What is “wealth”? How do dividends and investments play into that? Be very descriptive and show the mathematical reasoning behind your answers. How does long term debt play into the capital structure of an organization and how does it play into potential grow or innovation?
What is “wealth”? How do dividends and investments play into that? Be very descriptive and show the mathematical reasoning behind your answers. How does long term debt play into the capital structure of an organization and how does it play into potential grow or innovation?
This paper should be no less than 800 words. (not includes title and reference.)
Essential Activities:
1. Reading chapters 16-18 in in Textbook Finance: Applications and Theory will help in the completion of the assignment.
Notes:
This paper must be formatted in APA Style 7th edition.
Please refer to the written assignment rubric on the start here tab for this paper.
Requirements: in-depth example
530cor91411_ch16_530-563.indd 530 01/27/17 03:43 PMviewpointsPART EIGHTBusiness ApplicationSuppose that Kieran has decided that itÕs time to take her photography business, currently run on an all-equity basis, and leverage it so that itÕs funded with 50 percent debt. The business currently has $30,000 worth of assets and a 15 percent marginal tax rate. Kieran has in hand a bank quote at an interest rate of 9.5 percent on an interest-only loan. As long as Kieran doesnÕt anticipate any chance that the firm wonÕt be able to cover the required interest payments on the loan, or that the bank wonÕt renew the loan at the end of its term, what economic benefits will accrue to Kieran by re-leveraging the firm? (See the solution at the end of the chapter.)Personal ApplicationGunter has just graduated from college and started a new job. HeÕs thinking about buying a townhouse for $150,000 but doesnÕt have a down payment. His bank has offered to lend him 80 percent of the moneyÑa 30-year mortgage at a rate of 5.875 percent. Further, the bank will lend Gunter the other $30,000 through a home equity loan at a rate of 7.90 percent. His applicable tax rate is 25 percent. If he accepts the bankÕs offer, what weighted-average after-tax interest rate will Gunter pay for the purchase of the townhouse? (See the solution at the end of the chapter.)What other options does Gunter have for financing his home purchase?Assessing Long-Term Debt, Equity, and Capital Structure16Final PDF to printer
531cor91411_ch16_530-563.indd 531 01/27/17 03:43 PM© Maksym yemelyanov/123RF So far, weÕve assumed that a firmÕs capital structureÑthe mix of debt and equity the firm uses to finance its operationsÑis either given or irrelevant to the deci-sions weÕve been making. Although this assumption works well in the short term, firms can and do change their capital structures in the longer term. Therefore, we need to analyze factors that affect the firmÕs decision to change its funding mix over the longer term.As weÕll see, two main factors come into play: (1) whether debt interest payments are tax deduct-ible and (2) how increased debt might affect the likelihood of the firm either going bankrupt or enter-ing into financial distress (i.e., approaching bankruptcy). Financial managers carefully choose a capital structure that sets these two factorsÕ marginal effects equal to one another. capital structureThe mixture of debt and equity used to finance the firmÕs operations.financial distressThe condition in which a firm is near bankruptcy.By doing so, they simultaneously maximize firm value and minimize any new projectÕs financing costs.Learning Goals LG16-1 Differentiate between active and passive changes to capital structure. LG16-2 Explain why finance professionals refer to debt as Òleverage.Ó LG16-3 Show how the firm apportions risk and return among stock-holders and bondholders in a Òperfect world.Ó LG16-4 Describe how the optimal capital structure changes under corporate taxation. LG16-5 Demonstrate how individual shareholders can affect capital structure by borrowing and lend-ing on their own account. LG16-6 Calculate the EBIT and EPS levels at which sharehold-ers become indifferent when choosing between two capital structures. LG16-7 Describe how the firmÕs choice of optimal capital structure changes under the possibility of bankruptcy. LG16-8 Analyze whether real-world business practices reflect the theoretical basis for optimal capital structure.Final PDF to printer
532 part eight Capital Structure Issuescor91411_ch16_530-563.indd 532 01/27/17 03:43 PM16.1 ∙ Active versus Passive Capital Structure ChangesIn theory, firms seeking to change their capital structure can take one of two approaches. The first approach is to immediately sell additional claims of one type of capital and use the proceeds to retire other kinds of claims. This is a strategy of active management, and an example of this strategy would be if a firm sold bonds and used the proceeds to buy back shares of stock in order to increase (decrease) its debt ratio (equity ratio). The second approach is to simply wait until the firm requires additional capital to cover new capital budgeting needs, such as new projects or expansion in existing projects, and to then raise the necessary new capital by selling only the type(s) of claims it wants to weigh more heavily in its capital structure. This is a strategy of passive management. An example of this type of strategy would be if an all-equity firm wanted to increase its leverage from debt but held off on doing so until it had new projects to fund, at which time it would raise the capital for those new projects solely through a bond issue.For example, suppose that Kennemore Corp. currently has $10 million in assets, financed entirely with equity. The firm has decided to switch to a 50 percent debt/ 50 percent equity structure. With active capital structure management, it would sell $5 million of debt immediately and use the proceeds to retire half of the equity. Thus Kennemore would wind up with $5 million of debt and $5 million of equity today. With passive capital structure management, it would attempt to fund the next $10 million of assets for future projects entirely with debt, winding up with $10 million of debt and $10 million of equity at some point in the future.We sometimes call active capital structure management restructuring. If the firm wishes to dramatically change its capital structure in a relatively short period of time, restructuring is preferable, both from the firmÕs point of view and from financial analystsÕ perspective. The downside to restructuring, however, is the cost. The firm will need to pay at least one ÒextraÓ set of flotation costs: those associated with selling additional securities of the type of capital it wishes to increase and that it wouldnÕt incur if it wasnÕt doing the restructur-ing. It might also have to pay additional costs associated with retiring the type of capital it wishes to reduce as well, such as having to pay a call premium on bonds retired early.Which approachÑactive or passiveÑis better? It depends on ¥ How quickly the firm is growing. ¥ How much the firm will have to pay in flotation costs if it undertakes the active management approach. ¥ How strongly and how quickly the firm wishes to change the capital structure.In general, for businesses that expect to add significant assets in the near future (either due to growth or by replacing existing assets), the passive management approach works best. Such firms will be able to alter their structure relatively quickly without incurring the additional costs of active management.LG16-1 active capital structure managementThe policy of selling one type of claim (debt or equity) explicitly to retire the other type.passive capital structure managementThe policy of changing the capital structure gradually over time by funding new capital projects dispropor-tionately with the type of capital you want to increase in the capital structure.TIME OUT 16-1 Which strategy, active or passive capital structure management, would make the process of changing the firmÕs capital structure a longer-term proposition? Why? 16-2 Suppose that a firm was simultaneously evaluating the addition of a new capital budgeting project and a proposed capital structure change: Should the old capital structure or the proposed new capital structure be used in determining the WACC for the new project? Having said that, in this chapter we will focus on examining situations involving active capital structure management. This focus will allow us to examine the benefits of a proposed capital structure change without having to separate out the additional impacts of capital budgeting decisions.Final PDF to printer
chapter 16 Assessing Long-Term Debt, Equity, and Capital Structure 533cor91411_ch16_530-563.indd 533 01/27/17 03:43 PM16.2 ∙ Capital Structure Theory: The Effect of Financial LeverageIn finance, we refer to using debt within a firmÕs capital structure as financial leverage.1 Why? Because just as a physical lever magnifies force in one direction and movement in another, the force of debt on one side magnifies the effect of potential expected return on the other. It also magnifies variability, or risk, around that return. To see why it does so, we first need to tie up some theoretical loose ends.Modigliani and MillerÕs ÒPerfect WorldÓThe basic tool for examining various variablesÕ effects on the firmÕs choice of optimal capital structure is the Modigliani-Miller (M&M) theorem, named after its authors, Franco Modigliani and Merton Miller, who completed the theorem in 1958. The full development of the M&M theorem starts with a Òperfect world,Ó one that features ¥ No taxes. ¥ No chance of bankruptcy. ¥ Perfectly efficient markets. ¥ Symmetric information sets for all participants.In this perfect world, the M&M theoremÕs two main propositions are Proposition I ( perfect world ) : V L = V U (16-1)whereVU is the value of an unleveraged, or all-equity-financed, firm.VL is the value of a leveraged firm (i.e., one whose capital structure contains debt). Proposition II ( perfect world ) : i E = i E, 0 + D __ E ( i E, 0 − i D ) (16-2)whereiE,0 is the cost of capital for an all-equity firm.iE and iD are the costs of equity and debt in a leveraged firm.Both of these propositions reflect a common underlying intuition, which we sometimes refer to as the capital structure irrelevance assertion. Merton Miller, in his testimony in Glendale Federal BankÕs lawsuit against the U.S. government in December 1997, prob-ably put it best:I have a simple explanation [for the first Modigliani-Miller proposition]. ItÕs after the ball game, and the pizza man comes up to Yogi Berra and he says, ÒYogi, how do you want me to cut this pizza, into quarters?Ó Yogi says, ÒNo, cut it into eight pieces, IÕm feeling hungry tonight.Ó Now when I tell that story, the usual reaction is, ÒAnd you mean to say that they gave you a [Nobel] prize for that?ÓIn terms of Proposition I, what Miller is saying is that, in this perfect world, the firm will be worth the same no matter how it is financed. However, if we were to think of the risk of the firm as the toppings of the pizza, having those toppings distributed unevenly would imply that slices with more toppings (risk) would be expected to offer more Òtaste sensationÓ (i.e., rate of return). To see why, letÕs take a closer look at Proposition II.THE EFFECT OF LEVERAGE ON THE COST OF EQUITY Even Proposition II, which explicitly deals with the cost increase of equity capital as a function of the firmÕs D/E ratio, LG16-2 financial leverageThe extent to which debt securities are used by a firm.Modigliani-Miller (M&M) theorem In an efficient market with-out taxes and bankruptcy costs, the value of a firm does not depend upon the firmÕs capital structure.capital structure irrelevance assertionAnother name for the Modigliani-Miller theorem.1In addition to financial leverage, firms also make use of operating leverage, which refers to the use of fixed versus variable expenses to potentially magnify the firmÕs earnings. Together, these two types of leverage are often referred to as total leverage.Final PDF to printer
534 part eight Capital Structure Issuescor91411_ch16_530-563.indd 534 01/27/17 03:43 PMstems from this same argument of capital structure irrelevance. To see this, we need to combine a couple of observations from earlier chapters with a new bit of information: 1. First, think back to our previous discussion of WACC in Chapter 11. From this, we know that WACC will have to be equal to iE,0 for an all-equity firm, as equity will be the only component cost of capital with any weight in the WACC: WACC = E _____ E + 0 i E,0 + 0 ______ E + D i D × (1 − T C ) = i E,0 for an all-equity firm 2. Second, think back to the IRR rule discussed in Chapter 13. If firms will only accept projects for which the expected rate of return is at least as large as the required, or target, rate of return, then we can think of the WACC not only as the average rate that the firm will pay to capital providers but also as the minimum average expected rate of return on the firmÕs asset investments that must be earned if the firm wants to be able to pay back the capital providers. IRR ≥ i E,0 ⇒ i E,0 = Minimum acceptable expected rate of return 3. Finally, letÕs address the question of what will happen to a firmÕs WACC in M&MÕs perfect world as the capital structure changes. Irving FisherÕs seminal work on the the-ory of investment2 included the separation principle, which states that, with a well-functioning capital market, the firmÕs capital budgeting decisions are separate from its capital structure decisions. That is, what you do with the money and where you get it are two distinctly separate decisions. So changing the firmÕs capital structure in our perfect world should not affect the group of projects chosen, or the minimum accept-able rate of return dictated by those projectsÕ lower boundary of expected returns. WACC = i E,0 for all values of D __ E Putting all of this together with a simplified3 version of the formula for WACC from Chapter 11 allows us to solve the WACC formula for iE: WACC = E ______ E + D i E + D ______ E + D i D i E,0 = E ______ E + D i E + D ______ E + D i D ⇒ i E = E + D ______ E [ i E,0 − D ______ E + D i D ] = E + D ______ E i E,0 − ( E + D ______ E × D ______ E + D ) i D = ( E __ E + D __ E ) i E,0 − D __ E i D = i E,0 + D __ E i E,0 − D __ E i D i E = i E,0 + D __ E ( i E,0 − i D ) separation principleTheory maintaining that the sources and uses of capital should be decided upon independently.2See Irving Fisher, The Theory of Interest, as Determined by Impatience to Spend Income and Opportunity to Invest It (New York: Macmillan, 1930).3The two simplifications that we have made are that we can use the before-tax cost of debt instead of the after-tax cost (as we are operating in a world without taxes for right now), and we have left out any consideration of preferred stock so as to make our analysis a little more succinct. Given preferred stockÕs aspect as a hybrid form of debt and equity, leaving it in wouldnÕt really add any intuition to the subsequent discussion, but would instead merely make it needlessly more complex.Final PDF to printer
chapter 16 Assessing Long-Term Debt, Equity, and Capital Structure 535cor91411_ch16_530-563.indd 535 01/27/17 03:43 PMThis derivation shows that the firmÕs cost of equity increases with the use of debt in the capital structure. But the fact that WACC, iE,0, is constant in the D/E ratio implies that a positive relationship between the cost of equity capital and the use of debt in the capital structure is solely due to reapportioning the expected rate of return to the firmÕs assets among claimholders. It does not imply any addition or subtraction of the total amount of return available. That is, the cost of equity goes up as the amount of debt increases, but the WACC stays the same.THE EFFECT OF LEVERAGE ON THE WACC Since debt is cheaper than equity, the firm uses less expensive equity and more relatively cheap debt at a rate that just off-sets the effect on WACC of the increased cost of equity. This leads us to what we will call Proposition IIa, which M&MÕs theorem implies (but to which we donÕt usually refer so formally): Proposition IIa (perfect world): WACC = i E,0 = E ______ E + D i E + D ______ E + D i D (16-3)which will be constant in D/E.LetÕs extend Merton MillerÕs pizza analogy and turn that pizza into a two-layer cake, dividing up the two layers among a group of people on the TV show Survivor. If you have ever seen this show, you are probably aware that it consists of following the day-to-day activities of groups of people ÒstrandedÓ in some exotic locale with very few resources. The survivors usually have access to some plentiful staple food source, but the partici-pants all get rather sick of this plain fare after the first couple of weeks. Periodic infu-sions of small delicacies, either as prizes in a game or simply to stave off a rebellion, go a long way toward making the winners more satisfied with their participation.Assume that one such group has been given the task of eating the two-layered cake. If itÕs a cake that everyone likes, then the most basic logical distribution of the finished product would be to give each person a proportionate share of the cake. However, show producers are rarely nice enough to just drop off delicacies for no reason at all. So letÕs assume that, while one layer of this cake is filled with some savory delight that everyone likes, the other layer is filled with exotic cockroaches, which all group members loathe, albeit to different degrees. Furthermore, letÕs assume that the showÕs producers have dic-tated that the group must finish off the entire cake in a certain amount of time, or some-one will be Òkicked off the island.ÓYou can see that this situation might prompt the group to make some very interesting allotment decisions concerning who gets to/has to eat how much of the cake. The group might decide that the people who agree to take more of the cockroach layer get a larger, proportionate share of the enjoyable layer, too. Or the group may decide that people who eat a slight majority of the disgusting layer get virtually all of the enjoyable layer.These two allocation schemes correspond exactly to the situation seen in all equity and mixed debt/equity capital structures, respectively. If we logically assume that all humans are risk averse, then any financial claim against a firm comes with some of the layer that everyone wantsÑreturns. But any financial claim will also come with some less desirable layer that everyone loathesÑrisks. In an all-equity firm, the equity hold-ers share the firmÕs expected return and expected risk in strictly proportional amounts. Someone who has put in one-fourth of the equity, thereby buying one-fourth of the firmÕs shares, can in return expect to receive one-fourth of the firmÕs returns on its assets. That investor has at risk only the money sheÕs paid for those shares. Someone who put in twice as much money would expect twice as much in return but would also run the risk of los-ing twice as much money, and so forth.In a firm that employs a mixture of debt and equity, however, the parties have implic-itly agreed to a disproportionate sharing of the risk and return layers of the firm. The debt holders have put in a certain portion of the firmÕs capital and thereby expect exactly the return (and the return of their capital) as spelled out in the bond indenture. Their Final PDF to printer
536 part eight Capital Structure Issuescor91411_ch16_530-563.indd 536 01/27/17 03:43 PMEXAMPLE 16-1Impact on Expected Return and Volatility of Increasing Leverage in a Perfect WorldSuppose we are in M&MÕs perfect world, and we have a firm with $100 million in assets, cur-rently financed entirely with equity. Equity is worth $100 per share, and book value of equity is equal to market value of equity.4 Also, letÕs assume that the firmÕs expected EBIT values depend on which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown below:StateRecessionAverageBoomProbability of state0.20.60.2Expected EBIT in state$10 million$25 million$35 millionThe firm is considering switching to either a 30-percent- or 60-percent-debt capital structure and has determined that it would have to pay an 8 percent yield on perpetual debt in either event.5 What will be the effect on expected EPS and the volatility of that EPS if the firm stays with its current capital structure or switches to either of the two proposed structures?SOLUTION: If the firm stays with its all-equity structure, it will have $100 million/$100 = 1 million shares outstanding, and the EPS under each state of nature will beStateRecessionAverageBoomEBIT$10,000,000$25,000,000$35,000,000Less: Interest 0 0 0EBT$10,000,000$25,000,000$35,000,000Less: Taxes 0 0 0Net income$10,000,000$25,000,000$35,000,000EPS$ 10.00$ 25.00$ 35.00The expected EPS and standard deviation of the EPS will be E (EPS) = 0.2 × $10.00 + 0.6 × $25.00 + 0.2 × $35.00 = $24.00 σ EPS = √ ___________________________________________________________ 0.2($10.00 − $24.00 ) 2 + 0.6($25.00 − $24.00 ) 2 + 0.2($35.00 − $24.00 ) 2 = $8.00 If the firm refinances 30 percent of the capital by selling $30 million in debt and uses the pro-ceeds to retire $30 million in equity, the interest on the debt will amount to 0.08 × $30 million = $2.4 million, and the firm will have $70 million/$100 = 700,000 shares outstanding, and the EPS under each state of nature will beFor interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.LG16-34Please note that this assumption is made purely to simplify the math. Having the market and book values of equity differ would add to the complexity of this example, but would not change the basic intuition.5This assumption is also made to simplify the calculations. We could consider a situation in which debt had a finite maturity, but to the extent that a firm would want to stick with a particular capital structure, any retire-ment of debt would have to be perfectly offset with an equivalent issue of new debt, which would add much numerical complexity of the example, but nothing to the intuition.expected returns will never change; they will get exactly what they signed up for, with no business risk on the line. The equity holders, in accepting for themselves a residual claim on the companyÕs future proceeds, have agreed to accept more than their fair share of the risk layerÑthey take on both business and financial risk. In return, they also expect a disproportionately large share of the expected return layer.This is what we are seeing in equation 16-2. The reason that iE increases as D/E increases is to compensate the remaining stockholders for bearing more and more resid-ual risk as the number of stockholders declines.Final PDF to printer
chapter 16 Assessing Long-Term Debt, Equity, and Capital Structure 537cor91411_ch16_530-563.indd 537 01/27/17 03:43 PMStateRecessionAverageBoomEBIT$10,000,000$25,000,000$35,000,000Less: Interest2,400,0002,400,0002,400,000EBT$ 7,600,000$22,600,000$32,600,000Less: Taxes 0 0 0Net income$ 7,600,000$22,600,000$32,600,000EPS$ 10.86$ 32.29$ 46.57The expected EPS and standard deviation of the EPS will be E(EPS) = 0.2 × $10.86 + 0.6 × $32.29 + 0.2 × $46.57 = $30.86 σ EPS = √ ________________________________________________________________ 0.2($10.86 − $30.86 ) 2 + 0.6($32.29 − $30.86 ) 2 + 0.2($46.57 − $30.86 ) 2 = $11.43 If the firm refinances 60 percent of the capital by selling $60 million in debt and using the proceeds to retire $60 million in equity, the interest on the debt will amount to 0.08 × $60 million = $4.8 million, and it will have $40 million/$100 = 400,000 shares outstanding, and the EPS under each state of nature will beStateRecessionAverageBoomEBIT$10,000,000$25,000,000$35,000,000Less: Interest4,800,0004,800,0004,800,000EBT$ 5,200,000$20,200,000$30,200,000Less: Taxes 0 0 0Net income$ 5,200,000$20,200,000$30,200,000EPS$ 13.00$ 50.50$ 75.50The expected EPS and standard deviation of the EPS will be E ( EPS ) = 0.2 × $13.00 + 0.6 × $50.50 + 0.2 × $75.50 = $48.00 σ EPS = √ ________________________________________________________________ 0.2($13.00 − $48.00 ) 2 + 0.6($50.50 − $48.00 ) 2 + 0.2($75.50 − $48.00 ) 2 = $20.00 Similar to Problems 16-5, 16-6, 16-7, 16-8, Self-Test Problem 1As this example shows, increasing the amount of debt in the capital structure will increase the expected EPS level, but it will also increase the variationÑalso known as riskÑthat we can expect around that expected EPS. This basic intuition is driven by the fact that stockholders hold the residual claim to earnings. Thus they bear more of the business risk, also known as the state-of-nature-induced volatility, than debt holders do. In fact, as long as EBIT is large enough to ensure that debt holders receive their promised interest payments even in the worst state of nature, then equity holders are the only claim holders of the firm that can possibly lose money; therefore, they bear all of the risk once debt is introduced into a firmÕs capital structure.Of course, please keep in mind that this intuition only holds true here because weÕre assuming weÕre in M&MÕs perfect world, the one where, since thereÕs no chance of bankruptcy, thereÕs also no chance that debt holders wonÕt get all the money owed them, regardless of which state of the economy occurs.M&M with Corporate TaxesThe value of the M&M theorem does not really lie in the wisdom of their two proposi-tions, which are driven by the very unrealistic set of Òperfect worldÓ assumptions listed previously. Instead, the value lies in examining what happens to these two propositions when we relax the unrealistic assumptions and move closer to what we see in real life.LG16-4 Final PDF to printer
538 part eight Capital Structure Issuescor91411_ch16_530-563.indd 538 01/28/17 01:09 PMFor example, if we slightly relax the assumptions above and allow ourselves to assume that corporations are taxed, that corporate debt is perpetual, and that interest is tax deductible, then the main propositions of the M&M theorem become:6 Proposition I ( with corporate taxes ) : V L = V U + D T C (16-4)whereVU is the value of an unleveraged firm.VL is the value of a leveraged firm.D is the level of perpetual firm debt.TC is the applicable coporate tax rate. Proposition II (with corporate taxes): i E = i E,0 + D __ E ( i E,0 − i D ) × (1 − T C ) (16-5)whereiE,0 is the cost of capital of capital for an all-equity firm.iE and iD are the costs of equity and debt in a leveraged firm.Proposition IIa ( with corporate taxes ) : WACC = E ______ E + D i E + D ______ E + D i D (1 − T C ) (16-6) which will be decreasing in D/E.We often refer to this situation as the ÒThe More Debt, the BetterÓ condition. Under this condition implied by M&M, the firmÕs value forever increases (and the WACC forever decreases) as the firm takes on larger and larger amounts of debt, as implied in Proposition I.Note how a relatively minor change in our assumptions has dramatically altered the firmÕs suggested capital structure strategy. In the perfect world, capital structure did not matter, so the firm was free to choose whichever level of debt it preferred. In this slightly more realistic world with corporate taxes, managers can maximize the firmÕs value by taking on as much debt as possible. Thus the firm should try to be as close to 100 percent debt-financed as possible.What caused this change in optimal strategy? ItÕs not so much that we have added taxation, but that we have added it differentially: any money paid out to stockholders is taxable, so that a dollar paid in dividends actually means removing $1.00/(1 − TC) in company earnings. On the other hand, paying a dollar in interest to service debt carries no equivalent tax Òsurcharge.ÓHowever, though adding corporate taxes to our environment changes the firmÕs opti-mal strategy, it does not really change the effect that an increase in leverage has on the stockholdersÕ expected returns and the volatility of those returns.6The assumption of perpetual debt makes the mathematical expressions for Propositions I and II concise: with perpetual debt, the present value of the tax shields to interest on debt are the present value of the perpe-tuity, PV = [(D × iD) × TC]/iD, which simplifies to DTC.EXAMPLE 16-2LG16-4Impact of Leverage on ShareholdersÕ Expected Return and Volatility with Corporate TaxesReexamine the situation we described in Example 16-1. Now suppose that the firm faces a 35 percent tax rate. What will be the effect on expected EPS and the volatility of that EPS if the firm stays with its current capital structure or switches to either of the two proposed structures?For interactive v
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