Financial Analysis puzzles, solved step by step

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  1. 026A company trades at 15x earnings and 6x EBITDA. Market cap is Rs 300 crore, net debt is Rs 180 crore, interest expense is Rs 18 crore and depreciation and amortisation is Rs 30 crore. What is the implied effective tax rate, and what does it suggest about the company?Valuation and multiples riddlesHardEquity researchTransaction advisory

    Try it first

    Before you calculate: which two numbers must you find first?

    Show the worked solution

    The implied tax rate is 37.5%. Market cap of 300 at 15x earnings gives net income of 20. Adding net debt of 180 gives EV of 480, so EBITDA at 6x is 80. Less D&A of 30 is EBIT of 50; less interest of 18 is pre-tax profit of 32. Tax is 32 minus 20, which is 12, and 12 over 32 is 37.5%, high enough to ask why.

    Where do you start when six numbers arrive at once?

    Think of working out a friend's take-home pay from what they spend and what they save. You do not start with their job title; you start with the two numbers that pin the answer. A tax rate is tax divided by pre-tax profit, so every other number in the question is a road to net income or to pre-tax profit. Say that first. Net income is one step: 300 over 15 is 20. Pre-tax profit needs EBITDA, which needs EV, which needs the net debt you were handed.

    Find the two profit lines either side of tax, then the rate is the gapMarket cap 300 / P/E 15Net income = 20300 + net debt 180EV = 480EV 480 / 6xEBITDA = 80Pre-tax 32 less net income 20Tax = 1280EBITDA-30D&A-18Interest32Pre-tax-12Tax20Net incomeTax / pre-tax profit = 12 / 32Tax rate = 37.5%EBIT is 50 after D&A; interest of 18 implies about 10% on the net debt
    Market cap of 300 at 15x gives net income of 20, and adding net debt of 180 gives EV of 480 and EBITDA of 80 at 6x. EBITDA less D&A of 30 and interest of 18 leaves pre-tax profit of 32, so a tax charge of 12 is a 37.5% rate.
    The relationship
    t=PBT−NIPBT=(480/6−30−18)−300/15480/6−30−18=1232=37.5%t = \frac{\text{PBT} - \text{NI}}{\text{PBT}} = \frac{(480/6 - 30 - 18) - 300/15}{480/6 - 30 - 18} = \frac{12}{32} = 37.5\%
    PBTpre-tax profit: EBITDA less D&A less interest
    NInet income: market cap over the P/E
    480enterprise value: market cap 300 plus net debt 180
    What it says in wordsBuild pre-tax profit from the EV multiple, build net income from the P/E, and the tax rate is the share of pre-tax profit that did not survive.

    What does a 37.5% rate tell you, and what have you assumed?

    You assumed there are no minority interests, no associates and no interest income on cash, so EV is just market cap plus net debt and every rupee of pre-tax profit belongs to shareholders. Say that. Then read the number. An effective rate well above the statutory rate usually means some costs are not tax deductible, some losses sit in units that cannot use them, or there are one-off tax charges. Compare it with the statutory rate the company actually pays, which you should confirm for the year in question. A second check: interest of 18 on net debt of 180 is 10%, which is plausible, so the inputs hang together.

    Where candidates lose it

    Candidates reach EBITDA of 80, subtract tax from somewhere and forget one of the two lines between EBITDA and pre-tax profit, usually D&A. Walk the income statement in order, one line per step, and the missing line has nowhere to hide.

    The second loss is stopping at 37.5%. The interviewer asked what it suggests. One sentence on non-deductible costs or loss-making units turns arithmetic into analysis.

    What the interviewer asks next

    • If the company also held Rs 40 crore of cash earning 5%, how does the implied rate change?
    • Which items typically push an effective tax rate above the statutory rate?
    • What happens to the implied rate if the P/E rises to 20x with everything else fixed?
  2. 097A stock trades at 30 times next year's earnings. Its cost of equity is 12%, and it earns a 20% return on the profit it reinvests. What perpetual growth rate is the market pricing in?Valuation and multiples riddlesHardEquity researchBuy-side research

    Try it first

    What does the 30x multiple say about growth?

    Show the worked solution

    About 10.4% a year, forever, with the company paying out 48% of its earnings. A forward P/E equals the payout ratio divided by the cost of equity less growth, and with a fixed ROE the payout is set by growth: payout = 1 minus g/ROE. So 30 = (1 minus g/0.20) / (0.12 minus g). Multiply out: 3.6 minus 30g = 1 minus 5g, so 25g = 2.6 and g = 10.4%. Check: a dividend yield of 48% / 30 = 1.6% plus 10.4% growth is the 12% cost of equity.

    Where does a multiple hide a growth forecast?

    If someone offers to sell you a shop for thirty years of its current profit, they are not quoting a price; they are telling you how fast they expect the profit to grow. The multiple is the forecast. Under the Gordon growth model a share is worth next year's dividend over (r minus g), so dividing by next year's earnings gives P/E = payout / (r minus g), and a given P/E can be solved for g. The one thing people forget is that the payout is not free to choose: growth has to be paid for with retained profit.

    With a fixed return on reinvested profit, growth equals ROE times the retention rate, so retention is g/ROE and payout is 1 minus g/ROE. At a 20% ROE, growing at 10% means keeping half the earnings. Put that into the multiple: 30 = (1 minus 5g) / (0.12 minus g). Cross-multiply: 3.6 minus 30g = 1 minus 5g, so 2.6 = 25g and g = 10.4%. The implied payout is 1 minus 0.104/0.20 = 48%, and the implied dividend yield is 48% of a 3.33% earnings yield, 1.6%.

    The relationship
    P0E1=1−g/ROEr−g30=1−g/0.200.12−g  ⇒  g=1−30(0.12)1/0.20−30=10.4%\frac{P_0}{E_1} = \frac{1 - g/\text{ROE}}{r - g} \qquad 30 = \frac{1 - g/0.20}{0.12 - g} \;\Rightarrow\; g = \frac{1 - 30(0.12)}{1/0.20 - 30} = 10.4\%
    P0 / E1the forward P/E, price over next year's earnings
    1 minus g/ROEthe payout ratio once growth is funded from retained profit
    rthe cost of equity, 12%
    gthe perpetual growth rate the price implies
    What it says in wordsThe forward P/E is the payout ratio over the gap between cost of equity and growth, and the payout is whatever is left after funding growth at the ROE.
    A multiple is a growth forecast in disguise: where the curve meets 30x10x20x30x40x50x0%2%4%6%8%10%Perpetual growth rate gForward P/Eg = 10.4% at ROE 20%the market's forecast8%: 15x10%: 25xno growth: 1 / r = 8.3xCost of equity 12%ROE 20%30x needs g = 10.4%ROE 15%30x needs g = 11.1%ROE = 12% = rP/E stays 8.3xat any growth rate
    At a 12% cost of equity and a 20% ROE, the P/E curve starts at 8.3x with no growth, passes 15x at 8% and 25x at 10%, and crosses 30x at 10.4%, while at a 15% ROE the same 30x needs 11.1% because more of each rupee must be retained to grow.

    Why does the ROE matter as much as the growth rate?

    Because the ROE sets how much growth costs. At a 15% ROE the same 30x needs 11.1% growth, since a bigger share of earnings has to be retained to fund each point of it. At an ROE equal to the cost of equity, 12%, the multiple is 1/r = 8.3x whatever the growth rate, because every retained rupee earns exactly what shareholders could earn elsewhere. Growth adds value only when the reinvested profit earns more than the cost of equity; the multiple prices the spread between ROE and r as much as it prices g. The curve is also steep near the answer: at 10% the multiple is 25x, at 11% it is 45x, so a 30x stock is one point of growth away from either 25x or 45x.

    Now say the limitation. 10.4% growth forever, only 1.6 points below the discount rate, is not a forecast anyone would defend; no company outgrows the economy indefinitely. The honest reading is that 30x prices a long period of fast growth that will fade, and a two-stage model, say 10.4% for a decade and a lower rate after, is the next thing to build. The one-line solve is still worth doing, because it converts a multiple into a sentence you can argue with: the market expects this company to compound earnings at about 10% for a very long time while earning 20% on what it retains.

    Where candidates lose it

    The common slip is using P/E = 1 / (r minus g), which gives 30 = 1 / (0.12 minus g) and g = 8.7%. That formula pays out every rupee and still grows, which is impossible: growth has to be funded. Put the payout in as 1 minus g/ROE and the answer moves to 10.4%.

    The second loss is reporting the number as a forecast. It is what the price implies, not what will happen, and it rests on three assumptions the interviewer wants named: a constant 20% ROE on new investment, a 12% cost of equity, and growth held forever at a rate no company sustains.

    What the interviewer asks next

    • If the return on new investment falls to 12%, what multiple is justified at any growth rate, and why?
    • The stock pays out 48% of earnings. What dividend yield does that give at 30x, and how does it reconcile with the 12% cost of equity?
    • How would you restate the implied growth as ten years of fast growth followed by 4% forever?