Debt holders have no votes. They generally cannot appoint directors to the board for their lack of votes, unlike shareholders who may vote on the company's decisions including the appointment of directors.
Debt payments are mandatory. Borrowing companies must pay the principal and interest payments that they promised or else they can be sent bankrupt by their creditors.
Equity payments are voluntary. Firms are not forced to pay dividends or undertake buy-backs. Some firms have never paid a dividend or completed a buy-back, including Google which once stated on its investor relations website in July 2014 'we have never declared or paid a cash dividend nor do we expect to pay any cash dividends in the foreseeable future' .
Note that many countries' corporate laws restrict firms from paying out shareholders if it will be detrimental to debt holders. Most have a rule that dividends and buybacks are not allowed if it will result in negative retained profits. This prevents firms from raising debt capital, paying it straight to shareholders and then declaring bankruptcy, leaving nothing for the debt holders.
A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?
The debt-to-equity ratio can be divided by one without changing its value : ###\dfrac{D}{E} = 0.6 = \dfrac{0.6}{1}###
So debt ##(D)## could be 0.6 and equity ##(E)## could be 1. Therefore the value of assets ##(V)## could be: ###\begin{aligned} V &= D+E \\ &= 0.6+1 \\ &= 1.6 \\ \end{aligned}###
To find the debt-to-assets ratio: ###\dfrac{D}{V} = \dfrac{0.6}{1.6} = 0.375###
The more mathematically rigorous approach is to use simultaneous equations:
###\dfrac{D}{E} = 0.6### ###E = \dfrac{D}{0.6} ### ###V=D+E### ###V = D + \dfrac{D}{0.6}### ###0.6V = 0.6D + D### ###V = \dfrac{1.6D}{0.6}### ###\dfrac{D}{V} = \dfrac{0.6}{1.6} = 0.375###In the home loan market, the acronym LVR stands for Loan to Valuation Ratio. If you bought a house worth one million dollars, partly funded by an $800,000 home loan, then your LVR was 80%. The LVR is equivalent to which of the following ratios?
The loan-to-valuation ratio (LVR) is a debt-to-assets ratio since it divides the loan liability value by the house asset value that secures the loan.
If the house asset value is ##V## and this is funded by the loan debt liability ##D## and the home owner's deposit or equity in the house ##E## (so ##V = D+E##), then:
###\text{LVR} = \dfrac{D}{V}###Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.
In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.
If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?
Assume that:
- No income (rent) was received from the house during the short time over which house prices fell.
- Your friend will not declare bankruptcy, he will always pay off his debts.
The key thing to realise in this question is that when house prices fall by 15%, the bank will not take pity and reduce the debt owing.
In the below table, 'm' means million. Remembering that V=D+E and filling in the values for all except the equity value at t=1, we can calculate that E = V - D = 0.85m - 0.9m = -0.05m, so equity should be -0.05m which is -$50,000. Therefore the poor borrower has negative equity or negative wealth.
| Asset, Debt and Equity Values | |||
| Millions of dollars | |||
| Time | V | D | E |
| 0 | 1 | 0.9 | 0.1 |
| 1 | 0.85 | 0.9 | -0.05 |
The fall in equity from $0.1m (=1m-0.9m) to -0.05m (=0.85m-0.9m) corresponds to a 150% fall in equity:
###\begin{aligned} r_{\text{E, }0\rightarrow1} &= \frac{p_1-p_0+c_1}{p_0} \\ &= \frac{-0.05m-0.1m+0}{0.1m} \\ &= \frac{-0.15m}{0.1m} \\ &= -1.5 = -150\% \\ \end{aligned} ###
Negative wealth is very unfortunate. Many people would declare themselves bankrupt (or for a company, insolvent) because there is no point paying off a house worth less than the value of the loan. However there are costs and limitations on people who are bankrupt for 5 years in Australia and 2 years in America, which is designed to deter bankruptcy. If the person decided to declare bankruptcy, his change in net wealth would be -100%. But in this question we must assume that he will pay his debts, therefore his change in net wealth is -150%.
One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.
The interest rate on the margin loan was 7.84% pa.
Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.
What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
There are a few ways to think about this problem. One is to think of the share assets as being financed by a portfolio of debt and equity, where the total historical return on the share assets equals the weighted average total historical return on the debt and equity. Note that the total historical return on the share assets is 9%, the sum of the 4% dividend yield plus the 5% capital yield. This equation is actually the weighted average cost of capital (WACC) before tax:
###r_V = r_D.\dfrac{D}{V} + r_E.\dfrac{E}{V} ### ###0.09 = 0.0784 \times \dfrac{70k}{100k} + r_E.\dfrac{30k}{100k} ### ###r_E.\dfrac{30k}{100k} = 0.09 - 0.0784 \times \dfrac{70k}{100k} ### ###\begin{aligned}r_E &= \left( 0.09 - 0.0784 \times \dfrac{70k}{100k} \right).\dfrac{100k}{30k} \\ &= 0.117067 \\ \end{aligned}###Alternatively, a table can be used. After filling in all of the known values, the unknown return on equity from time -1 to 0 can be calculated.
| Price and Income Values | ||||||
| Time | V | D | E | |||
| -1 | 100k | 70k | 30k | |||
| 0 | 109k | 75.488k | 33.512k | |||
The capital and income components of the equity rose from 30k to 33.512k (=109k-75.488k) which corresponds to a total return on equity of:
###\begin{aligned} r_{\text{E, }-1 \rightarrow 0} &= \frac{P_0-P_{-1}+C_0}{P_{-1}} \\ &= \frac{33.512k-30k+0}{30k} \\ &= \frac{3.512k}{30k} \\ &= 0.117067 = 11.7067\% \\ \end{aligned} ###
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $48.5m | Operating free cash flow |
| ##\text{FFCF or CFFA}## | $50m | Firm free cash flow or cash flow from assets |
| ##g## | 0% pa | Growth rate of OFCF and FFCF |
| ##\text{WACC}_\text{BeforeTax}## | 10% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 9.7% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Cost of debt |
| ##r_\text{EL}## | 11.25% pa | Cost of levered equity |
| ##D/V_L## | 20% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
The cash flows continue forever so we'll use the perpetuity formula to price the company's assets ##(V)##.
###V=\dfrac{\text{FreeCashFlow}}{r_\text{WACC}-g} ###'Textbook method' of firm valuation with interest tax shields
The textbook method includes the interest tax shields in the discount rate by discounting the operating free cash flow (OFCF) by the weighted average cost of capital after tax:
###\begin{aligned} V_L &= \dfrac{\text{OFCF}}{\text{WACC}_\text{AfterTax} - g} \\ &= \dfrac{48.5m}{0.097 - 0} \\ &= 500m \\ \end{aligned}###'Harder method' of firm valuation with interest tax shields
The harder method includes the interest tax shields in the cash flow by discounting the firm free cash flow (FFCF) by the weighted average cost of capital before tax:
###\begin{aligned} V_L &= \dfrac{\text{FFCF}}{\text{WACC}_\text{BeforeTax} - g} \\ &= \dfrac{50m}{0.1 - 0} \\ &= 500m \\ \end{aligned}###Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?
Select one of the following answers. Note that D is the value of debt which is constant through time, and ##r_D## is the cost of debt.
Accountants use the 'effective interest method' to calculate interest expense which is the yield on the debt multiplied by its book value at the beginning of the period, with accrual adjustments if the debt matures during the year. Mathematically this is:
###IntExp_1 = r_D.D_0###A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?
Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.
The unlevered service project's cash flows should be discounted by other service firms' WACC after tax.
There are two parts to this question. The first is about how to take the interest tax shield into account. The second is about how to adjust for the higher systematic risk of the project.
Treatment of the interest tax shieldTo find the value of the levered project (##V_L##), the unlevered CFFA, also called the operating free cash flow (OFCF), should be discounted by the WACC after tax. This is called the 'text book' method of valuation. If the unlevered CFFA will occur in perpetuity with no growth, then:
###V_L = \frac{CFFA_U}{r_\text{WACC after tax}} = \frac{NI+Depr-CapEx - \varDelta NWC}{r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L}}###The tax shield is taken into account in the discount rate (##r_\text{WACC after tax}##), not the cash flow (##CFFA_U##). The after tax WACC takes the interest tax shield into account by reducing the cost of debt by the corporate tax rate: ###r_\text{WACC after tax} = r_D.\mathbf{(1-t_c)}.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L}###
The unlevered CFFA (##CFFA_U##) excludes interest expense (##IntExp=0##) and therefore doesn't take the interest tax shield into account:
###CFFA_U=NI+Depr-CapEx - \varDelta NWC### Treatment of the higher systematic risk of the projectThe WACC after (and before) tax is supposed to reflect the systematic risk of the cash flows. Since the project is in the more systematically risky services industry, the high WACC of a services firm should be used, not the low WACC of the manufacturing firm which has less systematic risk.
Additionally, discounting by the WACC after tax only works if the firm always has the same proportion of debt. If the debt-to-assets ratio changes then the amount of tax shields will change and the after-tax WACC must be recalculated every year.
The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.
Assume the following:
- Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
- Motorola had a 20% after-tax WACC before it merged with Google.
- Google and Motorola have the same level of gearing.
- Both companies operate in a classical tax system.
You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.
The mobile phone manufacturing project's:
The discount rate should reflect the systematic risk of the project. Before merging with Google, Motorola manufactured mobile phones, so its WACC would have reflected the systematic risk of making phones. Cash flows from the phone manufacturing project should therefore be discounted by Motorola's WACC.
The interest tax shields should be counted only once in either the cash flow or the discount rate. Therefore, unlevered CFFA (which excludes interest tax shields) should be discounted by the WACC after tax (which includes interest tax shields). Since only the after tax WACC is given as an answer option, this is the correct answer. But another possible answer which isn't available in this question, is to discount levered CFFA (which includes interest tax shields) by the WACC before tax (which excludes interest tax shields). Both methods should give the same answer.
There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.
But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?
It's better to incur depreciation expense sooner rather than later because then you have lower taxable income and pay less tax now. Of course you'll pay more tax later when you have less depreciation and higher taxable income, but it's better to pay less tax now and keep the money in the bank earning interest for longer before having to pay the money as tax to the government. Ideally, assets should be instantly depreciated so that the minimum amount of tax can be paid now.
Higher depreciation expense leads to lower taxable profit and lower taxes. It may seem that depreciation expense is a cost that should be paid as late as possible. But depreciation is actually a non-cash expense, it's an imaginary thing made up by accountants. Tax, on the other hand, is a cash flow cost that's best paid as late as we can. This way we can keep the cash in the bank as long as possible before it's paid as tax to the government.
Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?
The net income (NI) equation and cash flow from assets (CFFA) equations are:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
Substituting NI into CFFA and then expanding and collecting like terms,
###\begin{aligned} CFFA &= (Rev-COGS-FC-Depr-IntExp).(1-t_c)+Depr-CapEx - \varDelta NWC+IntExp \\ &= (Rev-COGS-FC).(1-t_c)+\mathbf{Depr.t_c} -CapEx - \varDelta NWC+\mathbf{IntExp.t_c} \\ \end{aligned}###
The last bold term is called the interest tax shield (##IntExp.t_c##) which is the tax saving per year. Clearly, an increase in interest expense (IntExp) will lead to an increase in CFFA. This is because higher IntExp results in lower tax payments to the government since before-tax NI is lower. But IntExp does not affect CFFA since IntExp is a funding cost and has nothing to do with the firm's assets themselves, similarly for dividends.
It's quite surprising that higher interest expense actually leads to a CFFA increase and at the same time a NI decrease. It shows how CFFA (or better, the net present value of CFFA) can give quite a different picture of firm value compared with NI.
Note that the depreciation tax shield (##Depr.t_c##) is also shown in bold in the above equation. It's the tax saving per year from paying less tax to the government due to depreciation.
With regards to answers a and e, cash flows to creditors and equity holders equal CFFA, so if dividends or interest payments fall then CFFA must have fallen. Note that interest payments are not necessarily equal to interest expense, for example a zero coupon bond has no interest payments until maturity yet it has interest expense every year.
A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.
Buying less capital assets (non-current assets) such as land, buildings and trucks will decrease CapEx and increase CFFA.
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###There will be less depreciation and therefore a lower depreciation tax shield, causing a decrease in CFFA, but this is likely to be a small effect compared to the fall in CapEx.
###\begin{aligned} CFFA &= NI+Depr-CapEx - \varDelta NWC+IntExp \\ &= (Rev-COGS-FC-Depr-IntExp).(1-t_c)+Depr-CapEx - \varDelta NWC+IntExp \\ &= (Rev-COGS-FC).(1-t_c)+\mathbf{Depr.t_c} -CapEx - \varDelta NWC+IntExp.t_c \\ \end{aligned}###
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
Remember:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###An increase in IntExp decreases NI and increases CFFA. This is very counter-intuitive, but it's because IntExp reduces taxes since it is subtracted from pre-tax income.
But since IntExp is a 'financing cash flow' which has nothing to do with the cash flow from the assets, it is added back in CFFA, and its only lingering effect is the reduction in taxes.
This is the so-called 'interest tax shield' effect of having debt and therefore interest expense.
A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###
The above FFCF equation doesn't include the interest tax shield. This can be seen after expanding and collecting like terms and noticing that there are no interest expense ##(IntExp)## terms left:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ &= FFCF_\text{xITS} \\ \end{aligned} \\###Because there is no ##IntExp.t_c## term, there is no interest tax shield being included in this FFCF. Therefore this is FFCF excluding the interest tax shield: ##FFCF_\text{xITS}##.
Note that the firm free cash flow excluding interest tax shields ##(FFCF_\text{xITS})## should be discounted by the WACC after tax ##(r_\text{WACC after tax})##. This will give the value of the levered firm or project with interest tax shields ##(V_\text{wITS})##. The weighted average cost of capital after tax is:
###r_\text{WACC after tax} = \dfrac{D}{V}.r_D.(1-t_c) + \dfrac{E}{V}.r_E###One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###
The above FFCF equation doesn't include the interest tax shield. This can be seen after expanding and collecting like terms and noticing that there are no interest expense ##(IntExp)## terms left:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC + 0 \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ &= FFCF_\text{xITS} \\ \end{aligned} \\###Because there is no ##IntExp.t_c## term, there is no interest tax shield being included in this FFCF. Therefore this is FFCF excluding the interest tax shield: ##FFCF_\text{xITS}##.
Note that when interest expense is ignored and set to zero, the inside of the net income equation is actually what an accountant would call earnings before interest and tax (EBIT): ###\begin{aligned} FFCF_\text{xITS} &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC + 0 \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###
Note that the firm free cash flow excluding interest tax shields ##(FFCF_\text{xITS})## should be discounted by the WACC after tax ##(r_\text{WACC after tax})##. This will give the value of the levered firm or project with interest tax shields ##(V_\text{wITS})##. The weighted average cost of capital after tax is:
###r_\text{WACC after tax} = \dfrac{D}{V}.r_D.(1-t_c) + \dfrac{E}{V}.r_E###Question 413 CFFA, interest tax shield, depreciation tax shield
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).
One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:
###FFCF=NI + Depr - CapEx -ΔNWC + IntExp###
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )###
Another popular method is to use EBITDA rather than net income. EBITDA is defined as:
###EBITDA=Rev - COGS - FC###
One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?
The equivalence of answer c to the FFCF equation can be seen below:
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c)### ###\begin{aligned} FFCF &= NI + Depr - CapEx -ΔNWC + IntExp \\ &= (Rev - COGS - Depr - FC - IntExp).(1-t_c) + Depr - CapEx -ΔNWC + IntExp \\ &= (Rev - COGS - FC).(1-t_c) -Depr.(1-t_c) -IntExp.(1-t_c) + Depr - CapEx -ΔNWC + IntExp \\ &= EBITDA.(1-t_c) -Depr + Depr.t_c -IntExp + IntExp.t_c + Depr - CapEx -ΔNWC + IntExp \\ &= EBITDA.(1-t_c) + Depr.t_c + IntExp.t_c - CapEx -ΔNWC \\ \end{aligned}###The hardest and most important aspect of business project valuation is the estimation of the:
The cash flows from assets are the most important aspect of business project valuation since estimates can vary wildly from the reality and net present values are highly sensitive to these cash flow inputs. This is one reason why marketing is so important, because the marketers make the sales forecasts. They gauge consumer interest using surveys and product trials which they hope will lead to more accurate revenue estimates and therefore better project valuations.
Question 658 CFFA, income statement, balance sheet, no explanation
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance.
No explanation provided.
A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar market risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
The firm's assets' systematic risk (or market risk, measured by beta) remains the same so the firm's pre tax WACC (or required return on assets) will also be unchanged.
All that has changed is the way that the assets are funded. There will be more debt and less equity. This will create a larger interest tax shield which leads to higher levered cash flow from assets and a lower after tax WACC.
Note also that with proportionally more debt the amount of leverage is increasing so ##D/V## and ##D/E## will increase. The cost of equity will be higher since there will be more creditors who get paid first before the equity holders. Equity holders' residual claim on the firm's assets is made more junior when the amount of debt increases.
Question 241 Miller and Modigliani, leverage, payout policy, diversification, NPV
One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage in a world with zero taxes and perfect information since investors can make their own leverage. Therefore corporate capital structure policy is irrelevant since investors can achieve their own desired leverage at the personal level by borrowing or lending on their own.
This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:
(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.
(II) Agency costs: a firm's managers should not try to minimise agency costs.
(III) Diversification: a firm's managers should not try to diversify across industries.
(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.
Which of the above statement(s) are true?
A firm's managers should not try to achieve a particular pattern of equity payout, or diversify the firm's cash flow across industries. This is because of home-made or DIY payout and diversification. Shareholders can easily achieve a particular payout policy themselves, for example by selling a small amount of stocks in a non-dividend paying firm to replicate a dividend, or re-investing dividends to replicate a capital gain. Shareholders can also easily diversify across industries by purchasing stocks in those industries.
But managers should try to maximise shareholders' wealth since that is supposed to be their main aim. Ans they should try to minimise agency costs such as perks, paying themselves too much and not working hard since that reduces shareholder wealth.