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  1. 004A comparable company's unlevered beta is 0.8. Your company targets a debt-to-equity ratio of 0.5 and pays 25% tax. The risk-free rate is 7% and the equity risk premium is 6%. What is your company's cost of equity? What if its debt-to-equity rises to 1.0?Cost of capital, leverage and ratesCoreLazardSan Francisco · 2026

    Try it first

    With debt-to-equity of 0.5, what is the levered beta?

    Show the worked solution

    The cost of equity is 13.6% at debt-to-equity of 0.5, and 15.4% at 1.0. Relevering puts your own debt back onto the peer's business risk: 0.8 times (1 plus 0.75 times 0.5) gives a beta of 1.10, and 7% plus 1.10 times 6% is 13.6%. At 1.0 the beta is 1.40, so the cost of equity is 15.4%.

    Why unlever the peer's beta and then relever it?

    Two friends buy identical flats. One pays cash; the other borrows 60% of the price. When flat prices move 10%, the cash buyer's wealth moves 10%, while the borrower's stake moves far more, because the loan does not shrink with the price. A peer's observed beta mixes two things, the risk of its business and the risk its own debt adds, so you strip out its debt before borrowing its business risk. Then you add back your own debt, because your shareholders carry your leverage, not the peer's.

    The relationship
    βL=βU[1+(1−t)DE]=0.8 [1+0.75×0.5]=1.10\beta_L = \beta_U\left[1 + (1-t)\frac{D}{E}\right] = 0.8\,[1 + 0.75 \times 0.5] = 1.10
    β_Uunlevered beta, the business risk alone, 0.8
    ttax rate, 25%
    D/Eyour target debt to equity, 0.5
    β_Llevered beta your shareholders bear
    What it says in wordsYour shareholders' beta is the business beta scaled up by how much after-tax debt sits in front of them.

    This is the Hamada relation, which assumes debt carries no market risk of its own. Then the capital asset pricing model does the rest: cost of equity is the risk-free rate plus beta times the equity risk premium, so 7% plus 1.10 times 6% is 13.6%. At debt-to-equity of 1.0, beta becomes 0.8 times 1.75, or 1.40, and the cost of equity is 15.4%.

    Cost of equity rises in a straight line with the target's own leverage12%14%16%18%10%0.00.51.01.5Target debt to equityCost of equityNo debt: beta 0.80, 11.8%D/E 0.5: beta 1.10, 13.6%D/E 1.0: beta 1.40, 15.4%1.5: 1.70, 17.2%
    With an unlevered beta of 0.8, cost of equity rises in a straight line from 11.8% with no debt to 13.6% at debt-to-equity of 0.5 and 15.4% at 1.0, because each extra 1.0 of debt-to-equity adds 0.6 to beta after the tax shield.

    Does more debt make the company more expensive to fund overall?

    Not by this alone. Equity gets dearer as debt rises, but debt is cheaper than equity and its interest is tax-deductible, so the weighted cost of capital can fall even while the cost of equity climbs. Where it turns is where lenders start charging more and distress becomes real, which this formula does not capture. Say that limit out loud: the straight line only holds while debt is safe.

    Where candidates lose it

    The common error is using the peer's beta of 0.8 directly. That prices your equity as if you had no debt, which understates the cost of equity by nearly two points at a debt-to-equity of 0.5.

    The second is dropping the tax term and getting 1.20. Say the formula before the numbers, so a slip in arithmetic does not look like a gap in understanding.

    What the interviewer asks next

    • Your pre-tax cost of debt is 9%. What is the WACC at debt-to-equity of 0.5 and at 1.0?
    • The peer's observed beta was 1.2 at a debt-to-equity of 0.6. Check that its unlevered beta is about 0.8.
    • Why might you use a median of several peers' unlevered betas instead of one?

    Asked at Lazard, Investment Banking, San Francisco, 2026 (Wall Street Oasis): They tested core valuation concepts (full DCF walkthrough, WACC, unlevering/relevering beta, and LBO basics)

  2. 031A software company has EBITDA of Rs 800 crore and debt of 7x EBITDA. If its EV/EBITDA multiple falls from 10x to 8x, what happens to its equity value, and what does 7x leverage tell you about the sensitivity?Cost of capital, leverage and ratesCoreMoelis & CompanyNew York · 2026

    Try it first

    The multiple falls 20%, from 10x to 8x. Roughly how far does equity value fall?

    Show the worked solution

    Equity falls from Rs 2,400 crore to Rs 800 crore, a 66.7% drop on a 20% fall in EV. Debt is 7 x 800 = Rs 5,600 crore. At 10x, EV is Rs 8,000 crore; at 8x it is Rs 6,400 crore. Debt keeps its claim, so the equity slice absorbs the whole Rs 1,600 crore. At 7x leverage, equity moves 3.3 times as fast as EV, and a 7x multiple wipes it out.

    Why does equity fall so much further than the business?

    Think of a flat bought for Rs 1 crore with a Rs 70 lakh home loan. If the flat's price drops 20% to Rs 80 lakh, the bank still wants its Rs 70 lakh, so the owner's stake falls from Rs 30 lakh to Rs 10 lakh, a two-thirds loss. Debt is a fixed claim in rupees, so any change in enterprise value lands entirely on the equity that sits on top. Here debt is 7 x 800 = Rs 5,600 crore. At 10x, EV is Rs 8,000 crore and equity is Rs 2,400 crore, only 30% of the value.

    Debt stays at Rs 5,600 crore, so every rupee lost from EV comes out of equityDebt5,600Equity 2,400EV 8,00010x EBITDADebt5,600Equity 800EV 6,4008x EBITDADebt5,600Equity 0EV 5,6007x EBITDAEquity share of EV at 10x2,400 / 8,000 = 30%Multiplier = EV / equity8,000 / 2,400 = 3.33xMove from 10x to 8xEV-20.0%Equity-66.7%20% x 3.33 = 66.7%
    With debt fixed at Rs 5,600 crore, a fall in the multiple from 10x to 8x takes EV from Rs 8,000 crore to Rs 6,400 crore and equity from Rs 2,400 crore to Rs 800 crore, a 66.7% loss on a 20% fall in EV, and at 7x the equity is gone.
    The relationship
    ΔEE=ΔEVEV×EVE=−20%×8,0002,400=−66.7%\frac{\Delta E}{E} = \frac{\Delta EV}{EV} \times \frac{EV}{E} = -20\% \times \frac{8{,}000}{2{,}400} = -66.7\%
    Eequity value: EV less debt
    EVenterprise value: EBITDA times the multiple
    EV/Ethe leverage multiplier, how many rupees of business each rupee of equity carries
    What it says in wordsThe percentage move in equity is the percentage move in EV multiplied by EV over equity.

    So what does 7x leverage tell you about sensitivity?

    Leverage of 7x EBITDA means the debt alone is worth 7x EBITDA. Whenever the valuation multiple sits close to the leverage multiple, equity is a thin slice of the gap between them, and small changes in the multiple swing it hard. At 10x the gap is 3 turns; each turn of multiple is Rs 800 crore, a third of the equity. Software companies can carry this because their cash flows recur and their multiples are high, but the same 7x on a business valued at 8x leaves one turn of cushion. Say the limitation: the sum assumes debt is worth its face value, while in distress the debt itself would trade below par and soak up some of the loss.

    Where candidates lose it

    The common slip is answering 20%: the multiple fell 20%, so equity must too. That treats equity as if it were the whole business. Draw the stack, debt at the bottom in fixed rupees, and the answer is plain.

    The second loss is giving the number without the read. The interviewer asked what 7x tells you, and the answer is a sentence about equity being a thin, highly geared slice whose value is the gap between two multiples.

    What the interviewer asks next

    • At what EV/EBITDA multiple is the equity worth exactly zero?
    • If the company used Rs 800 crore of cash to repay debt first, how much would equity fall on the same de-rating?
    • How would a lender look at the same 7x number differently from an equity investor?

    Asked at Moelis & Company, Generalist, New York, 2026 (Wall Street Oasis): A tech company has leverage rate of 7X. What does it tell you about the about the impact on sensitivity?

  3. 056A private equity fund buys a company for Rs 1,000 crore, funding it with Rs 600 crore of debt and Rs 400 crore of equity. Five years later it sells the company for Rs 1,000 crore, having used the company's cash flow to repay debt down to Rs 200 crore. How did the fund make money, and what are its MOIC and IRR?Cost of capital, leverage and ratesCoreTD SecuritiesToronto · 2026

    Try it first

    What are the fund's MOIC and IRR on its equity?

    Show the worked solution

    The company's own cash repaid Rs 400 crore of debt, and every rupee repaid moved a rupee of the unchanged Rs 1,000 crore value from lenders to the fund. Equity went in at Rs 400 crore and came out at Rs 800 crore: a MOIC of 2.0x and, over five years, an IRR of about 14.9%. No growth and no change in multiple were needed.

    Where did the gain come from if the price did not move?

    Think of a flat bought for Rs 1 crore with a Rs 60 lakh home loan. The rent covers the loan payments and brings the loan down to Rs 20 lakh over five years. You sell the flat for exactly Rs 1 crore, yet your stake has grown from Rs 40 lakh to Rs 80 lakh. Enterprise value is a pie shared between lenders and owners, and each rupee of debt repaid from the business's own cash moves a rupee of that pie to the owners. The price never had to rise.

    Same price in and out: the gain is the debt the company's cash repaidDebt 600Equity 400EV 1,000Entry, year 0Debt 200Equity 800EV 1,000Exit, year 5+400 was debtRs 400 crore repaid from cash flow moves acrossWith 600 of debt at entryEquity 400 in, 800 out2.0xIRR 14.9% a year2 to the power 1/5, less 1Same business, no debt1,000 in; 1,000 + 400 of cash out1.4x and 7.0% a year
    Enterprise value is Rs 1,000 crore at both entry and exit, but Rs 400 crore of debt repaid from cash flow has become equity, so the fund's stake doubles from Rs 400 crore to Rs 800 crore: 2.0x and about 14.9% a year.

    The return arithmetic follows. MOIC, the multiple on invested capital, is Rs 800 crore out over Rs 400 crore in, 2.0x. IRR is the yearly rate that turns 400 into 800 over five years: 2 to the power one fifth, less 1, which is 14.87%. The rule of 72 gives a quick check: doubling in five years is roughly 72 / 5, about 14.4%.

    The relationship
    MOIC=1,000−2001,000−600=800400=2.0×IRR=2.01/5−1≈14.9%\text{MOIC} = \frac{1{,}000 - 200}{1{,}000 - 600} = \frac{800}{400} = 2.0\times \qquad \text{IRR} = 2.0^{1/5} - 1 \approx 14.9\%
    1,000enterprise value at both entry and exit, Rs crore
    600, 200debt at entry and at exit, Rs crore
    1/5one over the five-year holding period
    What it says in wordsEquity is what is left of the same enterprise value after debt, and repaying debt from cash flow doubles it here.

    Is that skill or just leverage?

    Run the same business with no debt. The fund pays Rs 1,000 crore of equity, the company's cash flow piles up as at least Rs 400 crore of cash, and at exit the fund receives Rs 1,000 crore plus that cash, about Rs 1,400 crore. That is 1.4x and about 7.0% a year, before adding the interest it never paid. Debt did not create the Rs 400 crore; the business earned it. Debt let a smaller cheque claim all of it, which lifts the return from 1.4x to 2.0x.

    Leverage cuts both ways, and saying so is the limit worth stating. Had the company sold for only Rs 500 crore, the levered fund would get back Rs 300 crore on Rs 400 crore, 0.75x, a loss, while the unlevered owner would hold 0.9x. The same debt that doubled the good outcome deepened the bad one.

    What does the interviewer listen for?

    Name the three ways a buyout makes money: EBITDA growth, a higher exit multiple, and debt paydown. This deal used only the third, which is the point of the question. Then add time: the same 2.0x earned over three years instead of five is about 26% a year, which is why funds care about IRR and not only the multiple. A finishing touch is noting that the Rs 400 crore repaid is cash after interest, so the business had to earn more than Rs 400 crore to do it.

    Where candidates lose it

    The instinct is to say the fund made nothing because it sold at the price it paid. That reads the enterprise value as the fund's money, when the fund owned only the equity slice, and that slice doubled.

    The second loss is the IRR. Dividing a 100% gain by five years gives 20%, which ignores compounding and overstates the rate by about five points. Doubling over five years is about 14.9%, and the rule of 72 gets you there in your head.

    What the interviewer asks next

    • The fund also grows EBITDA so the exit price is Rs 1,200 crore. What are MOIC and IRR now?
    • Instead of repaying debt, the company pays the fund a Rs 400 crore dividend in year 3. What happens to IRR and to MOIC?
    • Why might the same deal look better on IRR than on MOIC if it is sold after two years?

    Asked at TD Securities, Investment Banking, Toronto, 2026 (Wall Street Oasis): PE firm bought a company at $1k and sold at $1k, how did they make money?

  4. 069A company is funded half by debt and half by equity at market value. Its shares trade at 10 times earnings, its cost of debt is 6% and its tax rate is 25%. Assuming no growth, what is its WACC?Cost of capital, leverage and ratesCoreCitiNew York · 2026

    Try it first

    What is the WACC?

    Show the worked solution

    WACC is 7.25%. With no growth, a P/E of 10 means an earnings yield of 1 / 10 = 10%, which stands in for the cost of equity. Debt costs 6% before tax and 6% x (1 - 25%) = 4.5% after. Weighted half and half: 0.5 x 10% + 0.5 x 4.5% = 5% + 2.25% = 7.25%.

    Why can the P/E stand in for the cost of equity?

    Suppose you buy a shop for ten years of its profit, and the profit never grows and is all paid to you. Each year you collect a tenth of what you paid: a 10% return. With no growth and all earnings paid out, the price is earnings divided by the cost of equity, so the earnings yield, one over the P/E, is the return shareholders require. At 10x that is 10%.

    Weight each source by its share and use the after-tax cost of debt10.0%Equity, 50%1 / P/E = 1 / 104.5%Debt, 50%6% x (1 - 25%)tax saves 1.50.5 x 10 = 5.00.5 x 4.5 = 2.25WACC 7.25%Weighted cost8.0%pre-tax slip
    Equity at a 10% earnings yield and debt at 4.5% after tax, each weighted at half, stack to a WACC of 7.25%; forgetting the tax shield on debt would give 8.0%.
    The relationship
    WACC=EVke+DVkd(1−t)=0.5×10%+0.5×6%×0.75=7.25%\text{WACC} = \tfrac{E}{V} k_e + \tfrac{D}{V} k_d (1 - t) = 0.5 \times 10\% + 0.5 \times 6\% \times 0.75 = 7.25\%
    E/V, D/Vequity and debt as shares of total market value, half each
    k_ecost of equity, 1 / P/E = 10% with no growth
    k_d (1 - t)cost of debt after tax: 6% x (1 - 25%) = 4.5%
    What it says in wordsEach source of capital is charged at its own after-tax cost and weighted by its share of the market value of the firm.

    The tax step matters because interest is deducted before tax is calculated. Every Rs 100 of interest saves Rs 25 of tax, so lenders cost the company only Rs 75 of every Rs 100 they receive. Dividends earn no such deduction, so equity gets no adjustment.

    When does the shortcut break?

    When earnings grow. The dividend growth relation gives P/E = payout / (k - g), so with growth the same 10x implies a higher cost of equity. At a 70% payout and 4% growth, k = 0.7 / 10 + 4% = 11%, and WACC becomes 7.75%. With growth, the earnings yield understates the cost of equity, because part of the shareholder's return comes from growth rather than from today's earnings. That is why the question says no growth.

    What would an interviewer probe next?

    Two things. First, weights: they must be market values, not book values, because WACC is the return investors require on what their claims are worth today. Second, leverage: the 10x P/E belongs to shares in a company already carrying 50% debt, so the 10% already includes the extra risk that debt places on equity. Unlever it before applying it to a company with a different capital structure. The tax shield is only real if the company has profits to deduct interest from, which is the limit to name.

    Where candidates lose it

    The most common loss is using the pre-tax 6% for debt and getting 8.0%. Interest is tax deductible, and leaving the shield out overstates the cost of capital and so undervalues every project discounted at it.

    The second loss is freezing at the P/E, not knowing how a multiple becomes a rate. Under no growth, its inverse is the rate; say that out loud, and add that growth would break it.

    What the interviewer asks next

    • The company moves to 70% debt at the same 6% cost. Why would the P/E and the cost of equity change?
    • Earnings are expected to grow 3% a year with a 70% payout. What cost of equity does a 10x P/E imply?
    • Why do we use the after-tax cost of debt in WACC but not in the interest line of the income statement?

    Asked at Citi, Capital Markets, New York, 2026 (Wall Street Oasis): $50 debt, $50 equity, P/E 10x, Cost of Debt 6%, what is WACC