Case 077Capital budgetingWarm up

A textile mill can keep an old loom or replace it with a new one. Using the running costs, both salvage values and an 11% discount rate, should it replace?

VanguardMalvern · 2024

The situation

Nandikeshwar Looms, an invented weaving mill, runs an old loom that could be sold today for Rs 2 crore. Kept, it costs Rs 5 crore a year to run in power, repairs and wasted yarn, lasts five more years and is worth nothing at the end.

A new loom costs Rs 12 crore. It costs Rs 2 crore a year to run, also lasts five years, and could be sold for Rs 1 crore at the end. Both looms make the same cloth at the same speed, so revenue does not change. Ignore tax and assume running costs are paid at the end of each year. The mill's discount rate is 11%.

Your task

Should Nandikeshwar replace the loom, by how much does the decision win or lose, and how sensitive is it?

Quick check

What is the right cash outlay at year 0 for the replace decision?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Replace: the incremental NPV is about Rs 1.7 crore at 11%. Replacing costs a net Rs 10 crore today, after selling the old loom for Rs 2 crore, and saves Rs 3 crore a year for five years plus Rs 1 crore of salvage at the end. Those savings are worth Rs 11.68 crore today. The margin is modest: the saving only needs to fall to Rs 2.55 crore a year for the decision to break even.

Step 1Which cash flows belong in the decision?

Only the ones that change because of the choice. Think of replacing an old scooter: you count the price of the new one, the money a buyer gives you for the old one, and the petrol you stop wasting. What you paid for the old scooter years ago does not enter. The old loom's salvage is a saving today, and its original cost is sunkAlready spent and unrecoverable whatever you decide now, so it cannot change which choice is better.. So the decision is: pay Rs 12 crore, receive Rs 2 crore now, save Rs 3 crore of running cost each year, and collect Rs 1 crore at the end.

Keep against replace, and the only line that matters: the differenceYear 0Year 1Year 2Year 3Year 4Year 5Keep old loom0-5-5-5-5-5Buy new loom-10-2-2-2-2-1Replace minus keep-10+3+3+3+3+4-12 new + 2 salvage-2 run + 1 salvagePV of +3 a year for 5 years and +1 at the end, at 11%: 11.68. Less 10 today: NPV = +1.68
Keeping the old loom costs Rs 5 crore a year; replacing it costs a net Rs 10 crore today and Rs 2 crore a year with Rs 1 crore back at the end, so the difference is minus Rs 10 crore now and plus Rs 3 crore a year, worth an incremental NPV of Rs 1.68 crore at 11%.
Step 2How do you work the NPV quickly?

Use the annuity factor for five years at 11%, 3.6959. Rs 3 crore a year for five years is worth Rs 11.09 crore today, and the Rs 1 crore salvage in year 5 adds Rs 0.59 crore. Together that is Rs 11.68 crore against Rs 10 crore paid today, an NPV of Rs 1.68 crore. You can reach the same number by valuing each option's costs separately: keeping costs Rs 18.48 crore in present value, replacing costs Rs 16.80 crore, and the gap is the same Rs 1.68 crore.

The relationship
NPV=−10+3×3.6959+11.115=−10+11.088+0.593=1.681\text{NPV} = -10 + 3 \times 3.6959 + \frac{1}{1.11^5} = -10 + 11.088 + 0.593 = 1.681
-10new loom Rs 12 crore less old loom salvage Rs 2 crore, paid today
3yearly running cost saved, Rs 5 crore less Rs 2 crore
3.6959five-year annuity factor at 11%
1 / 1.11^5the new loom's Rs 1 crore salvage, discounted from year 5
What it says in wordsReplacing creates about Rs 1.68 crore of value, because Rs 3 crore a year of savings and the end salvage are worth more today than the Rs 10 crore net outlay.
Step 3How robust is the answer?

The IRR of the incremental cash flows is about 17.2%, against an 11% hurdle, a cushion of roughly six points. Put the sensitivity in rupees: the yearly saving can fall from Rs 3.00 crore to Rs 2.55 crore before replacing stops paying. That is a 15% margin, so the case rests on whether the Rs 2 crore running cost of the new loom is a supplier promise or a measured figure from similar mills. Ask for the second.

The same loom, three answers: only one is rightCorrect: incremental, discounted+1.68Forgot the old loom's salvage-0.32No discounting at all+6.000: indifferent
Done correctly, replacing the loom is worth plus Rs 1.68 crore; forgetting the old loom's Rs 2 crore salvage turns that into minus Rs 0.32 crore and flips the decision, while ignoring discounting inflates it to plus Rs 6 crore.

Two limits are worth naming. Tax would change the numbers, because the new loom brings depreciation that shields profit and the old loom's sale may create a taxable gain or loss against its book value. And the two lives are equal here; if the new loom lasted eight years, you would compare equivalent annual costs rather than five-year totals. Equal lives are what let you compare the two options head to head.

Where candidates lose it

The usual loss is leaving the old loom's Rs 2 crore resale value out of the decision, or treating it as income from some separate deal. Without it the NPV turns negative and you recommend keeping a loom that costs the mill money.

The second is dragging in the old loom's book value or original price. That money is gone whatever the mill decides; a candidate who subtracts it is answering a question about accounting history, not about the decision in front of the board.

What the interviewer asks next

  • With tax at 25% and straight-line depreciation on the new loom, does the decision change?
  • The new loom lasts eight years instead of five. How would you compare them?
  • What running cost saving makes the mill indifferent?

Asked at Vanguard, Mutual Funds, Malvern, 2024 (Wall Street Oasis): A DCF walkthrough was asked for along with NPV with a whole question on CPV

Company names and figures are illustrative.