MRP Finance Internship Unit 09

Unit 09 · Practice solutions

Practice solutions

Company Valuation: Discounted Cash Flow · Kenya · KSh

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

9.1

  1. The machinery is identical — free cash flow, discounting, an explicit forecast, sensitivity testing. What differs is that a project has a defined end, so its terminal value can sometimes be a genuine salvage figure, while a company is assumed to continue indefinitely. That means the terminal value must capture an infinite stream and typically accounts for the majority of the answer, which makes the assumptions behind it far more consequential.
  2. Use KSh 97M — operating profit of 120 less the 9 of interest income and the 14 gain on disposal, neither of which is produced by the operating business. The interest income is accounted for by adding the cash balance in the bridge; the gain on disposal is a one-off and is excluded entirely, though the proceeds would appear as cash if still held.
  3. FCFF is the cash available to all providers of capital before any debt service, and is discounted at the WACC to give enterprise value. FCFE is what remains after interest and principal payments to lenders, and is discounted at the cost of equity to give equity value directly.
  4. Recurring contracted revenue is far more predictable than one-off installation work, so a high proportion reduces the business risk of the whole firm and therefore the rate at which its cash flows should be discounted — it also survives a downturn better. I would want to know the average remaining term and renewal rate of those contracts, and whether they are with the company or effectively with the founder personally.

9.2

  1. Year 1: revenue 600 × 1.08 = KSh 648M; EBIT = 648 × 12% = KSh 77.76M; after tax = KSh 54.43M; ΔWC = 15% × 48 = KSh 7.2M. FCFF = 54.43 + 25 − 30 − 7.2 = KSh 42.23M. Year 2: revenue = KSh 699.84M; EBIT = KSh 83.98M; after tax = KSh 58.79M; ΔWC = 15% × 51.84 = KSh 7.78M. FCFF = 58.79 + 25 − 30 − 7.78 = KSh 46.01M.
  2. Capex below depreciation deserves investigation because it may indicate that the model is harvesting tangible assets and temporarily inflating cash flow, but it is not automatic proof of error. Growth may use spare capacity or arrive through acquisitions, leases, intangible investment or working capital rather than owned fixed assets; depreciation may also reflect historical cost and accounting lives that do not match current replacement spending. Reconcile growth to total reinvestment — net capex, incremental working capital and economically equivalent acquisitions, leases and intangibles — and test whether any use of spare capacity is finite and explicitly modelled. In terminal steady state, the harder constraint is `g = ROIC × reinvestment rate`; perpetual growth with zero total reinvestment is impossible.
  3. First, ten years of 22% growth means the firm becomes roughly 7.3 times its current size, which for most companies implies capturing an implausible share of its market — the forecast should be checked against total market size. Second, the jump from 22% to 3% at a single point is a discontinuity no business experiences; growth decays gradually, and a forecast that steps down abruptly at the terminal year usually means the horizon was too short and the terminal value is doing work the forecast should have done.
  4. Two-thirds of the value sits beyond the explicit forecast, so refining the near-term forecast has limited leverage while the terminal assumptions dominate. The analytical effort should go into the two assumptions inside the terminal value: the discount rate and the terminal growth rate. That is also why the sensitivity grid in 9.6 varies exactly those two.

9.3

  1. TV = 80 × 1.06 / (0.15 − 0.06) = 84.8 / 0.09 = KSh 942.2M. Implied multiple = 942.2 / 145 = 6.5×. Comparables trade at 7×, so the perpetuity is slightly more conservative than the market — the two are consistent, which supports the valuation. If anything it suggests the growth or discount-rate assumptions are modestly cautious.
  2. Real growth = 1.04/1.03 − 1 = 0.97%. Defensible for a mature manufacturer: it assumes the firm grows very slightly faster than inflation forever, holding roughly its position in a growing economy without gaining share. A figure much above real GDP growth would not be defensible.
  3. Liquidation is appropriate when the assets are worth more than the cash flows they generate — a depleting resource, a retailer whose property exceeds the value of its retail operation, or a distressed firm a buyer would break up. If liquidation value exceeds going-concern value, the operating business is destroying value: the owners would be better off selling the assets and closing, and management should be asked why it continues.
  4. The discount rate may be too low; the terminal growth rate may be too high; or the firm may genuinely deserve a premium — higher margins, better growth, stronger competitive position than the comparables. I would investigate the discount rate first, because it is the least observable of the three and because a 14× implied multiple against a 6× market is such a large gap that a modelling error is more likely than a genuine premium of that size.

9.4

  1. 900 − 220 + 40 − 60 + 55 = KSh 715M. Debt and the minority interest are subtracted as prior claims; cash and the associate stake are added as assets not captured in the operating cash flows.
  2. The DCF discounted only the cash flows produced by the operating business, and a bank balance produces none — it simply sits there. Since the shareholders own that balance in addition to the operating business, it must be added separately. Including it in the DCF instead would require forecasting interest income, which then has to be stripped out to avoid double-counting.
  3. At book: 500 − 400 = KSh 100M. At market: 500 − (400 × 0.55) = 500 − 220 = KSh 280M. The market figure is correct — the lenders' claim is worth what the market says it is worth, and that is what it would cost to extinguish it. Using face value here understates equity value by KSh 180M, which for a distressed firm is the difference between an equity stub worth almost nothing and a meaningful claim.
  4. The error is double-counting the cash: the DCF has already capitalised the interest income the cash produces, and the bridge then adds the cash itself. It overstates equity value. Interest income of 100 × 9% = KSh 9M capitalised at a 14% WACC is worth roughly 9/0.14 = KSh 64M, and the bridge adds KSh 100M on top — so the cash is being valued at about KSh 164M instead of KSh 100M, an overstatement of roughly KSh 64M.

9.5

  1. (a) Country risk — business risk is low (stable demand) and financial risk is nil (no debt), so what remains is whatever the operating environment imposes. (b) Financial risk — high leverage against a cyclical, illiquid asset base. (c) Country risk — the business itself may be sound and unlevered, but a regulator that can change the rules is the dominant threat. (d) Business risk — no proven model and no revenue, and there is no debt to create financial risk.
  2. The operating cash flows are produced by the assets and are unaffected by how those assets were funded. But interest is a fixed claim that must be paid before the owners receive anything, so the owners' return is the operating cash flow minus a constant. Subtracting a constant from a variable quantity leaves the same absolute variation concentrated on a smaller base, which means a much larger proportional swing. That amplification is financial risk, and it exists even though nothing about the business has changed.
  3. Because business risk usually dominates financial risk. The utility's revenue is regulated, contracted, and largely insensitive to the economy, so even a heavily levered claim on it has fairly predictable cash flows — and the debt exists precisely because the stability supports it. The software start-up has no debt but also no proven revenue, so its equity cash flows range from nothing to a great deal with no contractual floor beneath them.
  4. The difference is the total premium the valuation is charging for everything that makes this company riskier than lending to the Ugandan government — credit risk, the equity's residual position behind that credit risk, and illiquidity. Three points is far too little for all three. An ordinary corporate bond from a solid private borrower would already trade several points wide of the sovereign, and equity ranks *behind* that bond, so the equity premium alone should exceed the credit spread. A more defensible range would be roughly 22% to 26%: the sovereign at 16%, plus something like three to five points of corporate credit risk, plus a further three to five points for the residual position and for the fact that no one can sell this stake quickly at any price. The precise figure is Week 10's work; the point here is that a gap this narrow is not a judgement about the company, it is a sign that nobody checked the rate against the risk-free alternative at all.

9.6

  1. At g = 5%: 60 × 1.05 = 63; TV at 13% = 63/0.08 = 787.5; at 15% = 63/0.10 = 630.0; at 17% = 63/0.12 = 525.0. At g = 7%: 60 × 1.07 = 64.2; at 13% = 64.2/0.06 = 1,070.0; at 15% = 64.2/0.08 = 802.5; at 17% = 64.2/0.10 = 642.0.
  2. Because the denominator is WACC − g, so a higher g makes the denominator smaller before the WACC change is applied. At g = 5% moving WACC from 13% to 17% changes the denominator from 0.08 to 0.12, a 50% increase, cutting the value by a third. At g = 7% the same move changes it from 0.06 to 0.10, a 67% increase, cutting the value by 40%. The closer g gets to WACC, the more violent the effect of any change in either.
  3. Because the range reflects genuine uncertainty about two assumptions that cannot be observed — the appropriate discount rate for a private business and its growth rate in perpetuity. A single point estimate would not reduce that uncertainty; it would conceal it and imply a precision the analysis does not have. The grid is the analysis reporting honestly what it knows and what it does not, which is more useful to a decision-maker than a false point.
  4. Model answer: "Our central estimate puts the business at close to the asking price, so on our base assumptions this is neither a bargain nor an overpayment. The answer is however sensitive to the discount rate, which moves the value by roughly a third across the range we would consider defensible. We would therefore not recommend paying the asking price without first satisfying ourselves on that rate, and we would set a walk-away price at the level implied by the more conservative end of the range. If the seller will not move below that level, the transaction does not create value for you and you should be prepared to decline."
  5. The grid varies *financial* assumptions — the discount rate and terminal growth — while holding the forecast itself constant. The managing director's departure is a risk to the forecast, not to the rate: if the relationships behind 60% of revenue leave with him, revenue may fall outright rather than grow, and no cell anywhere on the grid describes that outcome. Widening the grid does not help either, because the risk is not that the assumptions are imprecise; it is that they are conditional on something the grid does not contain. Two structures address it. An earn-out makes part of the price contingent on revenue or profit being sustained for two or three years after completion, so the seller carries the risk of the thing only the seller can influence. A retention arrangement keeps him in a defined transitional role — typically twelve to twenty-four months of formal handover to named account managers — with part of the consideration deferred against it. Both work by moving the risk back toward the person best placed to manage it, which is the general principle worth remembering: when a risk sits outside the model, the answer is usually a change to the deal rather than a change to the discount rate.