MRP Finance Internship Unit 08

Unit 08 · Practice solutions

Practice solutions

Project Valuation · Nigeria · ₦

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

8.1

  1. (a) Project — commits capital now for lower running costs and improved conditions over years. (b) Not a project — a recurring operating cost with no capital committed against future returns. (c) Project — cost incurred now for higher sales over subsequent periods; the fact that it is expensed rather than capitalised does not change the economics. (d) Project in the financial sense — cash committed now to avoid future interest payments, and it should be evaluated against alternative uses of the same cash. (e) Project — payment now for future gross profit from those customers.
  2. What specifically is different about this market or offer that supports revenue 40% above anything achieved before? What did the last three forecasts this team produced deliver against actual? What would the NPV be at the company's historical best rather than at the forecast? If the answers are unconvincing, do not reject outright — re-run the analysis at a defensible revenue level, show what the project is worth at that level, and let the decision be made on the realistic case rather than on an argument about optimism.
  3. The discounting is mechanical arithmetic that a spreadsheet performs identically every time, and the formulas are short enough to check. The judgment is entirely in the inputs — revenue, costs, capital spending, terminal assumptions — and each of those is an estimate that can be materially wrong. A model with perfect discounting and a 20% revenue error produces a 20%-wrong answer with complete internal consistency.
  4. First, identify the assumption the answer depends on and hand it back as a question — "this works if the site does ₦148M in year one; is that achievable?" — which converts a verdict into a discussion the operations director can win with evidence. Second, state what would have to change for the answer to flip: a lower fit-out cost, a different lease structure, a smaller initial format. Both keep finance in the role of informing the decision rather than making it, which is also more likely to be listened to next time.

8.2

  1. (a) Exclude — sunk; spent regardless of the decision. (b) Include — opportunity cost; the firm forgoes rent it could otherwise collect. (c) Exclude — financing cost, already captured in the discount rate. (d) Include — a side effect on the rest of the firm, and a real reduction in total cash flow. (e) Exclude — those salaries are paid whether or not the project proceeds, so they fail the incremental test; any additional finance staff hired for the project would be included.
  2. ₦180M — the current market value, as an opportunity cost at Year 0. The ₦30M paid ten years ago is sunk and irrelevant. Using the land for the project means giving up the ability to sell it for ₦180M, and that forgone amount is what the project must justify. (If the land would be retained and sold at the end of the project, the treatment is an outflow of ₦180M now and an inflow of its expected value later.)
  3. New revenue: ₦60M × 45% = ₦27.0M of contribution. Lost revenue at the existing product: ₦60M × 30% = ₦18M, at a 55% margin = ₦9.9M of contribution lost. Incremental contribution = 27.0 − 9.9 = ₦17.1M, not ₦27.0M — the naive figure overstates by 58%.
  4. Because the discount rate already represents the return required by everyone who funded the project, including the lenders. Deducting interest from the cash flows and then discounting at a rate that includes the cost of debt charges for the same thing twice. The free-cash-flow construct deliberately measures cash available to all providers of capital, before any of them are paid. Whether the project is funded with debt or equity is a separate decision that does not change what the project itself produces.
  5. Compare the residential catchment of the two sites and estimate walking and driving times between them. Ask the existing branches for prescription or loyalty-card address data, or run a short survey at the busiest branch asking where customers live and work. And look for a natural experiment inside the firm's own history: when the fourth branch opened, what happened to the sales of the branch nearest it? A chain with four branches has almost certainly run this experiment already without recognising it as one. If none of the three is obtainable, do not assume zero: model a range of 0% to 10%, present the NPV across it, and state plainly that the project's viability depends on an unmeasured quantity.

8.3

  1. EBIT = 240 − 186 − 22 = ₦32M. After tax = 32 × 0.70 = ₦22.4M. FCF = 22.4 + 22 − 15 − 6 = ₦23.4M.
  2. It is subtracted before tax because tax authorities allow it as a deduction, so it genuinely reduces the cash tax bill — ignoring it would overstate tax paid. It is added back afterwards because no money actually left the business: the cash went out when the asset was purchased. The net effect is that depreciation is not a cash cost but does produce a cash benefit equal to the tax saved, which is exactly what this treatment captures.
  3. A benign explanation is a large late-period sale to a strong customer or a deliberate extension of terms to sound customers; the cash-flow forecast should then carry the longer collection period and fund the additional working capital. An aggressive explanation is premature revenue recognition combined with an inadequate loss allowance; forecast revenue and receivables may both be overstated, so simply financing the balance is not enough. Distinguish them with the receivables ageing, post-period cash collections, customer concentration, returns or credit notes, contract terms, and the history of provision adequacy. The question is whether the model contains genuine working-capital investment, weak collection, or revenue that was never economically earned.
  4. Year 3 operating expenses at 15% growth = 62 × 1.15² = ₦81.99M, against ₦77.77M at 12% — ₦4.22M higher. EBIT falls from ₦10.26M to ₦6.04M. After-tax EBIT = ₦4.23M; FCF = 4.23 + 17 − 0.62 = ₦20.61M, down from ₦23.56M. A three-point change in one cost growth rate removes 12.5% of that year's free cash flow, which shows how little protection a 5.6% operating margin provides against cost inflation.

8.4

  1. Naïve: FCF₆ = 40 × 1.06 = ₦42.40M; TV = 42.40/(0.18 − 0.06) = ₦353.33M. Economic bridge: EBIT₆ = 34 × 1.06 = ₦36.04M; NOPAT₆ = 36.04 × 70% = ₦25.23M; required reinvestment rate = 6%/12% = 50%; FCF₆ = 25.23 × (1 − 50%) = ₦12.61M; TV = 12.61/0.12 = ₦105.12M. The naïve terminal value is overstated by ₦248.21M.
  2. Depreciation is an approximate measure of assets consumed, so capex equal to depreciation is a useful check that existing capacity is being maintained. It does not fund the additional operating assets required for perpetual growth. The complete test reconciles total reinvestment — net capex, working capital and economically equivalent acquisitions, leases or intangibles — to `g/ROIC`. A model can therefore pass the maintenance-capex screen and still overstate terminal free cash flow.
  3. Real growth = 1.03/1.18 − 1 = −12.7%. The assumption implies the business shrinks by nearly thirteen percent a year in real terms, forever — which is not conservative, it is drastic, and it would substantially understate the value of any healthy business. The analyst has imported a real growth rate into a nominal model.
  4. First, that the valuation rests overwhelmingly on assumptions about a period nobody can forecast, so the apparent precision of the explicit forecast is misleading. Second, that the answer will be highly sensitive to r and g, both of which appear in the terminal-value denominator. In presenting it I would show the NPV across a grid of r and g values rather than a single figure, and state explicitly what share of the total value comes from beyond the forecast horizon.
  5. The five-year discount factor at 20% is 1/1.20⁵ = 0.4019. At 4×: TV = 4 × 46 = ₦184M; PV = 184 × 0.4019 = ₦73.95M; NPV = −200 + 112 + 73.95 = −₦14.05M. At 6×: TV = ₦276M; PV = ₦110.92M; NPV = +₦22.92M. Present both, and lead with neither. The honest statement is that the project's value depends almost entirely on an assumption about what a buyer will pay in five years — a claim about market conditions at a future date rather than about this business — and that the assumption is large enough to decide the answer on its own. A recommendation that leads with +₦22.92M has quietly chosen the exit multiple that produced the conclusion it wanted; one that leads with −₦14.05M has done the same thing in the other direction. Present the range, name the multiple as the driver, and say what evidence would narrow it.

8.5

  1. (a) Below — the bakery knows its demand, the equipment is proven, and the incremental output is an extension of an existing operation with observable economics. (b) Well above — new regulatory regime, new currency, new competitors, no local track record, and banking is a business where local knowledge and relationships matter enormously. (c) Below — the hotel exists and its occupancy is observable; the uncertainty is confined to how much refurbishment lifts rates. (d) Well above — manufacturing has a completely different cost structure, capital intensity, and operating risk from distribution, and the firm has no experience of it.
  2. First, it will reject safe, high-quality maintenance and replacement projects whose true risk is well below 18%, gradually degrading the asset base and operating efficiency of the core business. Second, it will approve speculative new ventures whose true risk is 30% or more, because discounting them at 18% inflates their apparent value — so over ten years the firm will have starved what works and funded a series of things that did not.
  3. If Treasury bills yield about 20%, a 22% rate implies a risk premium of only about two percentage points over government paper for an equity-risk restaurant project — which is implausibly thin, since even a solid corporate bond would carry a wider spread than that. I would check what Nigerian Treasury yields and inflation expectations actually are at the date of the analysis, where the 22% came from and when it was last reviewed, and whether it was borrowed from a dollar-denominated context and applied to naira cash flows without adjustment.
  4. The colleague is right, but the reasoning needs stating precisely: a thin margin does not make the cash flows riskier in itself, it makes them more sensitive — the same absolute shock to revenue or cost destroys a much larger share of the profit. That greater variability in outcomes is genuine risk and does justify a higher rate. The more useful response, though, is to show it in the sensitivity table rather than bury it in the discount rate, since that tells the client which shock to worry about.

8.6

  1. Cumulative: 18, 40, 64, 84. Outlay of ₦50M is recovered during Year 3 — after Year 2 cumulative is ₦40M, leaving ₦10M of a ₦24M year, so payback ≈ 2.4 years. NPV at 15%: 18(0.8696) + 22(0.7561) + 24(0.6575) + 20(0.5718) = 15.65 + 16.63 + 15.78 + 11.44 = ₦59.50M, so NPV = +₦9.50M. At 25% the PV is about ₦50.9M, so the IRR is roughly 24%.
  2. Project A creates NPV of a few hundred thousand naira at most on a ₦5M outlay; Project B creates far more value in absolute terms on ₦120M at a 24% return against an 18% cost of capital. Since the firm can fund both, it should do both — but if forced to choose, B creates more value. The point is that IRR is a rate and value is an amount: a very high return on a very small base can be worth less than a moderate return on a large one, so IRR must never be used to rank mutually exclusive projects of different scale.
  3. It will reject projects with long build phases and large later cash flows — infrastructure, property, plantation agriculture, anything where the returns arrive in years four to ten. It will also reject projects with modest early cash flows and very long lives, which are often the highest-NPV opportunities available. A firm might legitimately keep the rule if its own funding is short-dated and uncertain, since a project it cannot finish is worth nothing regardless of its NPV — the rule is a crude constraint on liquidity risk rather than a valuation rule.
  4. PIs: A 100/80 = 1.25; B 69/60 = 1.15; C 68/50 = 1.36; D 103/90 = 1.14; E 46/40 = 1.15. Ranking by PI: C, A, B/E, D. Take C (₦50M) and A (₦80M) for ₦130M, leaving ₦70M — then B (₦60M) fits, using ₦190M for a total PV of 68 + 100 + 69 = ₦237M against ₦190M spent, an NPV of ₦47M. Checking alternatives: C + A + E uses ₦170M for PV of ₦214M (NPV ₦44M), and C + D + E uses ₦180M for ₦217M (NPV ₦37M). Best combination: C, A and B — NPV ₦47M. Note that strict PI ranking gets you there but should always be checked against the budget remainder.

8.7

  1. Fragile. The NPV crosses zero at roughly 18.7%, inside the range of rates a reasonable analyst might defend. I would say the project creates value only if the right discount rate is below about 18.7%, so the recommendation is really an argument about the riskiness of these cash flows rather than about the project — and I would want the rate justified against comparable investments before committing.
  2. Because operating profit is the small difference between two large numbers, so a given percentage change in revenue produces a much larger percentage change in profit when the margin is thin. Example: on ₦100M of revenue, the 4%-margin project earns ₦4M and the 20%-margin project earns ₦20M. A 5% revenue miss removes ₦5M of revenue; if costs are largely fixed, the first project's profit falls from ₦4M to −₦1M (a swing of 125%) while the second falls from ₦20M to ₦15M (a swing of 25%).
  3. Each 10% reduction in Year 1 revenue costs ₦31M of NPV, and the base case has ₦18M to give away. So the NPV reaches zero at 18/31 of a 10% step, which is a 5.81% shortfall — a Year 1 revenue of 95 × (1 − 0.0581) = approximately ₦89.5M, about ₦5.5M below plan. Whether that is small enough to worry about depends entirely on how forecasts at this firm have behaved before. A 5.8% miss is well inside the ordinary error of a first-year revenue forecast for a new site, so the correct reading is that the project is *fragile rather than unattractive*: it does not need anything to go badly wrong, only slightly less well than planned. The recommendation should say so explicitly and should ask for the firm's record of first-year forecasts before the money is committed.
  4. Sensitivity analysis changes one assumption at a time while holding all others at base, isolating each variable's individual effect. Scenario analysis moves several assumptions together in combinations that could plausibly occur, producing a small number of coherent pictures of the future. Sensitivity understates downside risk because in reality bad assumptions are correlated — a weak economy delivers lower revenue and a worse currency and higher input costs simultaneously, so the true bad case is worse than any single-variable row suggests.