Chapter 15 - Debt and taxes

Question 1

Recall how capital structure affects the value of the firm

Answer 1

It doesn as long as there are perfect capital markets.

This is because the total value of the firm is determiend by the assets that generate cash flows. We have to consider all cash flow distribitom channels, not just assume the perspective of an equity holder/investor.

Question 2

Name a reason(s) why capital structure is actually important to the firm

Answer 2

empirical evidence shows that firms spend huge sums of money on it. Investment banking fees etc.

Question 3

Why are firms havign different capital structures if it doesnt affect the value of the firm?

Answer 3

The key is that Modigliani and Millers ideas only apply to perfect capital markets.

in this chapter, we focus on one imperfection that cause friction in the perfect capital market theory: taxes

Question 4

How does itnerest payment relate to taxes?

Answer 4

Corporations pay taxes on profits AFTER interest payments are deducted. Therefore, interest payments reduce the amount of taxes a corporation must pay.

Question 5

Since corporations reduce their tax payments in the presence of interest payments, what does this do?

Answer 5

It creates an incentive to use debt.

Question 6

What can we say in general about using leverage in terms of what happens to the income

Answer 6

Altough the net income/profits that is left for equity holders may be less when using debt/leverage than without leverage, the total amount of money/cash available to ALL investors is higher with leverage.

when we add the debt payment and the equity payment together, we get this result. And this result is an outcome of the fact that using leverage decrease TAXES. Since taxes can be regarded as cash flow that is not going to investors, we naturally want to reduce this part. This is what happens when using leverage. By re-allocating cash flow from all-equity to leveraged equity, we will increase the proportion of the cash flows that remain inside of the “hands” of the various investors.

Question 7

Does leverage carry an effect on the value of the firm?

Answer 7

Yes, in the presence of taxes.

When taxes are present, and as long as interest is tax deductible, the firm can reduce the amount of cash that goes to taxes.

We increase debt, and by doing so, we increase the interest tax shield, which reduce the amount of money that does not go to investors.

The key to understanding this effect, is to consider the underlying assets of the firm. These assets generate cash flow, and will be given a market value thereafter. However, an investor will consider the value of these assets as relative to what he can get. by reducing the amount of taxes, we keep more of the cash flow produced by the assets, which means that these cash flows are available to the investors. It is all about keeping money to the investors.

Question 8

What can we say from this image?

Answer 8

The effect is leverage is displayed. Do not be fooled by the decreased net income. This only tells the equity-part of the story.

We want to look at the fact that the firm generate the same amount of cash flows regardless of capital structure. The assets remain the same, and still generate the same cash flows.
We can see that using leverage results in paying 140 less in taxes. This means, 140 less is payed OUT of the firm. This is the key result here.

Using leverage will decrease taxes the firm has to pay, which keeps more of the cash flows inside of the hands of the various investors.

Question 9

Let us say we have $400 million in interest payments. What is this sum called?

Answer 9

We say that this sum is shielded from taxes.

Question 10

Say we have $400 million in interest payment. What is the interest tax shield?

Answer 10

The 400 is shielded from taxes, and we can calculate the tax shield like this:

interest tax shield = corporateTaxRate x ShieldedAmount = 0.35 x 400 = 140

We basically get this equation from the regular tax equation:

(income - interest) x (1 - taxRate) =income - income x taxRate - interest + interest x taxRate

= income (1 - taxRate) - interest (1- taxRate)

= income (1 - taxRate) - interest + interest x taxRate

so, our profits is aided by the interest tax shield. At the same time, we still have to deduct interest, but as we know, this is value that still go to our investors.

Question 11

Answer 11

1) A firms value is equal to the total amount of cash delivered to its ivnestors. Taxes reduce this amount. Therefore, if we can find a way to reduce taxes, we will increase the value of a firm.
Since using leverage is a way to utilize the interest tax shield to reduce the amount of the cash flows that are strictly removed from the business, using leverage can increase the value of the firm.

2) interest tax shield is the amount of cash flows that we increase the firms value with by using the leverage. It is calculated as interestPayments x taxRate

Question 12

is the interest tax shield a one-time thing?

Answer 12

no, using leverage typically yield a shield for a number of years, specifically equal to the nubmer of years the firm pays interest.

Because of this, we consider the value of the interest tax shield to be equal to the present value of the stream of future interest tax shields the firm will receive.

Question 13

Give the yearly relationship between cash flows to investors with leverage and wihtout

Answer 13

Cash flows to investors with leverage must be equal (each year) to the cash flow given to investors without leverage + the interest tax shield

Question 14

what are we really doing to reduce taxes?

Answer 14

We have to reduce the amount of “pretax income”.

Question 15

How do we change MM1 proposition to fit taxes?

Answer 15

Value of cash flows Leveraged = Value of cash flows unlevered + PV(interest tax shields)

In other words:
the total value of the levered firm exceeds the total value of the unlevered firm by exactly the present value of the interest tax shield.

Question 16

ELaborate on issuing a perpetual consol bond

Answer 16

This is a kind of debt that pays interest forever (same dollar amount) but never repay the principal.

Question 17

Suppose a firm borrows debt D, and keeps it infinite by always refinancing so that D is kept.

What is the value of the interest tax shield?

Answer 17

We know that the interest payment in period will be D x rate. Therefore, the interest tax shield per period is: taxRate x D x interestRate

then we treat this as a perpetuity, which allows us to use the very simple formula of value/rate to get the perpetual present value:

(raxRate x D x interestRate) / interestRate = taxRate x D

This result means that for every dollar we increase the debt D with, the present value of the interest tax shield, and therefore also the entire firm, increase by the taxRate.

NB: we must not forget the assumption we make in this case. We assume that the firm has constant debt infinitely so that we can use teh perpetutiy formula.

Question 18

elaborate on effective borrowing rate

Answer 18

Using leverage in combination with an interest tax shield will actually reduce the after-tax cost of borrowing.

For instnace, if we borrow 100 000 at 10% interest, we’d expect to pay 10 000 each period. However, since we also have an interest tax shield included, we must account for it:
10 000 x taxRate = 10 000 x 0.21 = 2100. Therefore, the amount we actually have to pay to borrow, is 10 000 - 2 100 = 7900.
The effective borrow rate / cost of debt is therefore:

7900 / 10000 = 7.9% and not 10%.

In other words: THe effective after tax borrowing rate is: interestRate x (1 - taxRate)

Question 19

elaborate on WACC

Answer 19

Now we can finally add the tax component. We know that interest tax shield reduce the after tax cost of borrowing by a factor of (1-tax), so we add it to the formula.

Question 20

What can we say about the pretax WACC in regards to WACC?

Answer 20

Pretax will be larger because it doesnt account for the tax shield.

Question 21

Instead of maintaining constant level of debt, what is typically done by many firms?

Answer 21

Go for a specific target debt/equity ratio. The benefit of the debt - equity ratio is that it allows the debt to grow with the growth of the firm.

Question 22

what is a recapitalization?

Answer 22

A recapitalizaiton is whne a firm makes a significant change in its capital structure. Leveraged is one way to do this.

Question 23

In the case of perpetual constant debt, what can we say about the interest tax shield?

Answer 23

The interest tax shield is in these specific cases independent of the interest.

The interest tax shield each period is given by:

total debt x intrest rate x taxRate

Since we will be “payed” this value every period, we can treat it with the annuity formula:

(debt x interest rate x taxRate) / interest rate

= debt x taxRate

So, if a firm takes on 100 million in debt on a constant basis, the interest tax shield is 100 x taxRate

Question 24

elaborate on recapitalization using leverage. For instance going from all equity to leveraged

Answer 24

When we are all equity and start adding leverage, we know that the total value of the firm will increase by the interest tax shield added.
Since tax shield is going to the shareholders, this is equity.

Therefore, immediately after it is known that the firm will take on debt to recapitalize, the public will respond by shooting the price up (without a single purchase being sold; assuming intelligent investors).
We calculate the new share price by considering the new equity market value, and dividng by the shares outstanding.
The market value of equity is calculated by considering the market value of equity before hte news (shares outstanding x old share price) and adding the interest tax shield of debt x taxRate (perpetual debt).

The new share price represent less the old share price, together with the old/current shares outstanding, a proportion of equity equal to the tax shield.

now we buy shares, and equity of the firm is reduced by the debt amount.

so, equity market value is reduced, but total value of firm is increased. Also, original shareholders are better of (tax shield).

Question 25

elaborate on the process of recapitalization when taxes are included

(sort of wack)

Answer 25

A recap is typically intiiated with the expectaiton of increasing shareholder value and boost the stock price.

first, we need to examine the benefits of the taxes on the recapitaliaztion.

Say we have a firm with no debt that has a stock price of 15 and shares outstanding of 20 million. This give unlevered equity of 20 million x 15 = 300 million.

Then let us assume the debt is constant 100 million, and with tax rate of 21%, this gives 21 million in interest tax shield as the present value of the interest tax shield.

We know that the levered firm value must be equal to unlevered firm value + present value of the interest tax shield.
Levered firm = 300 million + 21 million = 321 million.

Now we can find the value of the equity, as we know the full firm value and the debt value:

Equity value = Firm value - debt value
Equity value = 321 - 100 = 221 million.

So, now we can say some things.
1) The recap has decreased the value of the equity from 300 to 221.
2) Shareholders will receive 100 million from the borrowed funds that have been used to buy stock. This means that the equity is now actually sort of worth 321 million, which means that we got the added benefit of the interest tax shield.

but does it lead to stock price increase?

There are now less shares outstanding.
The new equity value of 221 and the new number of shares outstanding yield a stock price of 16.575.

The difference in stock price multiplied by the number of shares that are now outstanding will be equal to the tax shield.

However, the question now is: If the shares are now worth 16.575, why would anyone sell them for 15?
This would be arbitrage.
in fact, once people know the recap is happning, the equity of the firm will immediately rise to 321 million, and since it is currently (before any purchase happens) 20 miilion shares outstanding, the stock is priced at 16.05.

At this price, shareholders who sell gain 16.05 - 15, same with the ones who hold, which gives 1.05 x 20 million = 21 million. this is the interest tax shield.

This has the following important result:
During a recap, the original shareholders will earn the benefit of the interest tax shield.

Question 26

What differnece to the market value balance sheet do we need to make whne including taxes?

Answer 26

We must list the tax shield as an asset

Question 27

Adding more leverage will reduce the firms equity. But can shareholders still capture some benefit?

Answer 27

Yes, shareholders still capture the interest tax shield.

When a recap happens, the anticipation of the event (more leverage, more shield) will increase the equity value before any repurchasing is done. 300 million + taxshield = 321 million. But, since no share has been purchased yet, the number of shares outstanding is still the same. Therefor,e the share price must rise.
When the recap is done, a number of shares has been bought. The shares bought has reduced shares outstanding, and the market value of equity will be reduced. However, since the share price has remained the same, the investors who held originally has seen an increase. this increase is due to the tax shield.

Question 28

How does personal taxes influence the shit?

Answer 28

if different securities has differnet tax rules, then this must be taken into consideration, as it will impact the decision making of investors.

Ultimately, the value generated by a firm to an investor, is what the investor receives after all taxes have been payed. This remaining sum is what he will price the security based on.

Question 29

What can we say about corporate and personal taxes in regards to their combined effect?

Answer 29

debt is not taxed at corporate level, but is usually taxed more heavily on the personal level.

equity is taxed twice, but weaker at the personal level.

The equity holders that receive a dividend is taxed like this: (1-taxRateCorporate) x (1-taxRateDividend)

while debt holders are taxed:
(1-taxRateInterestDebt)

consider, for instance:
corporate tax: 21%
dividend tax: 20%
debt tax: 37%

equity: (1-0.21)(1-0.2) = 0.632
debt: (1-0.37) = 0.63

this means, holding equity is slightly more beneficial. Or, it is a slight disadvantage to hold debt for some investors.

Question 30

effecetive tax advantage

Answer 30

it is defined as the relative advantage of debt vs equity in terms of taxation.

t-star = (taxRateDebt - taxRateCorporate)/(1-taxRateDebt)

the effective tax advantage can be interpreted as: if the corporaiton payed (1- effectiveTaxRate) in interest, debt holders would receive the same amount after taxes as equity holders would receive if the firm payed $1 in profits to its equity holders.
in other words:

(1-effectiveTaxAdvantage)x(1-taxRateDebt) = (1-taxRateCorporate)x(1-taxRateEquity)

We can re-structure this to get the formula for effectiveTaxAdvantage that looks a little better

Question 31

Modigliani and Miller concluded that in perfect capital markets, there is no optimal capital structure. How does taxes affect this conclusion?

Answer 31

As we have seen, by including taxes, there is a moment of interest tax shield that becomes important. It is not the shield in itself though, but rather the fact that by including taxes, we suddenly find ourselves in a situation where some of our earnings are distributed to someone who is no an investor. This is important, because this removes a part of the pie that is left for the actual investors. Investors consider the firm attractive because of the cash flows that its assets are able to generate for them. When some of the cash flows are suddenly removed, we get a more complicated case.
The reason why the interest tax shield is so important, is because of the fact that one does not pay taxes on interest payments.

Question 32

what is the most common way to raise funds for a firm?

Answer 32

debt. Not equity. in fact, in recent years, equity fundings are negative on aggregate, indicating that more firms are doing repurchasing of shares rather than issuing more.

Actually, when including the option if internal funding, capital expendutures from retained earnings is a big source.

Question 33

does a firm need to use 100% debt financing to receive the entire tax benefit?

Answer 33

No, not necessarily.

One must remember why the tax shield has an effect. It has an effect as long as the firm pay taxes. If no taxes are being payed, there is no benefit from the shield.

Question 34

what rule started in 2022 regarding taxation on interest?

Answer 34

The interest deductible can not exceed 30% of the earnings.

Applies to firm with revenue above 250 million.

Question 35

theoretically, what is the optimal amount of interest?

Answer 35

Interest should be at the point where it is exactly equal to the income limit of 30%.

Question 36

elaborate on growth and debt

Answer 36

Many growing firms are in expansion phase where they earn no earnings. Because of this, a tax shield is of no benefit.
These firms should mostl ikely use equity alone to fund investments.
Their value, which their equity is priced on, is based on the prospect of them eventually making positive earnings.

when the firm later becomes a cash cow, then ti surely makes a lot of sense to utilize a tax shield for what it is worth, in order to reduce the amount of tax we pay.

Question 37

why are firms typically underleveraged in the context of what our analysis would theoretically recommend?

Answer 37

Increasing leverage (debt) will also increase the risk of bankruptcy.
There are also certain aspects of debt that appear daunting. Debt represent a payment that MUST be made regardless of how the economy is doing or how our firm is doing. Equity, on the other hand, provide no such requirement, aside from the fact that investors become pissed.

Question 38

Consider the capital market with taxes. Consdier the interest tax shield. Who recieves this interest tax shield?

Answer 38

equity holders, and there is why:

We can set up the earnings equaiton:

earnings = (income - interest)x(1-tax)

earnings = income(1-tax) - interest + interest x tax

interest is payed to the debt holders.
The remaining income(1-tax) goes to equity holders.
Since debt holders has received all that they were promised, it is the equity holders that receive the interest tax shield.

If no taxes, we would have: earnings = income - interest
In such a case, investors would get the entire pie, but with differing capital structure.

Question 39

what is the value of a levered firm when personal taxation is included in the mix?

Answer 39