MRP Finance Internship Unit 04

Unit 04 · Practice solutions

Practice solutions

Working Capital and Short-Term Finance · 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

4.1

  1. Extra cash = 20.4% × 80 = ₦16.3M. Profit on the new sales at 6% = 80 × 6% = ₦4.8M, and on total revenue of ₦330M = ₦19.8M. The growth alone does not fund itself — ₦4.8M against ₦16.3M — but total retained profit of ₦19.8M would cover it if the firm pays no dividend and has no capital expenditure. Realistically it is close to the limit.
  2. Firm A must find ₦24M of additional cash before it sees any of the profit — it will need a facility or must slow down. Firm B receives ₦4M of cash as it grows, because customers pay before suppliers are paid. A is plausibly an industrial distributor, construction contractor, or anyone selling to government; B is plausibly a supermarket, restaurant chain, or mobile-money agent network.
  3. You are right that each sale is profitable, and nothing in the analysis disputes that — the business earns a margin on everything it sells. The problem is timing: each new sale requires you to buy stock and wait sixty days to be paid, so roughly twenty kobo of cash goes out and stays out for every naira of new annual sales. At 19.7% intensity, growing sales by ₦100M absorbs ₦19.7M of cash while generating perhaps ₦5M of profit. So the faster you grow, the larger the hole — and the business becomes more valuable and less solvent at the same time.

4.2

  1. Let X be the new sales. Receivables after = (180+X) × 75/365. Extra receivables = (180+X)(0.2055) − 22.19. Funding cost = 0.26 × that. Gross profit = 0.30X. Setting them equal: 0.30X = 0.26[0.2055(180+X) − 22.19] → 0.30X = 0.26[36.99 + 0.2055X − 22.19] → 0.30X = 3.848 + 0.05343X → 0.24657X = 3.848 → X ≈ ₦15.6M. Below about ₦15.6M of new sales the change destroys value.
  2. The benefit side scales with the gross margin while the cost side depends only on the receivable balance and the funding rate, which are the same for both firms. The 55%-margin firm earns ₦550,000 of gross profit per ₦1M of incremental sales against a funding cost of perhaps ₦45,000 on the associated receivable; the 12%-margin firm earns ₦120,000 against the same ₦45,000. The high-margin firm can therefore absorb far longer terms, more bad debt, and more non-incremental sales before the decision turns negative.
  3. The argument is that fixed costs are already incurred, so any order contributing positive gross margin improves profit — which is true as far as it goes and is the standard contribution argument. It fails here because the constraint is not fixed-cost recovery but cash: the order consumes ₦42.74M of funding, and no amount of fixed-cost coverage helps if the firm cannot fund the receivable. It would be correct if Ilupeju had spare cash and no funding constraint, and if the order were genuinely incremental — in that case ₦12M of contribution against zero incremental funding cost is clearly worth taking.

4.3

  1. The firm now gets 35 extra days instead of 20, so periods per year = 365/35 = 10.43, and the effective rate falls to (1.020408)^10.43 − 1 = 23.5%. It is cheaper, but the firm is taking credit it was not granted: it risks the supplier tightening terms, demanding cash on delivery, deprioritising its orders when stock is short, or — in a market where a reliable supply chain is the whole business — declining to supply at all. The 4.4 saving is small relative to that.
  2. Net period 60, discount period 10, so 50 days per period and 365/50 = 7.3 periods. We need (1 + d/(100−d))^7.3 − 1 ≤ 0.12, so 1 + d/(100−d) ≤ 1.12^(1/7.3) = 1.01565. Therefore d/(100−d) ≤ 0.01565, giving d ≤ 1.541. The largest offer is about 1.5/10 net 60, costing roughly 11.7% effective.

4.4

  1. Simple annualised = 3.5% × 12 = 42.0%. Effective = (1.035)^12 − 1 = 51.1%. They differ because the simple figure ignores compounding — each month's charge is levied on a balance that has not been reduced, so the borrower pays interest on interest across the year. The gap widens as the monthly rate rises.
  2. Most available first: supplier credit (needs only an existing trading relationship, no financial disclosure); LPO financing (secured on the order and the buyer's credit, requires almost nothing of the borrower); invoice discounting (requires an issued invoice and a verifiable customer, plus some documentation); bank term loan (requires audited accounts, history, security, and usually personal guarantees — unavailable to this firm). The ranking is almost exactly the reverse of the price ranking, which is the point of the video.
  3. LPO rolled continuously: 4% per month compounded is (1.04)^12 − 1 = 60.1% per year, or on a simple basis 120 × 48% = ₦57.6M; compounded the true cost is about ₦72M. At 27% a term loan costs 120 × 27% = ₦32.4M. The annual saving is roughly ₦25M on the simple basis and closer to ₦40M compounded — more than most such firms earn in a year. To obtain it the firm would need audited financial statements, two to three years of clean banking history, security over property or receivables, and personal guarantees from the owners.

4.5

  1. Days = 85 × 365 / 420 = 73.9 days. At 50 days, inventory = 420 × 50/365 = ₦57.53M, releasing ₦27.47M and saving 27.47 × 32% = ₦8.79M per year.
  2. Variability = 11 − 5 = 6 weeks. Safety stock = 6 × 3.2 = ₦19.2M. If the worst case falls to 7 weeks, variability = 2 weeks and safety stock = ₦6.4M, releasing ₦12.8M. At 30% carrying cost that improvement is worth ₦3.84M per year, plus the one-off ₦12.8M release.
  3. First, a uniform cut ignores that different lines have different stockout consequences — cutting a fast-moving line where failure loses a customer relationship is far more damaging than cutting a slow-moving line, and an across-the-board rule does the same thing to both. Second, it treats the symptom rather than the cause: much of the stock exists to cover supply variability, so cutting it without fixing lead-time reliability simply converts a carrying cost into a stockout cost, which is usually larger. Instead, segment the range — hold buffer stock only on high-value, relationship-critical lines; run the slow-moving tail to order; dual-source the items with the worst lead-time variability; and negotiate consignment terms where the supplier retains ownership until use.