The Tea-Processing Unit's Five-Year Deployment Decision
Ranjan Barua owns a small tea-processing unit near Jorhat. He has just sold a plot of land for ₹12,00,000 and must choose between two five-year uses of the money. Option A is a bank fixed deposit paying 8.5% per annum compounded quarterly; interest is reinvested and the principal is repaid at maturity. Option B is a lease-back arrangement with a local machinery supplier: Ranjan pays ₹12,00,000 now and receives ₹3,20,000 at the end of each of the next five years, plus a residual payment of ₹1,00,000 at the end of year 5. The supplier is a small, thinly capitalised firm, and the lease-back payments are unsecured. Ranjan's banker treats a similar unsecured exposure as requiring a 12% annual return. Ranjan is risk-averse, needs at least ₹15,00,000 at the end of year 5 for his daughter's education, and cannot borrow cheaply against the lease-back receipts. He asks you to compare the two options on both a stated-rate and a risk-adjusted basis and to comment on whether either meets his education target.
1. Calculate the maturity value and effective annual rate of Option A. Show the formula and each step.
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Option A: quarterly compounding means the periodic rate is 8.5%/4 = 2.125% and the number of periods is 5×4 = 20.
Maturity value = ₹12,00,000 × (1.02125)^20.
(1.02125)^20 ≈ 1.5228, so maturity ≈ ₹18,27,354.
Effective annual rate = (1.02125)^4 − 1 ≈ 0.08775, or 8.77%.
The stated rate is 8.5%, but the effective return is higher because interest is reinvested quarterly. The ₹15,00,000 education target is met by a margin of about ₹3.27 lakh if the deposit is held to maturity.
2. Value Option B at 8.5% and at 12%. What does the difference tell you about the price of credit risk?
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At 8.5%: annuity factor for five years = [1 − (1.085)^−5]/0.085 = 3.9406. PV of receipts = ₹3,20,000 × 3.9406 = ₹12,61,005. PV of residual = ₹1,00,000/(1.085)^5 = ₹66,505. Total PV ≈ ₹13,27,510; NPV = +₹1,27,510.
At 12%: annuity factor = [1 − (1.12)^−5]/0.12 = 3.6048. PV = ₹3,20,000 × 3.6048 = ₹11,53,529. Residual PV = ₹1,00,000/(1.12)^5 = ₹56,743. Total ≈ ₹12,10,272; NPV ≈ +₹10,272.
The risk-adjusted NPV is barely positive. The 12% rate removes almost all the apparent premium. That difference is the price the market charges for the supplier's credit risk and for the illiquidity of the receipts.
3. Which option should Ranjan choose, and does it meet the ₹15,00,000 target? State two non-numeric factors.
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On stated rates, Option B looks better; on risk-adjusted terms it is almost a tie, with only about ₹10,000 of value added for taking unsecured exposure to a thinly capitalised supplier. Ranjan is risk-averse and needs a reliable ₹15 lakh at year 5. The FD matures at about ₹18.27 lakh, so it meets the target with low credit risk, subject to deposit-insurance limits.
The lease-back's contractual receipts total ₹17 lakh before reinvestment, but the year-5 outcome depends on the supplier's solvency and on reinvestment rates. If receipts are reinvested at lower rates, the terminal fund may fall short. Recommendation: choose the FD unless the supplier provides a bank guarantee or escrow, which would justify re-evaluating at a lower discount rate. Non-numeric factors: liquidity needs before year 5 and the cost of monitoring the supplier.