Kaveri Appliances: Choosing a Transporter and Testing a Growth Target
Kaveri Appliances distributes small appliances through 60 dealers. Its board is reviewing two proposals in the annual plan. First, a change of transporter: Transporter A has delivered 40 consignments in the past year with a mean lead time of 12 days and a standard deviation of 1.5 days; Transporter B has delivered 32 consignments with a mean of 14 days and a standard deviation of 0.8 days. B's quote is ₹18,000 a year cheaper. Kaveri promises dealers delivery within 12 days and pays a penalty of ₹2,000 per consignment for each day of delay. Second, the sales plan: revenue was ₹4,000 lakh in 2019-20 and ₹6,912 lakh in 2022-23, and the sales head proposes a 2023-24 target of ₹8,500 lakh on the ground that 'we have been growing at 20 per cent'. The plant is rated for 25 per cent more volume than current sales, and the working capital limit is unchanged at ₹9 crore.
1. Compute the coefficient of variation for both transporters and advise which to appoint. Does the CV alone settle the choice?
Read the worked answer
Coefficients of variation
- CV(A) = 1.5 ÷ 12 = 12.5%
- CV(B) = 0.8 ÷ 14 = 5.71%
On relative variability B is the more consistent transporter - roughly half the CV of A.
But the CV alone does not settle the choice, because the means are not the same. CV is a valid comparison of consistency only when the averages are similar; here B is consistent around a mean that is two days worse than the promise. Reliable lateness is still lateness.
Penalty exposure against the 12-day promise:
| A | B | |
|---|---|---|
| Mean lead time | 12 days | 14 days |
| Consignments breaching 12 days | about half (mean equals the promise, SD 1.5) | effectively all |
| Approximate average breach | about 1.2 days | about 2 days |
| Annual penalty | ≈ 20 × 1.2 × 2,000 ≈ ₹48,000 | ≈ 32 × 2 × 2,000 ≈ ₹1,28,000 |
| Freight saving | - | ₹18,000 |
So B's ₹18,000 saving is swamped: it costs roughly ₹1,28,000 in penalties against A's ₹48,000.
Advice: appoint A, and use the quantified penalty exposure to negotiate with B - B has the tighter process control, so if it can pull its mean down to 12 days it becomes the better long-run supplier, or use both under a volume split to keep competitive tension.
2. Compute the compound annual growth rate of revenue from 2019-20 to 2022-23 and test the ₹8,500 lakh target. What is wrong with the sales head's method?
Read the worked answer
CAGR
CAGR = (6,912 ÷ 4,000)^(1/3) − 1 = (1.728)^(1/3) − 1 = 1.20 − 1 = 20% a year (three annual intervals: 2019-20 → 2020-21 → 2021-22 → 2022-23).
The sales head's growth claim is arithmetically correct.
Testing the target
- 20 per cent on ₹6,912 lakh gives 6,912 × 1.20 = ₹8,294 lakh, not ₹8,500 lakh.
- ₹8,500 lakh requires 8,500 ÷ 6,912 − 1 = 23.0%, three percentage points above the stated trend.
- So either the target or the trend assumption is wrong - the plan cannot claim 'we grow at 20 per cent' and set a 23 per cent number.
Capacity check: 25 per cent headroom gives a ceiling of 6,912 × 1.25 = ₹8,640 lakh. The ₹8,500 lakh target sits only 1.6 per cent below the ceiling, so any shift in product mix towards bulkier items, or any machine breakdown, makes it unattainable.
Methodological objections:
- Only three annual intervals and two endpoint values - a CAGR is a geometric average of the ends and ignores the path, including any flat or loss-making year.
- It mixes price inflation with volume growth; a target in rupees can be met by raising prices with no extra units sold.
- It ignores one-off causes, such as dealer additions, which may not repeat.
- A forecast is not a target: the plan needs a range, not a point.
3. If Transporter A is appointed, estimate the probability that at least one of the next five consignments arrives late, treating lead times as normally distributed. What does this imply for the 12-day promise?
Read the worked answer
Step 1 - probability that a single consignment is late.
The promise is 12 days and A's mean lead time is exactly 12 days, so the distribution is centred on the deadline:
P(late) = P(lead time > 12) = 0.5
Step 2 - probability that at least one of five is late.
Use the complement: P(none late) = 0.5^5 = 0.03125
P(at least one late) = 1 − 0.03125 = 0.96875, about 96.9%
Interpretation. A promise set exactly at the average lead time is breached almost every week over a run of five consignments - even by the better transporter. The average is being mistaken for the guarantee.
Expected penalty: 5 × 0.5 × 1.2 days × ₹2,000 ≈ ₹6,000 per five consignments, roughly ₹48,000 a year, which matches the exposure computed earlier.
What this implies:
- Either set the promise at a level the distribution can support. To keep late deliveries to about 5 per cent, the promise must be about 1.65 standard deviations above the mean: 12 + (1.65 × 1.5) ≈ 14.5 days.
- Or cut the mean lead time so that 12 days sits above it - a mean of about 9.5 days with the same SD gives roughly the same 5 per cent breach rate.
- Or price the penalty into the transport contract so the transporter, not Kaveri, carries the variability.