Chapter 18 - Capital budgeting and valuation with leverage

Question 1

recall the capital budgeting procedure from chaper 7

Answer 1

estimate the incremental free cash flow.

disocunt the free cash flow

Question 2

name the 3 methods of capital budgeting when using leverage as part of the calculations

Answer 2

1) WACC method
2) APV (adjusted present value) method
3) FTE method (Flow to equity method)

Question 3

What is the important thing regarding the capital budgeting methods in this chapter?

Answer 3

When appropriately used, they yield the same answer.

However, they are good in certain situations, so we dont necessarily just choose one arbitrarily.

Question 4

Recall advantage of debt

Answer 4

Interest tax shield

Question 5

Does WACC method account for the advantage of debt?

Answer 5

Yes. This is because when discounting using WACC, we use the after tax result.

Question 6

Elaborate on the assumptions of this chapter

Answer 6

1) Project has average risk. This means, we assume that the market risk of this project is equal to the average market risk of all the other projects of the firm. This allows us to find the cost of capital from the firm as a whole.

2) The firms debt-to-equity ratio is constant.

3) We assume that corporate taxes are the only type of market imperfection. We therefore assume no financial distress cost, issuance cost etc

Question 7

Recall the definition of free cash flow

Answer 7

The after tax cash flow before the cash flow is distributed. This means, before interest and before equity considerations.

Question 8

What is the assumption we need to make when using the WACC to discount multiple periods?

Answer 8

The debt to equity ratio must be the same/remain constant.

Question 9

Summarize the WACC method

Answer 9

Compute the FCF

Find the WACC

Discount the FCF’s using the WACC

Determine the NPV of the project’s cash flows.

Question 10

TODO: Debt capacity, and maintaining a constant debt to equity ratio

Question 11

Summarize the APV method

Answer 11

We will find the levered value of the investment by FIRST finding the unlevered value of the investment and adding the present value of the interest tax shield.

In order to get the unlevered value of the investment, we must discount it using the unlevered cost of capital.

The unlevered cost of capital can be considered equivalent to taking the role of an investor who buys the entire firm by taking a share of the equity and debt. Therefore, he has claim to the entire cash flow.

IF the risk of the project is the same as the overall risk of the firm, then we can use the firm’s pretax WACC as an estimate of the unlevered costo f capital for the project. This is because the unlevered cost of capital is all about capturing business risk. Since pretax WACC creates a scenario where teh investor has a claim to the entire cash flow, we essentially make this scenario.

Question 12

Main reason to consider the FTE method

Answer 12

It place emphasis on the outcome for the equity holders

Question 13

What is the difference between this FCF and the FCF of the other methods?

Answer 13

FTE FCF adds interest payment and that. Takes the thing one step further, and consider only the part of the cash flow that remains for the equity holders.

Question 14

The other methods compute unlevered net income. What does this method compute instead?

Answer 14

Incremental net income.

This actually refers to what we compute at the very same line in the financial statement. It reflects the fact that we now correctly have the additional income (as income is reported on the financial statement) that the project carry in terms of the entire firm.

Question 15

What is the requirement we need to ensure before being able to use the firms WACC in our calculations for a new project (Using the WACC method)?

Answer 15

In order to use the WACC to discount the cash flows of a project, we need to make sure that WACC is in fact appropriate for the specific project. Specifically, WACC is only appropriate for the project if the debt-to-equity ratio of the project match the debt-to-equity ratio of the firm AND if the risk profile of the project is the same as for the firm.
Regarding the debt to equity: If it is not matching, we basically have the wrong weight of equity and debt, which means that we get a skewed WACC. If the debt-to-equity ratio of the project is larger than that of the firm, we are basically discounting with a most likely too high rate, and we are too harsh on considering what is positive NPV and what is not. If opposite, we can be too optimistic in our NPV computations.
Regarding risk profile: If the project is less risky than the overall firm, investors will not require that much return from it. Therefore, it should be easier to raise funds. However, since the firm would believe the project is risky, it can be too strict/pessimistic in what projects are positive NPV.

Question 16

What is the nice thing about WACC?

Answer 16

It accounts for the interest tax shield.

Question 17

When we refer to the “levered value of an investment”, what are we talking about

Answer 17

Levered value of an investment refers to the value of the investment when considering the capital structure.

This means: We have the value of the firm that includes the financial risk of leverage, the financial benefit of interest tax shield, the financial distress costs etc.

Basically, when we use levered as a term, it is understood that is includes leverage, and everything that follow from using leverage.

Question 18

When using the WACC method, what is the outcome of the firm’s project not having the average risk of the firm?

Answer 18

We cannot use the firm’s capital structure to compute WACC.

The reason for this is that the WACC of the firm does not contain the correct information in regards to the financial risk of leverage that is specific to the investment/project.

Question 19

explain net debt

Answer 19

debt - cash.

For instance, if a firm has 320 million in debt, and 20 million in cash, we use debt as 300 million.

Question 20

What is the implication of using WACC in the WACC method in regards to capital structure?

Answer 20

The firm must make sure that the overall debt to equity ratio of the firm is the same before and after (and during) the project. This means, if you acquire assets, one way to do this is to finance these assets with the same capital structure as the overall firm.

Why must we do this?
If we dont, the WACC we use to discount the cash flows will not match the correct one. For instance, in the extreme case where the firm has a debt to equity ratio of 1, and a new project is financed by all equity, using the firm’s overall WACC will give us a more optimistic result than if we used the actual cost of capital, which would be purely the equity cost of capital in this case. Since equity is usually much more expensive than debt, the outcome would be that the project appears to have a larger NPV than it actually does. In certain extreme cases, this can result in the firm accepting projects that appear to have a positive NPV, but in reality have negative, and thus they are actually reudcing the value of the firm.

Question 21

Two ways to increase debt, as debt in capital structure

Answer 21

1) Reduce cash

2) increase debt by borrowing

Reducing cash means paying it as dividend or as a stock repurchase

Question 22

When using WACC method, and the firm maintains a constant debt to equity ratio. Assume the firm pays a dividend and borrow some in order to maintain the debt to equity. What is the total value added for hte shareholders?

Answer 22

the shareholders receive the total NPV of the project. in fact, shareholders receive the entire NPV of any project/investment. This is because all creditors have been taken care of through the funding and the debt cost of capital. To clarify, this only means that the NPV calculation is a sum that is entirely entitled to the shareholders.

The NPV of the investment/project equals the part of the cash flow that we are left with after financing the shit, but also added on the dividend.

Recall that NPV is after the debt investors receive their shit.

If the project’s assets will generate $70.73 million in present value, and the project requires $29 million to fund, the remaining $41.73 million is left to the shareholders.

Question 23

Define debt capacity

Answer 23

We define debt capacity to be the amount of debt required at time step ‘t’ to maintain the firm’s target debt to equity raito.

We use ‘d’ to represent the target debt to equity ratio.
We use ‘D_t’ to represent the debt capacity.
We use V^(L)_t to represent the levered value of hte firm at time t, or more specifically the firm’s levered continuation value. this is simply the value of its future cash flows at this point in time.

then we define debt capacity as: D_t = d x V^(L)_t

The important part here is the understand whatdebt cpacity is measuring. As the time goes by, we expect the continuation value of the project to decrease. Since the continuation value decrease, and the target debt-to-value ratio remains the same, we know that the debt capacity will decrease as well with time.

To summarize, debt capacity is PROJECT specific, and is time-specific.

Question 24

In the APV method, why does the unlevered cost of capital equal the pretax WACC?

Answer 24

This only apply to cases where the risk of the project equals the risk of the firm AND the target debt to equity ratio for the project is the same as for hte project.

Question 25

Why do we need the assumption of the project having average risk in reagrds to the firm?

Answer 25

Average risk means that there will be no difference in the risk of the firm after the project.

Question 26

elaborate deeply on the APV method

Answer 26

We start by considering the unlevered value of the investment. This includes the assumption on risk level.

when we find a value for the project, we need to account for the benefit from the interest tax shield.
To do this, we first figure out how much interest we will pay each year. This is done by finding the debt capacity at the different time steps, and multiplying it with the debt cost of capital.
Then we take this amount, and discount it using the project’s unlevered cost of capital.

Then we add the two values together for the final result.

Question 27

is the APV method for shareholders?

Answer 27

No, it is for all investors. There is a focus on the levered value of the firm, which assumes that equity is a part of the capital structure.

Question 28

benefit of APV?

Answer 28

Can be easier to use if the firm does not maintain a constant debt equity ratio

Question 29

what are we really doing here, in this chapter?

Answer 29

When we want to find the PV of a project, we need the discounting rate. And the entire point is that we want to assume a condition where we can use the overall firm capital structure and risk profile to find this discounting rate. One of the assumptions is that the cost of capital for a project generally follow the cost of capital of the firm.

The WACC method simply finds the equity cost of capital and the debt cost of capital from the firm, and then combine this with the capital structure of the firm to find the pretax WACC. We find the WACC by just including the tax-term to the debt part of the WACC. After this is found, we simply discount the cash flows from the project using this rate.

The APV method assumes that the factor we use to discount the project’s cash flows is the same as the pretax WACC of the firm, and we call it unlevered cost of capital. However, since this method has not included the tax benefits, we do so by adding the present value of the interest tax shield to the unlevered value of the investment, which will yield the levered value of the investment.

To summarize, we need to find a discounting rate that we will use on the projects to compute the correct PV and NPVs.

A crucial part of this, is to consider what happens to the capital structure when we add the project. The WACC method relies on the firm’s WACC, which means that the capital structure of the project must be so that the overall capital structure of the firm is the same before and during and after the project. This is necessary to ensure that the firm’s WACC is appropriate for the project.
The APV method also relies on the capital structure of the firm.

So, when faced with the question of “what value will this project carry?”, the challenge (beyond estimating cash flows) is to find the correct rate to discount the cash flows with. And this/these rate(s) depend on the assumptions we make regarding the firms’ capital structure dynamics

Question 30

What is the difference between the WACC, APV methods, and the FTE method?

Answer 30

The FTE method takes the cash flow statement one step further by including the “net borrowing”, which represent the change in borrowing. it can be considered a cash flow, as it represent how much cash is going to the debt holders. it also includes interest expense, which is the amount we pay as interest.

The outcome of this is that the cash flow statement of free cash flows now show how much the equity holders receive.
Because of this outcome, the discounting rate we need to use is the equity cost of capital.

Question 31

When are interest deducted on the cash flow sheet?

Answer 31

Before taxes

Question 32

Is there an alternative way to the cash flow sheet to find the FCFE?

Answer 32

Yes. If we have been given the FCF, we can turn it into FCFE by doing this:

FCFE = FCF - interest(1-TaxRate) + net borrowing

net borrowing is obviously negative if more cash goes out than in.
We need to subtract interest(1-tax) because the FCF is actually above this level in terms of looking at it from the perspective of all investors. FCF originally does not include any capital structure considerations. We add these by removing interest payments, but adding the interest tax shield. Then of course we also account for the debt level.

Question 33

Elaborate on the discounting when we use FTE, and what it entails

Answer 33

with the FTE method (Flow to Equity) we discount using the equity cost of capital instead of WACC or pretax WACC (and debt cost for the debt) because we have already accounted for the debt. However, I suppose this method also require the assumption of similar risk of the project as the overall firm because if not, then we’d have to find a new equity cost of capital. So, if we want to use the equity beta of the firm to compute the required return/equity cost of capital, then the risk must be the same. And for the risk to be the same, we should have similar risk profile AND similar capital structure

Question 34

Elaborate on PV vs NPV

Answer 34

NPV is actually shareholder perspective, because it accounts for the price of the project

Question 35

what is the weakest link in this chapter regarding advanced valuation?

Answer 35

The risk profile of the investment rarely match the risk profile of the firm.

Question 36

Elaborate on what we can gain from the unlevered cost of capital from comparables

Answer 36

comparable give us industry risk, which means that we can use the APV method. APV method requires market risk/industry risk and then the interest tax shield present value.

However, if we want to use WACC method, we can use the industry risk as a baseline to compute the equity cost of capital, assuming that the debt cost of capital is known

Question 37

What is hte formula we use to find equity cost of capital, given the unlevered cost of capital?

Answer 37

Firstly, the reason this is allowed is that the unlevered cost of capital is purely industry specific (or at least asset specific). Therefore, unlevered cost of capital makes no assumptions regarding the capital structure of individual firms.

The formula is based on: r_u = E/(E+D) r_e + D/(E+D)r_d
which gives:

r_e = r_u (E+D)/E - D/E r_d

r_e = r_u + r_uD/E - D/E r_d

r_e = r_u + D/E(r_u - r_d)

Question 38

Regaridng projects that has differnet risk profile as the firm, What is the preferred way of estimating r_wacc, and why?

Answer 38

r_wacc = r_u - dtr_d = unlevered cost of capital - debtToEquityRatio x corporateTaxRate x debtCostOfCapital

This method is preferred because it does not involve computing the equity cost of capital

Question 39

elaborate on incremental leverage

Answer 39

firstly, incremental leverage is the additional change in capital structure with vs without the project.

There are some key things regarding incremental leverage. For instance, if the project needs to finance a warehouse by using a mortgage, and the firm has a policy to maintain a target debt-equity-ratio, it will typically reduce the debt somewhere else. This is key, because the incremental leverage is not that of hte mortgage, but is rather the total change, which is likely the target rate.

Also, leverage should be valuated using net debt. Net debt includes cash as an offsetter to debt.

Question 40

if a firm does not maintain constant debt equity ratio, what other options can we do?

Answer 40

Constant interest coverage

Predetermined debt levels

Question 41

what can we say about equity cost of capital?

Answer 41

equity cost of capital ALWAYS includes the financial risk of leverage.

Question 42

What can we say about the WACC?

Answer 42

WACC always includes the financial risk of leverage AND the financial benefit of interest tax shield

Question 43

(IMP) elaborate on what happens if the project does not have the same risk profile as the firm

Answer 43

We cannot use the firm’s values. Therefore, we use comparables.

We estimate the unlevered cost of capital by comparing with firms that have this same industry risk.
this gives us the unlevered cost of capital. This means that we can now use the APV method.

However, if we want to use WACC method or FTE method, we first need to compute the equity cost of capital. For WACC method, this is because the unlevered cost of capital is not usable. We need to use the equity cost and debt cost along with tax etc.
For FTE, we also need the equity cost.

Question 44

why is debt capacity important to us?

Answer 44

During the lifetime of a project, the cash flows comes in at various rates. Perhaps not uniformly distributed.

By having debt capacity, we know how much debt the project needs to maintain at a time step in order to mantian the firm’s target debt to value ratio.

d = debt to value ratio
V_t^(L) = levered value of the investmet/project at time t
D_t = debt capacity at time t

Question 45

Case:

firm acquires assets that have 100 million in value. The cost of these assets was 80 million. Target debt-to-value=0.5.

What to do?

Answer 45

the firm received 100 million in assets. 50% of these must be financed through debt. IMPORTANT: it is not the cost that has 50% financed through debt, but the entire asset value.

50 million must be acquired using debt.
Since the acqusiition cost was 80 million, there is 30 million left. this is funded using equity.

What about the remaining 20?
The remaingin 20 million comes from the assets, and is just increase in equity. Since the sum is now 50-50, we are all good.

Question 46

How do we find the levered value of the project at each time step so that we can compute the debt capacity?

Answer 46

It is acutally the easiest ot start from the back, and compute our way back in time.

V_t = (FCF_(t+1) + V_(t+1) ) /discountRate(WACC)

Question 47

what is the distinction between unlevered value of a project and the unlevered FCF?

Answer 47

unlevered value is the unlevered FCF discounted using the unlevered cost of capital.

Do not confuse it with the levered value, which has been discounted using the WACC.

Question 48

Recall what unlevered cost of capital actually is

Answer 48

Required return from the assets as a whole, without regarding the capital structure.

It is equivalent to what equity holders would require from the assets if the project was all equity financed

Question 49

When we use the APV method, how do we know how much interest tax shield we get each period?

Answer 49

We must use the debt capacity.

We use the target leverage ratio along with the LEVERED value of the project to compute the debt capacity. Then we take the debt cost of capital and multiply by the debt capacity to get the amount of interest tax shield. Then we need to discount it.

We discount using unlevered cost of capital.

Question 50

does the APV method require constant debt equity ratio?

Answer 50

no, but we need to use differnet values for the unlevered cost of capital if it is not constant

Question 51

Consider a project based valuation approach. How do we find WACC wihtout computing equity cost of capital?

Answer 51

IF the firm maintains a target leverage ratio, then we have the relationship:

wacc = ru - d x taxRate x rd

Question 52

What can we say about debt and cash?

Answer 52

A firms leverage should be based on its net debt. net debt is equal to dbet less cash .

Therefore, if some investment will use retained cash, it is equivalent to adding leverage.

The opposite applies as well. If a project adds cash, this reduce leverage.

Question 53

firms may not always use a target leverage ratio, or debt to equity ratio. What can we do thhen?

Answer 53

we look at two different cases:
1) constant interest coverage
2) predetermined debt levels

Question 54

What is the outcome of relaxing the assumpiton of a constant debt equity ratio?

Answer 54

The WACC and equity cost of capital will change over time. If the debt equtiy ratio change, the WACC and equity cost of capital will change. this is why it is convenient to have a fixed and constant debt equity ratio.

Question 55

elaborate on the motivation behind constant interest coverage methods

Answer 55

Interest is used to add value to the firm by reducing taxes. We assume the firm has found its optimal level of debt and interest coverage.

Based on this, the assumption is that the interest coverage is a function of cash flow. If the cash flow increase or decrease, we want the interest coverage to follow.

Assuming that the interest should be a constant fraction of the free cash flow in any period, we arrive at the following function:

Interest paid period t = k x FCF period t

Question 56

What interest rate should we use to discount the present value of the interest tax shield using the APV method with a constant interest coverage procedure?

Answer 56

Since the interest coverage follow proportionally the cash flows, they have the exact same risk as the cash flows. Since the cash flows use the unlevered cost of capital as the rate, then we need to use the unlevered cost of capital ti discount the interest tax shield as well.

however, we can trick here:

Since the computation here involves discounting FCF at unlevered cost of capital, we actually get the unlevered value of the firm/project.

So, we get:

PV(interest tax shield) = t k PV(FCF) = t k V^(U)

So, when we add the present value of the taxshield to the previously computed result:

V^(L) = V^(U) + tkV^(U)

V^(L) = V^(U) (1 + tk)

Question 57

regarding the APV method. We found that we can solve it with a constant interest coverage with a very simple equation. Recall that equation.

The equaiton requires the unlevered cost of capital. how do we find it?

Answer 57

V^L = V^(U) (1 - tk), where t is tax rate and k is the proportion of interest coverage in regards to the FCF.

If we use a comparable, we just take their asset cost of capital.

if not, we need to solve a system of equations.

Question 58

Recall the 3 cases of assumptions we make in this chapter

Answer 58

1) Constant target debt equity ratio

2) Constant interest coverage

3) Predetermined levels of debt

Question 59

Name some exmaples of predetermiend debt cases

Answer 59

Say we borrow an initial amount first, and then reduce it by say 10 million each year.

Question 60

What is the difference between predetermined levels of debt and the constant target debt equity?

Answer 60

Now, with predermined levels of debt, the debt can vary. We therefore will get a varying debt equity ratio. Since the debt equity ratio is varying, the WACC will change, wchich affect our ability to use the WACC method.

Also, since the debt change, the interest change. This affect the ability to use something like a constant interest coverage method.

The real issue is “what rate do we use to discount the interest tax shield”. We kind of give up the idea of using WACC method, because we need more flexibility in the method of choice.

Question 61

What is the key about a fixed debt schedule?

Answer 61

The tax shield is less risky than the project because it does not fluctuate.

because of this, we know that the discount factor needs to be lower than the project.

Question 62

What discount factor do we use with fixed debt schedules?

Answer 62

We use the debt cost of capital.

This is because the interest tax shield follow the same risk profile as the debt. If the firm fail to pay the interest to the debt holders, the firm will not get the shield. Therefore, it is appropriate to use the debt cost of capital to discount the shield.

Question 63

Say we have an initial borrowed amount, and we reduce it in fixed installments during the project. What is needed to treat it as a perpetuity?

Answer 63

We cant, because it is not the same value like that. We need to discount each period as always.

Question 64

What happens if the firm has a debt case where it keeps the same level of debt (NOT ratio) the same?

Answer 64

Special case. If the project has no duration ending, we use it like a perpetuity.

Recall that if perpetuity, we know the present value as: DxtaxRate

In such a case, we’d have APV method like this:

ValueLevered = ValueUnlevered + PV(TaxShield)

ValueLevered = ValueUnlevered + tD

Question 65

what is the caution with not having target debt to equity ratio?

Answer 65

pretax WACC of the firm is not usable as the unlevered cost of capital.

Question 66

From now on, we are talking about the weird cases

Question 67

if a firm has a fixed debt schedule, what effects do this entail?

Answer 67

If the debt levels are fixed, we essentially know that the risk of the interest tax shield is relatively safe, and that it will remove some risk from the firms equity that originally came frm the leverage.

We actually need to deduct these safe cash flows from the debt, just like if it was cash, when we want to evaluate the firm’s leverage.

If T^s is the present value of the interest tax shield, we do this:

D^s = D - T^s

The present value of the interest tax shield is still discounted using the debt cost of capital, as its risk is basically the same as being able to pay the debt+interest. If we dont pay interest, we get no shield.

Question 68

precisely define debt capacity

Answer 68

Debt capacity is the amount of debt at time t that is required to maintain the firm’s target debt to value ratio.

Question 69

Name the important thing about debt capacity

Answer 69

Debt capacity requires the levered value of the firm.

Because of this, it is difficult to use APV

Question 70

if a firm maintains a target debt to value ratio, what discount rate should we use for computing present value of the interest tax shield

Answer 70

Here is the key: What determines the risk of the interest tax shield?

A target debt to value ratio entails maintaining debt, and therefore also the interest tax shield, according to the specific cash flows (FCF) that is associated with each period. Therefore, the risk of the interest tax shield is exactly the same as the risk of the free cash flows. Therefore, we use the unlevered cost of capital to discount them.

Question 71

Alleged advantage of APV method?

Answer 71

Easier to maintain when the form does not use a target Debt to value ratio

Question 72

Benefit of constant interest coverage ratio

Answer 72

The APV method becomes trivial to solve.

THe unlevered value of the firm is computed as alwasy.

The present value of the interest tax shield is now much easier to find.

We define the interest coverage ratio we want, as k. k represent a proportion of the FCF that we always want to pay as interest.

Therefore, the amount we get in a period in interest tax shield, is taxRate x k x FCF

Then, to find the present value of this, we do:

PV(taxRate x k x FCF)

Now the interesting part: taxRate and k are just factors on each FCF, which means that we can separate them.
taxRate x k x PV(FCF)

this equals: taxRate x k x V^(U)

So, when we do the APV :

V^L = V^(U) + taxRate x k x V^(U)

V^L = V^(U) (1 + t k)

Question 73

A firm has a constant interest coverage ratio. What method to use?

Answer 73

APV with the simple formula

Question 74

Suppose a firm fix its debt to be on a schedule. generally speaking, what happens now?

Answer 74

The debt is known in advance. This means that the interest payment is also known in advance. Therefore, we can also know the interest tax shield in each period, in advance.

However, the interest tax shield is slightly risky. Why? Because the deciding factor in terms of whether we receive the shield or not, is the ability to pay the debt+interest. Therefore, the interest shield we receive, is exactly as risky as the debt. Therefore, we discount it using the debt cost of capital.

ALSO: When the target debt-value ratio change, the firm’s WACC change as well. Therefore, the WACC method is difficult to use, since it relies on using the same discount rate for various levels of debt.

Question 75

r wacc general formula for project based cases?

Answer 75

WACC-project = Ru - d x taxRate x [Rd + ø(Ru - Rd)]

If we have continously debt adjusted cases, meaning we go for the target debt value ratio, we set ø=0. This represents a case where we find the unlevered cost of capital, and subtract the portion that is from tax shield

If we have permanent debt,