MRP Finance Internship Unit 11

Unit 11 · Practice solutions

Practice solutions

Comparables and Multiples · Ghana · GH₵

Worked answers to the optional practice questions. The required question is turned in to the TAs, and its answer is not published here.

Practice solutions

11.1

  1. P/E = 0.50 × 1.04 / (0.11 − 0.04) = 0.52/0.07 = 7.43. At 6% growth: 0.50 × 1.06 / (0.11 − 0.06) = 0.53/0.05 = 10.60. Two percentage points of growth raises the multiple by 43%.
  2. Higher expected growth at the 14× firm; lower risk, whether from a stronger competitive position, more contracted revenue, or a safer balance sheet; and better cash conversion, meaning less reinvestment required per unit of earnings. Evidence: historical and forecast revenue growth and market position for the first; revenue contracting, customer concentration, and leverage for the second; capital expenditure and working capital as a share of earnings for the third.
  3. 12 = 0.35 × (1+g)/(0.13 − g). So 12(0.13 − g) = 0.35 + 0.35g → 1.56 − 12g = 0.35 + 0.35g → 1.21 = 12.35g → g = 9.8%. For a mature business that is implausibly high as a perpetual growth rate — it exceeds most economies' long-run nominal growth, so either the market expects a period of above-trend growth before settling, or the shares are expensively priced, or the payout ratio understates the cash actually returned.
  4. Because EBITDA is not cash — it is measured before capital expenditure, working capital investment, and tax. A firm that must reinvest most of its EBITDA to maintain and grow its asset base delivers far less cash to its owners per unit of EBITDA than an asset-light firm does. Since value is the present value of cash to owners, the capital-hungry firm is worth less for the same EBITDA. The multiple should therefore be lower, and any comparison that ignores capital intensity will overvalue the heavier business.

11.2

  1. (a) Incorrect — EV is a whole-firm measure, net income is post-interest; use EV/EBIT or EV/EBITDA, or P/E. (b) Correct — both equity-level. (c) Correct — both firm-level. (d) Incorrect — market capitalisation is equity-level, revenue is firm-level; use EV/Revenue. (e) Correct — both firm-level.
  2. (a) Bank — P/Book, because the balance sheet reflects the earning assets and returns are generated on book equity. (b) Loss-making software — EV/Revenue, because earnings are negative and uninformative. (c) Hotel group — EV per room or EV/EBITDA, because room count is a meaningful operating unit and the businesses are comparable per unit. (d) Cement — EV/EBITDA, because it is capital-intensive with varying leverage and depreciation policies across producers.
  3. The EV/EBITDA multiples are identical, because enterprise value includes debt and EBITDA is measured before interest — the financing choice affects neither. The P/E ratios differ: the levered firm has lower net income because of interest expense and lower equity value because of the debt, and the two do not move proportionally, so the ratios diverge. EV/EBITDA is the more useful comparison when the question is how the underlying businesses compare, because it isolates operating performance from financing choices.
  4. EBITDA is measured before depreciation and before capital expenditure, so it treats a business that must constantly replace equipment identically to one that does not. The capital-intensive business converts much less of its EBITDA into cash available to owners, because a large share is consumed by maintaining the asset base. Applying the same multiple to both therefore overvalues the heavier business. I would adjust by either using EV/(EBITDA − maintenance capex), or by applying an explicit downward adjustment to the multiple with the reasoning stated — as in the Jollof Express walk-down.

11.3

  1. Open; expect sets such as: listed developed-market hospital groups (highest multiples — scale, liquidity, stable regulated revenue); emerging-market private healthcare operators (middle — similar operating environment and growth profile); African listed healthcare and consumer services (lowest — closest on country risk, liquidity, and investor base). Mark for whether the direction of each is justified by the drivers rather than asserted.
  2. Mean = (6.2 + 6.8 + 7.1 + 7.4 + 19.6)/5 = 9.42. Median = 7.1. Report the median — the 19.6 is an outlier that drags the mean nearly 2.3 turns above where four of the five comparables sit. I would also investigate what is happening at that company, since it may be subject to a bid, in distress, or not genuinely comparable, and consider excluding it entirely with the reason stated.
  3. A franchisor earns royalties on revenue generated by outlets that franchisees paid to build and operate, so it carries very little capital and very low operating cost, producing high margins and excellent cash conversion. A company-owned operator funds every build-out and refit itself and carries all the operating costs, so a much smaller share of each unit of EBITDA becomes cash for owners. Since a multiple rises with cash conversion, the franchisor deserves a materially higher one. The two are in the same industry and are financially different businesses, which is why industry classification is a poor basis for comp selection.
  4. First, classifications group companies by what they sell rather than by how they make money — a franchisor and an operator, or a manufacturer and a distributor, can share a code while having entirely different economics. Second, they ignore size, country, and liquidity, so a multi-billion listed company and a small private one appear equally comparable. Instead: start from the classification as a candidate list, then assess each candidate on business model, size, growth prospects, operating environment, and liquidity, keep only those that genuinely resemble the target, and record explicitly which dimensions are stretched for the ones retained.

11.4

  1. Model answer: start at 9.0×. Less country risk for Nigeria versus Europe, perhaps −2.0×, reflecting currency, inflation, and policy exposure. Less private-company illiquidity, perhaps −1.0×. Less size and customer concentration, perhaps −0.5×. Possibly plus something for higher growth prospects in a less mature logistics market, perhaps +0.5×. That gives roughly 6.0×. Mark for whether each step has a stated direction and reason, not for the specific magnitudes.
  2. A multiple is approximately 1/(r − g), so it falls as r rises — the two are the same statement expressed in different units. Country risk raises the required return because investors face currency, inflation, policy, and enforcement risks that they do not face in a developed market. In a DCF that appears explicitly as a country risk premium added to the discount rate; in a comparables valuation it appears as a downward adjustment to the multiple. Applying both without noticing would double-count the same economics.
  3. The adjustments pull in opposite directions: higher growth raises the multiple, while worse cash conversion and higher risk both lower it. The net direction depends entirely on the relative magnitudes, and there is no general answer — a small growth advantage will not offset a large risk difference, and vice versa. This is precisely why each adjustment must be sized rather than merely listed, and why a walk-down that only names directions is incomplete.
  4. The error overstates the value, and by a substantial margin. The listed comparables are larger, more liquid, and tradeable immediately, while the private target is none of these — and empirical private-company discounts are typically in the range of twenty to thirty-five percent. If country and business-model differences also apply and are unadjusted, the overstatement can easily exceed fifty percent. The reasoning is that every dimension on which a private target typically differs from listed comparables pushes the multiple in the same downward direction.
  5. For zero: the size penalty is already captured in the −1.25× illiquidity and size step, so applying it again double-counts; and a nine-branch chain in a growing Accra market has materially more expansion runway than a saturated global operator, which is a genuine offsetting positive. For −2.0×: a twelve-outlet business has weak purchasing power against suppliers, no meaningful brand moat, and severe concentration risk in one city — losing two or three locations to lease disputes would be existential in a way it never is for a large chain. Stronger case: the argument for zero, because the growth runway is real and the size effect is genuinely double-counted; but the disagreement itself is the honest finding and should appear in the write-up as the range 5.5× to 6.5×.

11.5

  1. The forecast is too optimistic — most likely if it came from management; check it against the company's own history and against the comparables' actual growth rates. The discount rate is too low — check it against local corporate borrowing costs and against what the comparables' pricing implies. Or the company genuinely has better prospects than the comparables — this requires a specific, nameable reason such as a contracted expansion or a structural cost advantage, and if none can be named, the first two explanations are far more likely.
  2. Multiples derive value from what the market is currently paying for similar companies, so if every comparable is overpriced the method will conclude that your company is worth a correspondingly inflated amount. A DCF never looks at market prices — it derives value from the company's own expected cash flows and a discount rate constructed from first principles. It is therefore the only method capable of concluding that an entire industry is priced above what its fundamentals support.
  3. Averaging treats three estimates as equally reliable when they clearly are not — the GH₵50M figure is an outlier and the analyst has buried that fact rather than explaining it. The reported figure is one that no method produced and no reasoning supports. What should have been reported is the range, with the two clustered estimates identified as the core of the recommendation and the outlier presented separately with an explanation of why it is lower and how much weight it deserves.
  4. Model answer: "Our analysis supports a value of GH₵120 to 155 million, and we would recommend opening at around GH₵165 million. The two methods bracket the range rather than agreeing tightly, so we would treat the midpoint as a target rather than a floor. We would advise walking away below GH₵115 million, since that falls beneath both estimates and would require assumptions neither method supports. The main uncertainty is the discount rate, and we would want it tested before committing to the lower bound."

11.6

  1. Model answer: "The business is worth around GH₵140 million. That comes from two independent methods that agree — a discounted cash flow and comparable-company multiples. The number depends most on [named assumption], and we will come to the method if useful."
  2. Model answer: "The business is worth between GH₵200 and 240 million, and we would recommend opening at GH₵255 million and walking away below GH₵190 million. That range is supported by a DCF at GH₵215 million and comparable multiples giving GH₵205 to 238 million — two independent methods pointing at the same place. The answer depends most on the discount rate; if it is two points higher the value falls to around GH₵180 million, and that is the assumption we would most welcome challenge on. Three things could move this that are not in the model: customer concentration, the outcome of the pending lease renewals, and whether the current management team stays."
  3. What's driving the number? "The discount rate — at 34% in cedis we get GH₵36.5 million; at 40% we get about GH₵22 million." Why those comparables? "We started from global pharmacy retail groups and adjusted down for the company-owned model, Ghana country risk, and illiquidity — and that walk-down landed within a quarter turn of the African listed comparables we arrived at independently." What would change your mind? "Evidence that the two newest outlets are not converging on the maturity curve we assumed, or that a material share of trade depends on the founders personally." What don't you know? "The lease terms on four sites due for renewal within two years, and how concentrated the customer base is by daypart and location."
  4. Because the precision is not real — nothing in a valuation resting on a forecast discount rate and a selected comparable set supports three significant figures. Claiming it invites the audience to test the precision rather than engage with the reasoning, and the first challenge will expose it. A range communicates both the estimate and the confidence attached to it, which is the information the decision-maker actually needs.