Chapter 14 - Capital structure in a perfect market

Question 1

When a firm needs to raise funds to fund an activity or project, what does it need to do?

Answer 1

The firm needs to consider what kind of security it should use to raise the funds, and what combination. Are we talking all-equity, all-debt, combinaiton of both?

Question 2

Define perfect capital markets

Answer 2

Perfect markets are defined as:
- All securities are fairly priced
- no taxes or transaction costs
- Total cash flow from a project is not affected by how the firm choose to finance it.

Question 3

define capital structure

Answer 3

Capital structure refers to the proportions of hte firm that is financed through equity, debt and other securities

Question 4

if a projects returns depend on the overall movement of the economy, what can we say about it?

Answer 4

THe project contains market risk. An outcome of market risk is that investors will require a premium to offset the risk.

Question 5

In the absence of arbitrage, what is the price of a security?

Answer 5

In general, the value of its cash flows. present value, that is.

Question 6

equity in a firm with no debt is called…?

Answer 6

unlevered equity

Question 7

equity in a firm that has debt outstanding is called..?

Answer 7

levered equity.

Question 8

if economy is strong, a project delivers 1400 usd.
if weak: 900 bucks.

The project requires 800 bucks initially.

If 500 is funded with debt at 5%, what will equity holders be payed?

Answer 8

Equity holders are payed after debt holders.

500 x 1.05 = 525

strong: 1400 - 525 = 875
weak: 900 - 525 = 375

Question 9

What price should levered equity sell for?

What capital structure is best for the project?

Answer 9

In perfect capital markets, the total value of a firm does not depend on its capital structure. Why?
The cash flows that the project generates will be the same as the cash flows of the firm.
the law of one price then say that the price of the securities in the firm must equal the “total package” of debt+equity financing of the project. if this was not the case, then an investor could utilize the opportunity to gain arbitrage money.
So, if the cash flows generated is equal to 1000 in present value, then the cost of the equity and the debt must together be worth 1000. Therefore, if the project financed 500 worth through the use of debt, then the value of hte equity is simply 1000 - 500 = 500.

Question 10

There is something important that results from considering levered equity. Elaborate

Answer 10

The value of the firm (or project’s) equity is less when using debt to finance a part of it. Why is this the case?
Equity is worth less now because a part of the cash flows that are generated by the project must go to the creditor.

Changing capital structure is a change in cash flow distribution.

Question 11

How does the capital structure (in perfect capital markets) affect the decision of the project owner?

Answer 11

It does not affect him. He will be able to raise the money he needs regardless of the equity-debt split. This is because of the law of one price.

Assuming perfect capital markets include assuming no arbitrage. If no arbitrage exists, then we know that if the firm generates X dollars in cash flows, then the price of the firm’s equity AND the debt must be equal. Otherwise, an investor could buy one of them and sell the other etc.

Question 12

The traditional view was that the value of the levered equity would exceed 500 because:

(0.5 x 875 + 0.5 x 375 ) / 1.15 = 543, meaning that the expected value of the returns of the investment in the firms levered equity is greater than 500.

Why is this not correct?

Answer 12

It is about the cost of capital.

15% represent 5% risk free rate and a risk premium of 10% from the all-equity variant.

The equity is levered, which means that the expected returns that follow from it is partly because of the debt.

Investor that invest in levered equity require a larger risk premium.
This reason the levered equity is more risky than the unlevered equity, is because of how a proportion of the cash flows generated by the project MUST be allocated to the creditors before equity holders receive anything. Therefore, a project that would be NPV positive regardless of outcomes when unlevered through all-equity, could actually very fast become negative NPV because of the fixed sum required by the debt issuer.

also, consider what happens in the case of default. All return are given to creditors, nothing to equity holders.

The additional risk of buying levered equity will increase the risk premium demanded by the equity investors. Because of this, we cannot use the “unlevered cost of capital” to discount the cash flow. We must use a rate that will be higher, as it needs to accommodate for the larger risk.

Question 13

CASE:

CFO needs to raise 1000 bucks for a project. Assume the project is all the firm is undertaking.
If economy is strong, the project generates a cash flow of 1400 bucks. If weak: 900 bucks.
Equally likely to happen.

He choose to raise 500 through debt at the risk free rate of 5%. The remaining is equity.

What is the risk premium that the investors of equity will demand for holding equity in this project/firm?

Answer 13

The money that the creditors require regardless of the result, is 500 x 1.05 = 525 bucks.

The remaining cash flow is therefore either:
1) 875
2) 375

The price of the equity is 1000 - 500 = 500.
Why? The initial value of 1000 bucks must be equal to the cash flows that are generated by the project, because of the law of one price. If not, investors would have an aribtrage opportunity, which is assumed to not exist in perfect capital markets.
Since the capital sturcture worth of debt is 500, we know that the remainign is 500. Therefore, equity is worth 500.

IF the firms project was all equity (unlevered), we would have gotten the following properties of teh equity:
1) expected return 1400x0.5 + 900x0.5 / 1000 = 15%.
2) if economy is strong, equity holders would get 40% returns.
3) If economy is weak, equity holders would get -10% returns.

If the firms project is financed thorugh 500 usd (50%) worth of debt, the following properties arise for equity holders:
1) expected return: (875x0.5 + 375x0.5)/500 = 25%.
2) if economy is strong: 875/500 = 75% returns.
3) if economy is weak: 375/500 = negative 25%.

The risk premium is 20%, vs the 10% for the unlevered equity.

This case shows how the returns of the equity are effected by the capital structure.

However, in terms of the project and the cash flows of the project as a whole, the fund raising procedure does not matter at all. Of course, the project owner typically has equity and will be affected, but the cash flows generated by the project are not affected.

Question 14

true or false?:

leverage increases the risk of equity even when there is no risk of default

Answer 14

true.

The leverage will increase the fluctuations in return on the equity, and therefore the risk of equity.

Question 15

When we are talking about “return sensitivity” what are we tlaking about?

Answer 15

The difference between max and min returns, in percentage terms.

For instance, if the project will either return 75% or -25%, the return sensitiivty is 75 - (-25%) = 100%

Question 16

The law of one price says that leverage will not affect the total value of the firm. What does the law say that leverage affect?

Answer 16

The allocation of the firms cash flows. It does not alter the amount of cash flow generated by the project, only the split between equity and debt in terms of allocating the project flows.

Question 17

Modigliani and Miller showed that the capital structure independence etc holds under “perfect capital markets”. What are perfect capital markets?

Answer 17

Defined by 3 assumptions or conditions:

1) Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows.

2) There are no taxes, transition costs, issuance costs, associated with security trading.

3) A firms financing decisions does not change the cash flows generated by its investments, nor do they reveal new information about them.

Question 18

What is MM-proposition 1?

Answer 18

Under the conditions of perfect capital markets, the total value of a firms securities is equal to the market value of the total amount of cash flows generated by the firms assets, and is not affected by its capital structure.

NB: the firms securities include their equity and their debt.

Question 19

elaborate on what investors can do if they dont like the capital structure of a firm they want to invest in

Answer 19

They can engage in homemade leverage.

Homemade leverage is about borrowing money at your own wish so that you leverage yourself, and invest your leveraged equity into the firm. This makes you increase the risk.

if the investor want less debt in the capital structure, he can simply buy the debt and the equity of the firm.

Question 20

Elaborate on the market value balance sheet of the form

Answer 20

Similar to accounting balance sheet with 2 major distincitons:
1) All assets and liabilities of the firm are included. Even intangibles.
2) All values are current market values, rather than historical cost.

On the market balance sheet, the total value of the firms securities must equal the total value of its assets.

Question 21

How do we calculate market value of equity?

Answer 21

Market value of equity = market value of assets - market value of debt

Question 22

What is a leveraged recapitalization?

Answer 22

A leveraged recapitalization refer to the case where a firm use leverage (debt) to re purchase shares that is outstanding and not owned by the firm.

A leveraged recapiatlization can be regarded as a two step process:
1) the firm sells debt to raise a sum of money, like 80 million usd.
2) The firm use the cash, including the cash raised by debt, to re purchase shares.

Question 23

how does zero NPV transactions affect share price?

Answer 23

No effect. Only changes in net present value of the firm can change share price.

Question 24

Does a leveraged repurchase change share price?

Answer 24

No. Such an action is a zero NPV transaction.

A firm will first borrow say 80 million, and spend 80 million to repurchase shares.

Assets, which equals to liabilities + equity, will first increase with the cash borrowed, and then decrease again because the cash is used to buy shares.
The result is “80 million borrowed cash in, 80 million cash out, equity in”.
The firm gain 80 million in value because of the additional shares, but it also decreased 80 million in value because it borrowed 80 million.

The firm will now have to pay creditors a proportion of their cash flow.

The market cap (market value of equity) will decrease because the number of shares outstanding will be reduced, and the share price remains that same (because zero NPV transaction).

I think maybe the price remains the same if the repurchase happen at this price. Under such circumstances, we keep the ratio of market cap/shares the same, which cause the share price to remain the same.

Question 25

elaborate on MM proposition 2

Answer 25

Their second proposition is about how the equity cost of capital is affected by leverage through debt.

We start with the basic result frm MM1:

E + D = U = A

This equaiton says that the market value of assets of the firm must equal the unlevered equity market value, and this again is equal to debt market value + equity market value.

From this, we can establish the returns relationship as well:

Ru = (E / (E+D))Re + (D/(E+D))Rd

We solve this for Re to get the equity cost of capital:

Re (E / (E+D)) = Ru - (D/(E+D))Rd

Re = (E+D)/E Ru - D/E Rd

Re = E/ERu + D/E Ru - D/E Rd

Re = Ru + D/E (Ru - Rd)

This equation is important because it tells us an important relationship.

The equity cost of capital is equal to the unlevered cost of capital plus the ratio of debt and equity multiplied by the difference between unlevered cost of capital and debt cost of capital.
Ru and Rd is likely fixed.
Therefore, the equity cost of capital will grow most likely according to the debt to equity ratio.

This leads us to the final MM 2 proposition:

“The cost of capital of levered equity increases with the firms market value debt-equity ratio”

This equation, and its result, is exactly the same result as we found from the case earlier with the project fund raising.

Question 26

Elaborate on WACC in the context of perfect capital markets

Answer 26

No taxes means that pretax WACC = = WACC.

In fact, we have the following:

R_u = R_a = WACC

Weighted average cost of capital is also called unlevered cost of capital.

Question 27

What can we say about the WACC in perfect capital markets?

Answer 27

In perfect capital markets, the WACC is INDEPENDENT Of the capital structure, and is equal to its equity cost of capital if it is unlevered, which mathces the cost of capital of its assets.

Recall that WACC is the return you’d expect to get from owning all aspects of hte firm. This is (because of the LAW) the same you’d get from owning the assets that produce the cash flow.

Question 28

can a firm get a lower WACC from increasing debt?

Answer 28

No. This is a common misconception.

By increasing debt, we of course increase the proportion of the firm that is financed through a security that itself has a lower cost of capital. Debt cost of capital is generally a lot cheaper than the cost of equity.

However, when we add leverage, we increase the risk of equity. Since more debt means that the creditors require a larger amount, regardless of result, there will be less cash flow left for the equity holders. Because of this, equity holders will require a higher risk premium for investing in the equity.
The increase in risk premium required will exactly offset the benefit of lower debt cost of capital.

Question 29

Fill out on the betas

Question 30

Elaborate on the effect of holding excess cash

Answer 30

Excess cash is a risk free investment. It has the opposite effect of borrowing money, which means that it offsets some of the effect carried by debt.

We can view cash as negative debt.

It is common to use “net debt” when doing calculations that involve debt. If we have more cash than debt, the net debt becomes negative. We essentialyl just enter this net debt value into the equations as if it was just the debt.

Question 31

What happens to the equity of a firm if it has negative net debt?

Answer 31

Negative net debt cause the equity of the firm to be less risky than the underlying business.

Question 32

Elaborate on leverage effect on EPS

Answer 32

it is common to say that using more leverage will increase EPS.

Let us say we borrow money to repurchase shares.

In perfect capital markets, this will carry an effect of decreasing future earnings, because we have to pay the loan we just took. However, we also reduce the number of shares outstanding. This could very well increase earnings per share. There are cases where this is not the case, but with a low debt cost of capital, it generally is the case that EPS will increase.

But does it make shareholders better of?

it might seem contradictory, because we know from MM1 that the stock repurchase is a zero NPV transaction and should not alter anything of value. However, the earning per share has increased.

The reason for the increased EPS is because the increased debt has incresaed the leverage and therefore made the equity more risky. More risky equity requires a higher risk premium.

Question 33

Can we compare EPS and PE metrics across firms?

Answer 33

It is difficult, because their capital structures will yield different results.

We avoid this problem by using EBIT measures, since this is before interest is made.

Question 34

Consider raising funds by issuing equity. Will this reduce the value of current shares?

Answer 34

No, not as long as the shares are issued at a fair price.

If we issue new shares at the same price as the current stock price, we will raise new money. The cash raised will increase the market value of the firm. In fact, the market value per share doesnt change.

The key is the fair price though.

Question 35

Why is MM (Modigliani and Miller) results important?

Answer 35

it is more about how they derived their propositions, rather than the propositions themsevles.

they used the law of one price in competitive markets to show that the law indeed as a big effect on the pricing of securities and firm values.

their paper marks the beginning of modern theory of corporate finance.

Question 36

elaborate on the conservation of value principle for financial markets

Answer 36

Question 37

what did Modigliani and Miller argue?

Answer 37

They argued that with perfect capital markets, the total value of the firm should not depend on its capital structure.

Their reasoning:
the firms value is based on the total cash flow the firm produce. The cash flow generated by the firm, the present value of the cash flow that is, is the same regardless of capital structure. Then we use the law of one price to say that if the present value of the cash flows of the firm is equal to X, then the total “package” of its equity and debt must together reflect this value of X.
for instance, if X is 1000, and we know the firm has borrowed 500 in debt, then the remaining must be equity, which means that there will be 500 in equity as well.

The key is the reasoning using the law of one price. If the price of the equity happened to be less than indicated by the 1000 - 500 = 500 equation, then buying this equity would represent a risk free arbitrage opportunity. This is because the price of the equity would be lower than the equity portion of the cash flows.
we can also add the fact that in competitive markets, savvy investors will automatically drive the price of the equity towards the exact value.

Question 38

Modigliani and Millers first proposition say the following:

in a perfect capital market, the total value of a firms securities is equal to the market value of the total cash flows generated by its assets and is not affected by the choice of capital structure.

What is the reasoning behind this?

Answer 38

In the absence of taxes, transacation costs and all that (perfect capital markets), the total cash flow payed out to the securities’ holders (equity and debt and other potential instruments) will be equal to the cash flow generated by the firms assets.
By the law of one price, the value of these securities must therefore be worth the same as the assets that produced the cash flows. in other words, the securities and the assets must have the same market value.

We know how the law works. If the assets were price cheaper, investors could buy them to earn a risk free profit. Same with the case where the securies are cheaper.
Assuming competitive markets, the law will make the values equal.

Question 39

Consider this case:

two firms that both have return 1400 if economy is storng and 900 is weak.

The first firm is unlevered and its market value of equity is 990.
The other firm is levered as it has borrowed 500, and it has a market value of equity of 510.

The firms are identical except for capital structure.

Is MM1 violated?
Is there an arbitrage opportunity here?

Answer 39

The total market value of the second firm is 500+510 = 1010. this is different from the first firm, even though they produce the same cash flow. therefore, MM1 is violated.

Since the firms are identical, they have the same assets. These assets generate the same cash flow, but they are priced differnetly.

An investor that sees that MM1 is violated can do the following:
We loan 500 and buy the equity of firm 1 for 990. Our capital structure consists of 500 + 490 in equity. In other words, we have the same debt as the second firm, but our equity value is 20 bucks lower. Since we now own exactly the same assets, we have gained a profit of 20 relative to firm 2, whcih we get from selling the equity for its real price of 510.

Question 40

Also add the fact that the value of the assets is 1000, because this is the cash flow they are able to generate

Answer 40

Question 41

When a firm use leverage to buy shares outstanding of its own firm, what do we call it?

Answer 41

Leveraged recapiatlization

Question 42

Regarding leveraged recapitalizations. They raise funds at the expense of more debt. This adds interest payments. Surely this cannot still mean that the value of the firm remains the same?

Answer 42

adding debt will most likely reduce equity, but when one talk about the total value of a firm, one must take into account all different securities that are issued by the firm. Equity is one such security. Debt is another. There can also be other types.
However, in terms of “the value of the firm”, it is about the whole. Many people are so used to automatically assuming the role of a regular equity investor, so it can be difficult to understand how increasing debt won’t change the value of the firm, because they assume the value of the firm the same as the value of the equity.

There is a real dangerous misconception here regarding the difference between total market value of a firm and value of equity. We cannot make this mistake.

Increasing or decreasing debt only change the distribution of the cash flows.

Leveraged recapitalizations are considered zero NPV transactions because no value is added or destroyed. The firms assets remain the same, and produce the same cash flows. All that is changed, is where the cash flows are distributed. But that does absolutely nothing in regards to decreasing the value of the firm.

Question 43

Elaborate on owning all aspects of a firm in regards to MM1 and Law of one price

Answer 43

one can also consider what happens if one buys all aspects of a firm. Buying debt and equity etc. Then you’d get all the cash flows regardless of capital structure. There is no reason why one could not do this. From this perspective, it makes perfect sense why the law of one price would force the “market value of assets” to be the same as the price of the securities of the firm.

Question 44

how is market cap affected by leverage?

Answer 44

Market cap is widely affected by various capital structures, because market cap is the same as the total value of the firms equity. Since equity value will change with leverage, so will market vap.

Question 45

Why are investors indifferent to the firm’s capital structure?

Answer 45

Keyword: ‘investors’.

not ‘equity holder’.

Since investors can buy any of the securities of the firm, it should not matter what capital structure is used. the investor has access to all the cash flow distribution channels, and because there are no arbitrage opportunities in perfect capital markets, the securiteis are priced in a way that makes investors indifferent.

worth adding: if markets are competitive enough, the law of one price is relatively accurate.

Question 46

the MM proposition states that

E + D = U = A

How does this relate to the expected return of the portfolio?

Answer 46

We know that the return of a portfolio is equal to the return of the individual pieces weighted with their proportions.

Ra = Ru = Re (E/(E+D)) + Rd (D/(E+D))

This is the pretax WACC.

We can also add that by solving for equity cost of capital, or the return of the levered equity, we will get the equation:

Re = Ru + D/E (Ru - Rd)

This result show that by increasing debt to equity ratio, the “return of levered equity” will go up. This is because of the additional risk provided. It basically gives the expected return on the equity as a relation between debt and equity and total return expected from the firm.

Question 47

What is the appropriate cost of capital for a firm that is financed through both equity and debt?

Answer 47

WACC.

Question 48

elaborate on betas in regards to capital structures etc

Answer 48

The unlevered beta represent the market risk of the entire business. Therefore, it is tied to the assets that the firm use to generate cash flows.

if the firm choose to alter its capital structure, this has no effect on the underlying assets. As a result, the unlevered beta remains unchanged.

The same can be said about the debt beta. Debt beta depends on the riskiness of the business and the firm, and is not related to capital structure.

However, the equity beta will change if we change the capital structure. We end up with the exact same relationship as with the expected return on equity. This is because beta is also calculated as:

beta unlevered = beta equity x (proportion equity funded) + beta debt x (proportion debt funded)

this result gives us that beta of equity change when debt change. If we increase debt, we increase beta of equity. This means that the market risk exposure is amplified when you own equity and the debt increase.