Capital Structure and Leverages — Practice

Question 1

Explain the key difference in assumption between the Net Income approach and the Net Operating Income approach regarding how the cost of equity behaves as leverage increases, and state the consequence each assumption has for WACC.

Accepted Answer

The Net Income approach assumes that the cost of equity remains constant regardless of how much debt the firm takes on, so that substituting cheaper debt for equity mechanically lowers WACC as the weight of the cheap source rises, with no offsetting increase in the cost of the other source. The Net Operating Income approach assumes instead that the cost of equity rises as leverage increases, because equity shareholders perceive and demand compensation for the higher financial risk that greater debt creates, and this rising cost of equity exactly offsets the benefit of the cheaper debt weight, leaving WACC constant regardless of the debt-equity mix chosen. The consequence is that under the NI approach, WACC keeps falling as debt rises without limit, implying a firm should be financed almost entirely by debt, while under the NOI approach WACC and firm value are entirely unaffected by the financing mix, meaning there is no optimal capital structure to search for at all.

Question 2

Explain why the traditional approach implies an optimal capital structure exists, while the NI and NOI approaches each imply no genuine optimum, or an unbounded one.

Accepted Answer

The traditional approach implies a genuine, bounded optimal capital structure because it assumes the cost of equity rises only gradually at low to moderate levels of leverage, allowing the benefit of substituting cheaper debt for equity to dominate and WACC to fall as debt increases, but assumes this relationship changes beyond a certain point, where the market begins to perceive financial risk as materially elevated and the cost of equity, and eventually the cost of debt itself, begins rising steeply enough to outweigh the benefit of the cheap debt weight, causing WACC to rise again; the point where WACC is at its lowest before this reversal is the optimal capital structure. The NI approach implies no genuine bounded optimum because, under its assumption of a constant cost of equity regardless of leverage, WACC keeps falling monotonically as debt rises, with the implied 'optimum' being the unbounded extreme of almost entirely debt financing, which is not a realistic interior optimum at all. The NOI approach implies no optimum exists in the first place, since WACC is assumed constant at every level of leverage, making every capital structure equally value-maximising and the search for an optimal mix meaningless under that approach's own assumptions.

Question 3

Explain what the 'tax shield' refers to in MM Proposition I with taxes, and why the presence of corporate tax changes MM's conclusion from the no-tax version of the proposition.

Accepted Answer

The tax shield refers to the real, genuine cash saving a firm obtains because interest on debt is a tax-deductible expense, reducing the firm's taxable income and therefore its tax payable by an amount equal to the interest expense multiplied by the tax rate, a saving that does not exist for dividend payments on equity or preference capital, which are not tax-deductible. In the no-tax version of MM Proposition I, since there is no corporate tax at all, this tax shield does not exist, and MM show that firm value is identical regardless of capital structure, because investors can replicate any leverage the firm chooses through their own personal borrowing, homemade leverage, making the firm's financing choice unable to create value the investor could not already replicate independently. Once corporate tax is introduced, this reasoning changes because the tax shield is a genuine, additional cash benefit created specifically by the firm's own choice to use debt, a benefit that accrues to the firm and its investors collectively and cannot be replicated by investors on their own simply by borrowing personally, since personal borrowing does not create a corporate tax deduction for the firm; MM therefore revise their conclusion to show that a levered firm's value exceeds an otherwise identical unlevered firm's value by precisely the present value of this tax shield, meaning capital structure does affect firm value once taxes are present, in direct contrast to the no-tax conclusion.

Question 4

A company has sales of ₹50 lakh, variable costs of ₹30 lakh, and fixed operating costs of ₹12 lakh. Compute its degree of operating leverage and interpret the result.

Accepted Answer

Contribution = Sales − Variable costs = 50 − 30 = ₹20 lakh. EBIT = Contribution − Fixed operating costs = 20 − 12 = ₹8 lakh. DOL = Contribution ÷ EBIT = 20 ÷ 8 = 2.5. A DOL of 2.5 means that for every 1% change in sales, EBIT is expected to change by approximately 2.5%, in the same direction; so a 10% increase in sales would be expected to produce roughly a 25% increase in EBIT, and equally, a 10% fall in sales would be expected to produce roughly a 25% fall in EBIT, illustrating how the presence of ₹12 lakh of fixed operating costs magnifies the effect of sales changes on EBIT in both directions.

Question 5

A company has EBIT of ₹15 lakh and pays annual interest of ₹5 lakh on its debt. Compute its degree of financial leverage and interpret the result.

Accepted Answer

DFL = EBIT ÷ (EBIT − Interest) = 15 ÷ (15 − 5) = 15 ÷ 10 = 1.5. A DFL of 1.5 means that for every 1% change in EBIT, EPS is expected to change by approximately 1.5%, in the same direction, so a 10% increase in EBIT would be expected to produce roughly a 15% increase in EPS, and equally a 10% fall in EBIT would be expected to produce roughly a 15% fall in EPS, reflecting how the fixed annual interest obligation of ₹5 lakh, which does not change as EBIT changes, magnifies the effect of EBIT changes on the earnings ultimately left over for equity shareholders.

Question 6

Using the DOL of 2.5 and DFL of 1.5 computed for two companies in the previous problems, imagine instead both figures belong to the same single company. Compute its combined leverage and explain what a 20% fall in sales would be expected to do to its EPS.

Accepted Answer

DCL = DOL × DFL = 2.5 × 1.5 = 3.75. A combined leverage of 3.75 means that for every 1% change in sales, EPS is expected to change by approximately 3.75%, in the same direction, compounding both the operating leverage effect, from sales to EBIT, and the financial leverage effect, from EBIT to EPS, into one end-to-end sensitivity measure. A 20% fall in sales would therefore be expected to produce roughly a 75% fall in EPS (20% × 3.75), illustrating just how severely a company with both high fixed operating costs and high fixed financial costs can see its EPS deteriorate from what might seem like a moderate decline in sales, which is exactly why combined leverage is treated as a genuine risk measure rather than a purely mechanical computation.

Question 7

A company needs to raise ₹100 lakh of fresh capital and is considering two plans: Plan A, raising the entire amount through equity shares of ₹10 each, issuing 10 lakh shares; Plan B, raising ₹50 lakh through equity shares of ₹10 each, issuing 5 lakh shares, and the remaining ₹50 lakh through 10% debentures. The tax rate is 30%. Compute the EBIT-EPS indifference point between the two plans.

Accepted Answer

Under Plan A: no interest, so EPS = [EBIT × (1 − tax rate)] ÷ 10 lakh shares = [EBIT × 0.70] ÷ 10,00,000. Under Plan B: annual interest = 10% × ₹50 lakh = ₹5 lakh, so EPS = [(EBIT − 5,00,000) × 0.70] ÷ 5,00,000 shares. Setting the two EPS expressions equal to find the indifference EBIT: [EBIT × 0.70] ÷ 10,00,000 = [(EBIT − 5,00,000) × 0.70] ÷ 5,00,000. The 0.70 tax factor appears on both sides and cancels: EBIT ÷ 10,00,000 = (EBIT − 5,00,000) ÷ 5,00,000. Cross-multiplying: EBIT × 5,00,000 = (EBIT − 5,00,000) × 10,00,000, giving 5,00,000 × EBIT = 10,00,000 × EBIT − 50,00,00,00,000, which simplifies to 5,00,000 × EBIT = 50,00,00,00,000, so EBIT = 10,00,000, that is, ₹10 lakh. The indifference point is therefore at an EBIT of ₹10 lakh: below this level, Plan A, the all-equity plan, produces a higher EPS, since Plan B's fixed interest burden of ₹5 lakh weighs more heavily on a smaller earnings base; above ₹10 lakh of EBIT, Plan B, the debt-equity plan, produces a higher EPS, since the interest is more than covered and the earnings above that level accrue to a smaller base of equity shares, magnifying EPS through financial leverage.

Question 8

Using the indifference point of ₹10 lakh EBIT found in the previous problem, explain what a company should conclude if its actual expected EBIT is ₹18 lakh, and what it should conclude instead if expected EBIT is ₹7 lakh.

Accepted Answer

If the company's expected EBIT is ₹18 lakh, which lies above the indifference point of ₹10 lakh, Plan B, the plan using debt financing, would be expected to produce a higher EPS for shareholders than Plan A, because at this EBIT level the fixed interest cost under Plan B is comfortably covered, and the additional earnings above the interest cost accrue to a smaller equity base than under the all-equity Plan A, magnifying EPS through favourable financial leverage; the company should therefore prefer Plan B if maximising EPS at this expected earnings level is the goal. If the company's expected EBIT is instead ₹7 lakh, which lies below the indifference point, Plan A, the all-equity plan, would be expected to produce a higher EPS, because at this lower EBIT level Plan B's fixed interest obligation weighs disproportionately on a smaller earnings base and depresses EPS more severely than the larger share count under Plan A does; the company should therefore prefer Plan A at this lower expected earnings level. This illustrates that the 'right' financing choice under EBIT-EPS analysis is not fixed but depends directly on where the company's actual expected EBIT sits relative to the indifference point.

Question 9

Distinguish business risk from financial risk, and explain which leverage measure corresponds to each.

Accepted Answer

Business risk refers to the inherent variability in a firm's operating earnings, EBIT, arising from the nature of its business and its cost structure, independent of how that business happens to be financed — factors such as demand volatility, competitive intensity, and the proportion of fixed operating costs in the cost structure all contribute to business risk. Financial risk refers to the additional variability introduced into a firm's earnings per share specifically because of its financing choices, particularly its use of debt and preference capital carrying fixed financial charges, over and above whatever variability already exists in EBIT due to business risk alone. Operating leverage, measured by DOL, corresponds to business risk, since it captures how a firm's fixed operating cost structure magnifies the effect of sales changes on EBIT, a purely operating phenomenon unrelated to financing. Financial leverage, measured by DFL, corresponds to financial risk, since it captures how a firm's fixed financial cost structure, arising from its financing choices, magnifies the effect of EBIT changes on EPS, a phenomenon entirely attributable to how the firm chose to finance itself rather than to its underlying operations.

Question 10

Explain the mechanism of 'homemade leverage' that underlies MM Proposition I without taxes, using an example of an investor holding shares in an unlevered firm who wants to replicate the returns of holding shares in an otherwise identical levered firm.

Accepted Answer

Homemade leverage refers to an individual investor's ability to create the financial effect of corporate leverage on their own personal account, by borrowing personally, independent of any borrowing decision made by the firm itself. Consider an investor holding shares in an unlevered firm, U, who wishes to replicate the risk-return profile of holding shares in an otherwise identical but levered firm, L, which has taken on debt in its own capital structure. The investor can borrow personally, in their own name, an amount proportional to the debt the levered firm carries relative to its equity, and use this personal borrowing together with their own funds to buy a larger holding of firm U's shares than they could have bought with their own funds alone; because firm U's shares carry no corporate leverage, but the investor is now personally leveraged on top of that unlevered position, the investor's overall return pattern, including the effect of their own personal interest cost, replicates the return pattern they would have obtained by simply buying shares in the levered firm L directly. Since this replication is available to any investor at will, MM argue that firm L's leverage cannot command any value premium over firm U purely for providing leverage, because investors can manufacture the identical effect themselves at no additional cost the firm's own leverage could offer beyond what personal borrowing already achieves, which is the central mechanism behind MM's no-tax conclusion that capital structure is irrelevant to firm value.

Question 11

Explain why the degree of operating leverage for a given company is not a fixed, permanent number but changes depending on the sales level at which it is measured.

Accepted Answer

DOL = Contribution ÷ EBIT, and EBIT itself equals Contribution minus fixed operating costs; since fixed operating costs remain constant in absolute terms regardless of the sales level, EBIT becomes a progressively larger proportion of Contribution as sales, and therefore Contribution, rise, because the same fixed cost is being spread over, and covered by, a larger contribution base. As sales rise and EBIT grows relatively faster than Contribution due to the fixed cost being a shrinking proportion of the total, the ratio of Contribution to EBIT, that is, DOL, falls; conversely, at lower sales levels closer to the firm's break-even point, EBIT is small relative to Contribution, since most of the contribution is being absorbed by the fixed cost, making DOL correspondingly high, even approaching very large values as sales approach the exact break-even point where EBIT approaches zero. This means DOL should always be understood, and computed, at a specific stated level of sales or EBIT, not treated as one permanent number characterising the company at every possible level of activity.

Question 12

A company is comparing a debt-financing plan against a preference-share-financing plan, and both carry fixed periodic charges. Explain how the EBIT-EPS indifference point computation must be adjusted to correctly handle the preference dividend, given that preference dividend, unlike interest, is not tax-deductible.

Accepted Answer

For a plan financed by debt, EPS is computed as [(EBIT − Interest) × (1 − tax rate)] ÷ Number of equity shares, since interest is deducted before tax is applied, reflecting its tax-deductibility. For a plan financed by preference shares, EPS must instead be computed as [(EBIT × (1 − tax rate)) − Preference dividend] ÷ Number of equity shares, because preference dividend is not tax-deductible and is therefore deducted only after tax has already been computed on the full EBIT, not before. Setting up the indifference point by simply subtracting the preference dividend before applying the tax rate, treating it the same way interest is treated, would incorrectly understate the true earnings available to equity shareholders under the preference plan, since it would wrongly grant preference dividend a tax shield it does not actually receive. Getting this distinction right, applying the tax rate to the entire EBIT first for the preference plan and only afterward subtracting the preference dividend, while for the debt plan subtracting interest first and only afterward applying the tax rate, is essential to computing a correct indifference point whenever a question compares a preference financing alternative against a debt alternative rather than comparing debt against pure equity.

Question 13

Explain how the trade-off theory of capital structure combines MM's tax shield insight with the costs of financial distress to arrive at a conclusion resembling the traditional approach.

Accepted Answer

MM Proposition I with taxes shows that firm value rises continuously with debt because of the growing present value of the interest tax shield, implying, taken in isolation, that a firm should use as much debt as possible to maximise this benefit. The trade-off theory recognises that this conclusion ignores a real, offsetting cost that rises as leverage increases: the costs of financial distress, including the direct costs of bankruptcy proceedings such as legal and administrative expenses, and the indirect costs of financial distress, such as customers, suppliers and employees becoming wary of dealing with a financially strained firm, lost business opportunities, and the general erosion of firm value that can occur even before actual default, simply from the heightened risk of it. At low to moderate levels of debt, the present value of the tax shield exceeds the present value of these expected financial distress costs, so increasing debt still raises firm value, similar to the traditional approach's early-stage benefit-of-cheap-debt reasoning. Beyond a certain level of debt, however, the expected costs of financial distress grow large enough to outweigh the additional tax shield benefit from further borrowing, causing firm value to fall if leverage is increased further, which produces an interior optimal capital structure at the point where the marginal benefit of the tax shield exactly equals the marginal cost of financial distress, arriving at essentially the same qualitative conclusion as the traditional approach, an optimal, bounded capital structure exists, but arrived at through a more rigorous, cost-and-benefit-based theoretical foundation than the traditional approach's less formally derived reasoning.

Question 14

A company currently has EBIT of ₹20 lakh and interest of ₹4 lakh, giving a DFL of 1.25. If the company takes on additional debt raising its annual interest to ₹10 lakh, with EBIT unchanged at ₹20 lakh, recompute DFL and explain what this change indicates about the company's financial risk.

Accepted Answer

Original DFL = EBIT ÷ (EBIT − Interest) = 20 ÷ (20 − 4) = 20 ÷ 16 = 1.25, confirming the given figure. Revised DFL = 20 ÷ (20 − 10) = 20 ÷ 10 = 2.0. The DFL has risen from 1.25 to 2.0 as a direct consequence of the higher fixed interest obligation, meaning that for a given percentage change in EBIT, EPS will now swing by a proportionately larger amount than before the additional borrowing — a 10% change in EBIT would previously have produced roughly a 12.5% change in EPS, but will now produce roughly a 20% change in EPS. This indicates that the company's financial risk has increased materially as a direct result of the additional debt: shareholders now bear greater volatility in their earnings per share for the same underlying volatility in the company's operating earnings, since a larger fixed charge must be met before anything is left over for equity, and this magnification effect works unfavourably in a downturn just as it works favourably in an upturn.

Question 15

A firm with inherently high business risk, reflected in a DOL of 4, is considering financing a new plant entirely through debt, which would give it a DFL of 3. Explain why combining high business risk with high financial risk in this way is considered a particularly risky financing choice, even if each type of leverage is individually manageable in isolation.

Accepted Answer

Combined leverage, DCL, is the product of DOL and DFL, so a firm with a DOL of 4 and a DFL of 3 would have a combined leverage of 12, meaning a 1% change in sales is expected to produce roughly a 12% change in EPS, a very high degree of magnification arising precisely because the two sources of leverage compound multiplicatively rather than merely adding together. Even if a DOL of 4 alone might be considered a manageable, if elevated, level of business risk for a firm in a capital-intensive industry, and a DFL of 3 alone might similarly be considered a manageable, if aggressive, level of financial risk for a firm choosing heavy debt financing, combining both at once means the firm's EPS becomes extremely sensitive to even modest fluctuations in sales, since the sales-to-EBIT magnification from high fixed operating costs is then further magnified by the EBIT-to-EPS effect of high fixed financial costs. This is precisely why sound financial management practice generally advises firms with inherently high business risk, already facing volatile EBIT due to their cost structure, to be comparatively conservative in their financing decisions, favouring more equity and less debt, so as to avoid stacking a high degree of financial leverage on top of an already high degree of operating leverage and producing a combined leverage so extreme that even ordinary sales fluctuations threaten the firm's ability to maintain stable earnings for its shareholders.

Practice — Capital Structure and Leverages

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