Outright purchase vs instalments vs lease: a present-value judgement
Meera runs a two-colour offset press in Coimbatore and needs a new digital press that costs ₹6,00,000 if paid outright. The dealer offers two alternatives. Plan A: five annual instalments of ₹1,35,000 each, the first payable exactly one year after installation. Plan B: a five-year usage lease at ₹1,20,000 per year, payable in advance on the first day of each year, the machine returning to the lessor at the end of the term. Meera's bank will fund an outright purchase at 10% per annum, and she uses this rate for every comparison she makes. Her accountant argues that Plan A should be rejected because it costs ₹6,75,000 in total cash, while Plan B at ₹6,00,000 is 'the same as paying cash'. Meera is not convinced by either argument and wants the comparison done on a present-value basis, with the annuity-due nature of the lease handled correctly. Given: PVIFA(10%,5) = 3.7908; PVIFA(14%,5) = 3.4331.
1. Evaluate Plan A against outright purchase on a present-value basis and state which option Meera should prefer.
Read the worked answer
The instalments form an ordinary annuity: five equal payments, first at the end of year 1.
PV = 1,35,000 × PVIFA(10%,5) = 1,35,000 × 3.7908 = ₹5,11,758 (approximately).
Against an outright price of ₹6,00,000, Plan A saves ₹88,242 in today's money, so Plan A is cheaper.
The accountant's figure of ₹6,75,000 is a nominal total. It adds rupees paid in years 1–5 to rupees payable today, which is an invalid comparison because a rupee received later is worth less. Equally, comparing only cash totals would wrongly favour the lease. The correct test is: what lump sum today has the same value as the promised stream? That is what the ₹5,11,758 measures.
Judgement point: the decision is not 'instalments are always cheaper'. It flips if the dealer's cash price falls below the present value of the instalments.
2. Evaluate Plan B, showing how the annuity-due treatment changes the number, and comment on whether the lease is really 'the same as paying cash'.
Read the worked answer
The lease payments start on day one, so this is an annuity due; each payment is discounted one year less than in Plan A.
PV = 1,20,000 × PVIFA(10%,5) × (1 + 0.10) = 1,20,000 × 3.7908 × 1.10 = 1,20,000 × 4.16988 ≈ ₹5,00,386.
So on pure cash-flow grounds the ranking is: lease ₹5,00,386 < instalments ₹5,11,758 < cash ₹6,00,000.
The 'same as cash' reasoning is wrong twice over: ₹1,20,000 × 5 = ₹6,00,000 is a nominal total that ignores timing, and the payments begin immediately, which makes the lease dearer in nominal terms but cheaper in present-value terms than the instalment plan.
However, present value alone does not settle it. The lease buys use, not ownership: Meera gives up the press's residual value at the end of year 5 and any claim on the asset. The lease is genuinely preferable only if she is indifferent to owning the machine at the end, or if the residual value she forgoes is worth less than the ₹11,372 gap between Plan B and Plan A.
3. The bank revises its lending rate to 14%. Does the ranking change? Also state what outright price would make Meera indifferent between cash purchase and Plan A at 10%.
Read the worked answer
Recompute both annuities at 14%:
- Plan A: 1,35,000 × 3.4331 = ₹4,63,469
- Plan B: 1,20,000 × 3.4331 × 1.10 = 1,20,000 × 3.77641 ≈ ₹4,53,169
Ranking is unchanged (B < A < cash). More importantly, both present values fall: a higher discount rate shrinks the weight given to distant payments, so any deferred-payment plan gains relative to paying today. The gap between Plan A and cash widens from ₹88,242 to ₹1,36,531. Meera should not conclude that a rate rise makes borrowing unattractive - for a deferred plan it makes the deferral more valuable.
Indifference price at 10%: cash price would have to equal the present value of the instalments, i.e. ₹5,11,758. The dealer would need to cut the ₹6,00,000 price by ₹88,242, roughly 14.7%, before paying outright becomes the better decision.