑓 )
Additional Space for Notes #1
Where:
𝑟𝑓 = 𝑅𝑖𝑠𝑘 𝐹𝑟𝑒𝑒 𝑅𝑎𝑡𝑒
𝐸 𝑟𝑀 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑀𝑎𝑟𝑘𝑒𝑡 𝑅𝑒𝑡𝑢𝑟𝑛
𝐸 𝑟𝑀 − 𝑟𝑓 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑅𝑖𝑠𝑘 𝑃𝑟𝑒𝑚𝑖𝑢𝑚
The levered beta (also known as the equity beta) is given by:
𝛽𝐿 = 1 +
𝐵
∗ 1 − 𝑇𝐶
𝑆
𝛽𝑈
The unlevered beta (also known as the asset beta):
𝛽𝑈 =
𝛽𝐿
𝐵
1 + ∗ 1 − 𝑇𝐶
𝑆
APV Approach
𝐴𝑃𝑉 = 𝑁𝑃𝑉 + 𝑁𝑃𝑉𝐹
NPV
𝑁𝑃𝑉 = −𝐶0 + 𝑃𝑉 𝑃𝑟𝑜𝑓𝑖𝑡 + 𝑃𝑉 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑 + 𝑃𝑉(𝐸𝐶𝐹)
**Note that everything here is discounted by the unlevered cost of equity!!
For the PV of the depreciation tax shield, you would need to find what the
annual depreciation tax benefit is. For this, multiply the annual depreciation
expense by the tax rate. The annual depreciation expense is found by taking
the total amount that must be depreciated and dividing by how many years
you are depreciating the asset for.
𝑁𝑃𝑉𝐹 = 𝐿𝑜𝑎𝑛 𝑃𝑟𝑜𝑐𝑒𝑒𝑑𝑠 𝑁𝑒𝑡 𝑜𝑓 𝐹𝑙𝑜𝑎𝑡𝑎𝑡𝑖𝑜𝑛 − 𝑃𝑉 𝐴𝑓𝑡𝑒𝑟 𝑇𝑎𝑥 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 − 𝑃𝑉(𝑅𝑒𝑝𝑎𝑦𝑚𝑒𝑛𝑡)
**Note that everything here is discounted by the cost of debt.
FTE Approach
Value only the cash flows that accrue to the shareholders. This is called using
the levered cash flows. The discount rate here is the levered cost of equity,
and this is calculated as described on the other side of this aid sheet. To
find the free cash flows to equity holders, use this formula:
𝐹𝐶𝐹𝐸 = 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡 − 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 ∗ (1 − 𝑇𝐶 )
Note: This formula may “change” based on what the question gives! If it gives EBIT,
Then all you have to do is subtract interest, then multiply by 1 – tax rate. Note that EBIT
has other names, like operating earnings or operating profit!
Once you have your FCFE, discount these at the levered cost of equity.
WACC Approach
Value the firm using the unlevered free cash flows. The reason you use
unlevered (which means you ignore interest) is because the WACC is the
discount rate we use here, and it includes the effects of leverage. Typically,
unlevered cash flows is just EBIT * (1 – tax rate).
Once you have your unlevered cash flows, discount at the WACC. The WACC
is computed as discussed in the chapter 16 section of this sheet.
Additional Space for Notes #2