Two Loan Offers, a Seasonal Cash Flow and a Supplier Discount
Rana runs a stationery shop and needs 12,000 dinars to renovate before the school year. Bank A offers a 24-month loan at 12% annual flat (simple) interest with a 1% arrangement fee deducted from the disbursed amount. Bank B offers a 24-month reducing-balance loan at 14% annual interest with no fee and equal monthly payments of 576 dinars. Rana's net monthly cash from operations averages 620 dinars, but that average comes from twelve months in which three summer months produced 250 dinars each and the remaining nine months averaged 743 dinars. Her supplier offers terms of 2/10, net 60 on purchases of about 3,000 dinars a month, and she currently pays on day 60. She has 1,500 dinars of savings, no other borrowing capacity, and wants to keep at least 800 dinars of cash buffer at all times.
1. Compute the total cost and approximate effective annual cost of each loan and recommend which one Rana should take.
Read the worked answer
Bank A (flat rate + fee)
- Flat interest = 12,000 × 12% × 2 years = 2,880
- Total repayments = 14,880 → monthly = 14,880 ÷ 24 = 620
- Arrangement fee = 1% × 12,000 = 120, deducted up front, so cash actually received = 11,880
- True finance cost = 14,880 − 11,880 = 3,000 dinars
A flat rate is charged on the full 12,000 for both years even though the balance falls to zero. Rough effective cost: average outstanding ≈ 6,000, annual finance cost ≈ 1,500 → about 25% a year (a proper IRR on 11,880 received and 620 × 24 paid gives roughly 22–23% nominal, ~25% effective).
Bank B (reducing balance)
- Total repayments = 576 × 24 = 13,824 → interest = 1,824 dinars
- IRR: 12,000 = 576 × annuity factor → factor = 20.83, which corresponds to about 1.15% a month, i.e. roughly 14.7–15% a year effective.
Comparison: Bank B costs 1,824 versus Bank A's 3,000 - 1,176 dinars cheaper over two years. Bank A's '12%' is not comparable to Bank B's '14%': the flat quote conceals a rate roughly double the one printed. Recommendation: take Bank B on price - but see the affordability test below, because Bank A's 620 payment exactly equals her average cash flow and leaves no buffer at all.
2. Test whether Rana can actually service each loan given the seasonal pattern, and quantify the reserve she needs.
Read the worked answer
Reconstruct the annual cash flow: 3 summer months × 250 = 750; 9 months × 743 = 6,687; total 7,437 → monthly average 619.75 ≈ 620 dinars, confirming her figure. The average is real, but it hides the shape.
Bank B (576/month)
- Normal months: 743 − 576 = +167 surplus
- Summer months: 250 − 576 = −326 per month, × 3 = −978 dinar shortfall
- She must hold a reserve of at least 978 just to keep paying; with the 800 buffer she wants, required reserve = 1,778 dinars. She has 1,500 → short by about 278 dinars.
Bank A (620/month) - worse in the seasonal sense even though the total cost is higher:
- Summer months: 250 − 620 = −370, × 3 = −1,110, plus the 800 buffer = 1,910 needed versus 1,500 available.
- Normal months: only +123 surplus - almost no room to rebuild the reserve.
Judgement: neither loan is comfortably serviceable on savings alone. Options, in order of preference:
- Reduce the borrowing to about 10,000 dinars (renovate in two phases) so the Bank B payment falls to roughly 480 and the summer deficit shrinks to ~690.
- Ask Bank B for a seasonal structure: lower instalments in the three summer months and higher in the other nine, so payments track cash.
- Keep 1,500 untouched as reserve by financing part of the fit-out from the supplier discount savings (next task) rather than from the loan.
What she must not do is rely on the 620 average as if it were a monthly minimum.
3. Should Rana start taking the 2/10, net 60 discount? Show the calculation and the liquidity constraint, and state your recommendation.
Read the worked answer
Cost of giving up the discount (the standard formula):
- Discount = 2% of the invoice; the money is kept for 60 − 10 = 50 extra days.
- Cost = (0.02 ÷ 0.98) × (365 ÷ 50) = 2.041% × 7.3 = ≈14.9% a year
Compare with the alternatives: Bank B costs about 14.7–15%, Bank A about 25%. So the discount is roughly equal to Bank B's cost and clearly better than Bank A's - a borderline case, not an obvious yes.
The liquidity constraint is decisive. Paying on day 10 instead of day 60 means financing 50 extra days of purchases:
- Monthly purchases 3,000 → daily ≈ 100 → extra cash tied up ≈ 100 × 50 = 5,000 dinars
She has 1,500 of savings and no further borrowing capacity; the loan is fully committed to the renovation. To capture the full discount she would need about 5,000 of additional short-term finance, which she does not have - and taking it at ~15% to earn 14.9% adds risk for no gain.
Recommendation: a partial, cash-led approach.
- Do not take the discount in the three summer months when cash is 250 dinars.
- Take it on one invoice at a time in strong months, using surplus cash (up to 167 dinars a month under the loan) plus any one-off receipts - this earns 14.9% risk-free on the small amount she can actually fund.
- Negotiate with the supplier: 1/10 net 45, or 2/10 net 30 on a smaller monthly order, so the financing gap falls within her 1,500 of savings.
- Revisit once the renovation is paid off and monthly free cash rises.