Cost of Capital — Practice

Question 1

A company issues debentures carrying a coupon rate of 12% at par. The applicable tax rate is 30%. Compute the after-tax cost of debt.

Accepted Answer

Kd = Interest rate × (1 − Tax rate) = 12% × (1 − 0.30) = 12% × 0.70 = 8.4%. Since the debentures are issued at par, the coupon rate itself is the before-tax cost, and applying the tax adjustment reflects that the interest is a tax-deductible expense, reducing the company's genuine after-tax cost of borrowing to 8.4%, well below the stated coupon rate.

Question 2

A company issues debentures of face value ₹100 each at a discount, receiving net proceeds of ₹94 per debenture after flotation costs, carrying a coupon rate of 10%. The applicable tax rate is 25%. Compute the before-tax and after-tax cost of debt using net proceeds as the base.

Accepted Answer

Annual interest per debenture = 10% × ₹100 face value = ₹10, since interest is always computed on face value regardless of issue price. Before-tax cost of debt using net proceeds = Interest ÷ Net proceeds = 10 ÷ 94 = approximately 10.64%. After-tax cost of debt = 10.64% × (1 − 0.25) = 10.64% × 0.75 = approximately 7.98%. Using net proceeds of ₹94 rather than the face value of ₹100 as the base correctly reflects that the company actually received only ₹94 per debenture in hand, making its genuine cost of borrowing, both before and after tax, higher than it would appear if the face value were mistakenly used as the base.

Question 3

A company issues preference shares of face value ₹100 each, carrying a fixed dividend rate of 9%, at a net proceeds of ₹95 per share after issue expenses. Compute the cost of preference capital, and explain why no tax adjustment is applied.

Accepted Answer

Annual preference dividend per share = 9% × ₹100 face value = ₹9. Cost of preference capital, Kp = Preference dividend ÷ Net proceeds = 9 ÷ 95 = approximately 9.47%. No tax adjustment is applied because preference dividend, unlike debt interest, is an appropriation of profit rather than a tax-deductible expense; the company pays preference dividend only out of profit after tax has already been computed and deducted, so there is no tax shield to adjust for, in direct contrast to debt where the tax-deductibility of interest reduces the company's genuine after-tax cost below the stated rate.

Question 4

A company's share is currently trading at ₹80. It has just paid a dividend of ₹4 per share and dividends are expected to grow at a constant rate of 5% per annum indefinitely. Compute the cost of equity using the Gordon growth model.

Accepted Answer

D₁, the dividend expected next year, = D₀ × (1 + g) = 4 × 1.05 = ₹4.20. Ke = (D₁ ÷ P₀) + g = (4.20 ÷ 80) + 0.05 = 0.0525 + 0.05 = 0.1025, or 10.25%. The two components should be stated separately: the dividend yield of 5.25% represents the income return shareholders expect from the current dividend relative to price, and the growth rate of 5% represents the additional return they expect from the dividend, and correspondingly the share price, growing over time, and together these sum to the total 10.25% return shareholders require to hold the share at its current market price.

Question 5

The risk-free rate is 6%, the expected return on the market portfolio is 13%, and a company's share has a beta of 1.4. Compute the cost of equity using CAPM, and explain what the beta of 1.4 indicates about this share's risk relative to the market.

Accepted Answer

Ke = Rf + β(Rm − Rf) = 6% + 1.4 × (13% − 6%) = 6% + 1.4 × 7% = 6% + 9.8% = 15.8%. A beta of 1.4 indicates that this share is more volatile than the market as a whole — for a given percentage change in the overall market's return, this share's return tends to change by 1.4 times that amount on average, meaning it carries higher systematic risk than the market portfolio. This higher risk is exactly why the CAPM formula assigns this share a market risk premium of 9.8%, larger than the market's own risk premium of 7%, since β scales the premium upward for a riskier-than-market share, resulting in a required return of 15.8%, above the market's own expected return of 13%.

Question 6

A company's capital structure consists of equity shares with a book value of ₹50 lakh and a market value of ₹120 lakh, and debentures with both book and market value of ₹50 lakh. The cost of equity is 16% and the after-tax cost of debt is 7%. Compute WACC using market value weights, and separately using book value weights, and comment on the difference.

Accepted Answer

Using market value weights: total market value = 120 + 50 = ₹170 lakh. Weight of equity = 120/170 = 0.7059, weight of debt = 50/170 = 0.2941. WACC (market value) = (0.7059 × 16%) + (0.2941 × 7%) = 11.29% + 2.06% = approximately 13.35%. Using book value weights: total book value = 50 + 50 = ₹100 lakh. Weight of equity = 50/100 = 0.5, weight of debt = 50/100 = 0.5. WACC (book value) = (0.5 × 16%) + (0.5 × 7%) = 8% + 3.5% = 11.5%. The market-value-weighted WACC of 13.35% is higher than the book-value-weighted WACC of 11.5%, because the market value of equity, at ₹120 lakh, is far higher than its book value of ₹50 lakh, giving equity, the more expensive source at 16%, a much larger weight under market value weighting than under book value weighting, which pulls the blended average upward. This illustrates precisely why the choice of weighting base matters materially, and why the convention of using market value weights, since it reflects investors' actual current commitment and the firm's genuine current cost of raising fresh capital, should be used and explicitly stated unless the question specifies otherwise.

Question 7

Explain why the cost of retained earnings is generally taken to be approximately equal to the cost of equity, rather than treated as a zero-cost source of finance.

Accepted Answer

Retained earnings belong to the equity shareholders, representing profit that could have been distributed as dividend but was instead reinvested in the business on the shareholders' behalf. Shareholders forgoing that dividend expect the retained funds to be reinvested at a return at least equal to what they could have earned themselves had the profit been distributed and reinvested elsewhere at comparable risk, which is the opportunity cost of retained earnings. Because this opportunity cost is essentially the same required return shareholders apply to their equity investment generally, the cost of retained earnings is taken as approximately equal to the cost of equity, rather than as a zero-cost source, since treating it as free would understate the true cost of capital and could lead the firm to accept projects that actually destroy shareholder wealth relative to what shareholders could have earned by receiving and reinvesting the dividend themselves.

Question 8

A newly listed technology company has never paid a dividend and has no plans to do so in the near future, reinvesting all profit into growth. Explain why the Gordon growth model cannot be used to estimate its cost of equity, and why CAPM remains usable.

Accepted Answer

The Gordon growth model estimates the cost of equity as the dividend yield plus the expected constant growth rate of dividends, which requires an actual dividend, D₁, as a direct input to the formula; a company that has never paid a dividend and has no plans to do so has no dividend figure to use, and attempting to apply the formula with a dividend of zero would produce a cost of equity estimate of exactly the growth rate alone, understating the true required return and stripped of any meaningful income-yield component, making the model simply inapplicable in any meaningful sense for such a company. CAPM remains usable because its logic does not depend on dividends at all; it derives the cost of equity purely from the risk-free rate, the market risk premium, and the company's beta, which measures how the company's share price moves relative to the market, a figure that can be estimated from market price data alone even for a company that pays no dividend whatsoever, which is precisely why CAPM is the preferred approach for young, growth-oriented or non-dividend-paying companies where the dividend growth model has no meaningful input to work with.

Question 9

A firm's average cost of capital, based on capital already raised, is 12%. It is now evaluating a new project and must raise fresh capital to fund it, and the cost of raising this next increment of capital is estimated at 14%, since the firm has exhausted its cheaper retained earnings and must now issue fresh equity at a higher cost. Which rate should the firm use to discount the new project's cash flows, and why?

Accepted Answer

The firm should use the marginal cost of capital, 14%, to discount the new project's cash flows, not the average cost of capital of 12%. The theoretical justification is that a new investment decision is financed by the next increment of capital the firm raises, not by the capital it has already raised and which is sitting in its existing capital structure; since this next increment costs 14% to raise, that is the genuine, forward-looking cost the firm incurs specifically to fund this specific new project, and it is this genuine cost that must be compared against the project's expected return to judge whether the project is worth undertaking. Using the lower average cost of capital of 12% as the discount rate would risk accepting a project that, in reality, does not earn enough to cover the actual cost of the fresh capital being raised to fund it, even though it appears acceptable when measured against a historical average that no longer reflects the firm's true current cost of raising additional funds.

Question 10

A company issues 10% redeemable preference shares of face value ₹100 each at a net proceeds of ₹96, redeemable at a premium of ₹5 per share after 5 years. Explain, without a full IRR computation, why a simple Kp = Dividend ÷ Net proceeds formula understates the true cost of this preference capital, and what cash flows a correct computation must include.

Accepted Answer

The simple formula Kp = Dividend ÷ Net proceeds captures only the annual dividend cost relative to what the company received at issue, but it entirely omits two further cash flows that genuinely affect the company's cost of this capital: first, the redemption premium of ₹5 per share the company must pay in addition to the face value when the shares are redeemed after 5 years, which is a real, contractually committed additional cost of this financing; and second, the timing of the redemption outflow itself, occurring five years from now, which time-value-of-money principles say should be discounted back rather than simply added as an undiscounted lump sum, or conversely, in computing the rate that equates the net proceeds received today to the outflows over time, treated properly as part of a multi-period cash flow stream. A correct computation must treat this as a cash flow problem: an initial inflow to the company of the net proceeds ₹96, followed by five annual outflows of the ₹10 dividend, followed by a final outflow at year 5 of the face value ₹100 plus the redemption premium ₹5, that is, ₹105, and the true cost of preference capital is the discount rate, found by trial and error or interpolation, that equates the present value of all these outflows to the net proceeds received at issue. Because this correct computation includes the redemption premium and appropriately time-values the eventual repayment, it will show a cost of preference capital higher than the simple formula suggests, which is precisely why the simple ratio understates the true cost whenever a preference share is redeemable, particularly at a premium.

Question 11

Explain why including flotation costs in the cost of capital computation always increases the computed specific cost of a source, using cost of equity as the example.

Accepted Answer

Flotation costs are the expenses incurred in issuing a security, such as underwriting commissions, legal fees and other issue-related expenses, and including them means the funds a company actually receives net of these costs are less than the gross amount investors pay in. For cost of equity computed via the dividend growth model, incorporating flotation costs means the denominator, the price or proceeds base against which the dividend yield is computed, should be the net proceeds after flotation costs rather than the full market price, and since this net proceeds figure is smaller than the gross price, dividing the same dividend by a smaller base produces a larger dividend yield, and therefore a larger computed cost of equity, than would be obtained by ignoring flotation costs and using the full market price. This pattern generalises across every source: flotation costs always reduce what the company actually receives relative to the gross amount, and computing a specific cost against this smaller net-proceeds base always yields a higher computed cost than ignoring the flotation cost would, which is why flotation costs, wherever a question supplies them, should always be netted out of the proceeds base rather than ignored.

Question 12

A firm can raise up to ₹40 lakh of retained earnings at a cost of 12%, beyond which it must issue fresh equity at a higher cost of 15%. If the firm maintains a constant capital structure of 60% equity-type funds and 40% debt for every rupee raised, at what total amount of new capital raised does the firm's weighted marginal cost of capital schedule show a break point, and why does WACC rise beyond this point?

Accepted Answer

The break point occurs at the total amount of financing at which the cheaper source, retained earnings, is fully exhausted. Since retained earnings of ₹40 lakh are available and equity-type funds, which retained earnings fall within, make up 60% of every rupee raised under the firm's constant capital structure, the break point in terms of total capital raised is found by dividing the retained earnings available by the proportion of the total that equity-type funds represent: ₹40 lakh ÷ 0.60 = approximately ₹66.67 lakh. Up to this total amount of financing, the equity-type portion of every rupee raised can be sourced from the cheaper 12% retained earnings, but beyond ₹66.67 lakh of total financing, the equity-type portion must increasingly be sourced from fresh equity at the higher 15% cost, since retained earnings are by then fully used up. WACC rises beyond this break point because the equity-type component of the weighted average now reflects the higher 15% cost of fresh equity rather than the 12% cost of retained earnings, while the debt component and the weights themselves remain unchanged, so the blended weighted average necessarily increases once the cheaper source of the equity-type component is exhausted and replaced by the more expensive one.

Question 13

Explain the reasoning behind the earnings-based approach to estimating the cost of equity, and how it differs conceptually from the dividend-based approach.

Accepted Answer

The earnings-based approach treats the cost of equity as the rate that equates the present value of the company's expected future earnings, rather than specifically its future dividends, to the current market price, resting on the reasoning that a shareholder's claim on the company extends to the entirety of the company's earnings, not merely to whatever fraction of those earnings happens to be paid out as dividend in any given year, since retained earnings not distributed as dividend still belong to shareholders and are reinvested on their behalf, ultimately contributing to future share value. This differs conceptually from the dividend-based approach, which focuses narrowly on the actual cash dividend stream shareholders receive and its expected growth, implicitly treating the dividend as the relevant measure of shareholder return; the earnings-based approach instead takes the broader view that total earnings, whether distributed or retained, represent the true economic return generated for shareholders, and estimates the cost of equity with reference to that broader earnings base rather than the narrower, and sometimes more volatile or discretionary, dividend figure alone.

Question 14

A firm currently has a WACC of 12%, with a capital structure of 70% equity at 15% cost and 30% debt at 5% after-tax cost. If the firm shifts its capital structure to 50% equity and 50% debt, with the specific costs unchanged, recompute WACC and explain whether this shift necessarily benefits the firm's shareholders.

Accepted Answer

Original WACC = (0.70 × 15%) + (0.30 × 5%) = 10.5% + 1.5% = 12%, confirming the given figure. Revised WACC = (0.50 × 15%) + (0.50 × 5%) = 7.5% + 2.5% = 10%. The revised WACC of 10% is lower than the original 12%, since the shift increases the weight of the cheaper source, debt, at the expense of the more expensive source, equity. However, this lower WACC does not necessarily benefit shareholders, because the specific costs used in this computation are held artificially constant even though, in reality, increasing the proportion of debt in the capital structure typically increases the financial risk borne by both debt holders and equity holders, which would normally cause both the cost of debt and the cost of equity to rise as leverage increases, rather than remaining fixed at their original levels. A genuinely reliable comparison would need to re-estimate the specific costs of equity and debt at the new, higher leverage level to reflect this increased risk, and only after that re-estimation can a sound conclusion be drawn about whether the shift genuinely lowers the firm's true cost of capital or merely appears to on paper by holding risk-sensitive costs artificially fixed while changing the weights that depend on them.

Question 15

For the same company, the dividend growth model gives a cost of equity of 14%, while CAPM gives a cost of equity of 11%, using genuinely comparable current data. Explain two possible reasons for this divergence, without assuming either estimate is simply wrong.

Accepted Answer

One possible reason is that the constant growth rate assumed in the dividend growth model may not accurately reflect the market's true expectation of the company's future dividend growth; if the assumed growth rate is too high relative to what the market genuinely expects, the dividend growth model will produce an inflated cost of equity estimate relative to CAPM, which does not rely on any dividend growth assumption at all. A second possible reason is that the company's beta, used in the CAPM computation, may not fully capture all of the risk factors the market is actually pricing into the share; beta measures only systematic risk relative to a broad market index, and if the market is pricing in additional company-specific considerations not well captured by a historical beta estimate, CAPM could understate the true required return relative to what the dividend growth model, which is derived directly from the actual current market price and dividend data, implicitly reflects. In practice, since the two models rest on different underlying assumptions and different data inputs, a divergence between them is common and expected rather than necessarily indicating that one model has been computed incorrectly, and it is reasonable practice to compute both where data permits and to explain, rather than mechanically average away, any material difference between them.

Practice — Cost of Capital

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