CB1 · explained

Leasing against buying, and the only comparison that settles it

Both options get the machine onto the factory floor, so the question is purely which one costs less in present value terms. That makes it a short calculation with three traps in it: which cash flows belong, which rate to discount at, and what to leave out altogether.

CB1 · Business Finance · 9 min read

After this page you can

Compare leasing with buying by discounting the after-tax cash flows, two independent ways, and find the lease payment at which the two break even

What is actually being decided

A company has decided it wants a machine. That decision is already made, and it was made by appraising the machine: the cash it will generate, discounted, against what it costs. Nothing about leasing or buying changes whether the machine is worth having.

What remains is a financing decision: having decided to use the machine, is it cheaper to own it or to rent it? Because the machine produces the same output either way, every rupee it earns is identical under both options and cancels out of the comparison. So the operating cash flows do not appear in a lease-against-buy calculation at all.

That is the first and most useful simplification in the topic. You are not valuing a project. You are comparing two ways of paying for one, and the only cash flows that matter are the ones that differ.

Which cash flows differ

If the company buys: it pays the purchase price now. It owns the asset, so it claims the capital allowances against tax, and it receives any scrap proceeds at the end. If it borrows to buy, the interest is a cost of the borrowing, not of the asset — and it must not be entered as a cash flow, for the reason in the next section.

If the company leases: it pays lease rentals, usually in advance. The rentals are an operating expense, so the whole of each one attracts tax relief. It does not own the asset, so it claims no capital allowances and gets no scrap proceeds.

Set side by side, the differences are: the purchase price against the rentals, the capital allowances against the relief on the rentals, and the residual value against nothing. Those are the only entries.

The rate, and why it is not the cost of capital

This is the trap that separates a good answer from a plausible one. The discount rate for a lease-against-buy comparison is the company's after-tax cost of borrowing, not its weighted average cost of capital.

The reason is that the cash flows being compared are nearly certain. A lease rental is a contractual amount on a known date. A capital allowance is a tax computation. Neither carries the business risk of the project, and the weighted average cost of capital is a rate built to compensate for exactly that risk. Using it would discount safe cash flows as though they were risky, which systematically favours whichever option pushes its payments furthest into the future.

And this is why interest is excluded from the cash flows. Discounting at the cost of borrowing already charges the company for the finance; entering the interest payments as well would charge for it twice.

discount at kd(1 − t), and leave interest out of the cash flows

In words: the rate carries the cost of the money, so the cash flows must not.

Two ways to lay the comparison out

Two separate present values

Work out the present value of the cost of buying, work out the present value of the cost of leasing, and take the cheaper. Both figures are negative because both are costs, which trips people up: the better option is the one closer to zero, not the larger in magnitude.

One set of differential cash flows

Subtract one option's cash flows from the other's, year by year, and discount the differences. A single present value comes out, and its sign tells you which option wins.

The two methods must give answers that differ by exactly the same amount, and computing both is the cheapest available check on a calculation with this many sign errors waiting in it. The worked example does both and they agree to the paisa.

What the arithmetic leaves out

A complete answer says that the calculation is not the whole decision, and names what sits outside it.

Who bears obsolescence. A short lease on equipment that goes out of date quickly transfers that risk to the lessor, and that may be worth paying for however the present values fall.

Maintenance and service. A full-service lease bundles things an owner would pay for separately. If the rentals include them, the buy case must include them too or the comparison is not like for like.

Covenants and flexibility. Leasing may not count against a borrowing limit in the way a loan does, and it may be available to a company that cannot easily borrow at all.

The tax position actually being in place. Capital allowances are worth nothing to a company with no taxable profit to set them against. The commonest real reason leasing is cheaper is that the lessor can use allowances the lessee cannot, and shares part of that benefit through a lower rental.

Questions students ask

Should the residual value go in the buy case?

Yes, as an inflow at the end, and with its tax effect. Owning the asset means owning whatever it is worth at the end, and that is a real difference from leasing. If a question is silent on residual value, say you have assumed none.

What if the lease has a different term from the asset's life?

Then the two options do not provide the same thing, and the comparison needs adjusting before it is fair — by assuming a replacement lease, or by comparing equivalent annual costs instead of totals. A question that does this is testing whether you noticed.

Does it matter whether the lease is an operating or a finance lease?

For the cash flows in this calculation, hardly at all. For the accounts, a great deal: a finance lease puts both an asset and a liability on the balance sheet, which changes the gearing ratio and may touch a covenant. The cash comparison and the reporting consequence are two separate questions, and a good answer keeps them apart.

A worked example

An invented example. Every figure is made up for this page and describes no real machine, lease or company.

Shringar Tools Limited wants a press costing ₹10,00,000, with a four-year life and no residual value. Corporation tax is 25%, paid and relieved one year in arrear. Capital allowances are 25% of cost each year on a straight-line basis. The after-tax cost of borrowing is 6%.

The alternative is a four-year lease at ₹3,00,000 a year payable in advance.

  1. Discount factors at 6%

    v = 1/1.06 = 0.9433962, v2 = 0.8899964, v3 = 0.8396193, v4 = 0.7920937
    a3 = v + v2 + v3 = 2.6730119
    a4 = 3.4651056

  2. Buying

    Pay ₹10,00,000 at time 0. The allowance is 25% of ₹10,00,000 = ₹2,50,000 a year for four years, and the tax it saves is 25% of that:

    tax saved each year = 0.25 × 2,50,000 = ₹62,500, at times 1, 2, 3 and 4
    PV = −10,00,000 + 62,500 × 3.4651056
        = −10,00,000 + 2,16,569.10 = −₹7,83,430.90

  3. Leasing

    Four rentals of ₹3,00,000 at times 0, 1, 2 and 3. Each is fully deductible, so each saves 25% of ₹3,00,000 = ₹75,000, arriving a year later — at times 1, 2, 3 and 4.

    Setting the cash flows out year by year makes the overlap visible:

    TimeRentalTax savedNet
    0−3,00,000—−3,00,000
    1−3,00,000+75,000−2,25,000
    2−3,00,000+75,000−2,25,000
    3−3,00,000+75,000−2,25,000
    4—+75,000+75,000
    PV = −3,00,000 − 2,25,000 × 2.6730119 + 75,000 × 0.7920937
        = −3,00,000 − 6,01,427.68 + 59,407.03 = −₹8,42,020.66

    Worth checking that a second way before going on, by separating the rentals from the relief: the rentals are an annuity-due, 3,00,000 × (1 + a3) = 3,00,000 × 3.6730119 = ₹11,01,903.58, and the relief is 75,000 × a4 = ₹2,59,882.92. The difference is −11,01,903.58 + 2,59,882.92 = −₹8,42,020.66, the same figure.

  4. The decision

    buying −₹7,83,430.90 against leasing −₹8,42,020.66

    Buying is cheaper by ₹58,589.76 in present value. Both numbers are negative because both are costs; buying wins because its cost is the smaller one, not because −7,83,430 is the larger number.

  5. The same answer from the differential cash flows

    Subtract the buy cash flows from the lease cash flows, year by year:

    TimeLeaseBuyLease − buy
    0−3,00,000−10,00,000+7,00,000
    1−2,25,000+62,500−2,87,500
    2−2,25,000+62,500−2,87,500
    3−2,25,000+62,500−2,87,500
    4+75,000+62,500+12,500
    PV = 7,00,000 − 2,87,500 × 2.6730119 + 12,500 × 0.7920937
        = 7,00,000 − 7,68,490.92 + 9,901.17 = −₹58,589.75

    Against the difference of the two present values, −8,42,020.66 − (−7,83,430.90) = −₹58,589.76. The two agree to the paisa, the last digit differing only because the discount factors were rounded to seven places before use. The negative sign says leasing is worse, by the same ₹58,590.

    Notice what the differential table shows that the two separate present values do not: leasing is ₹7,00,000 better off at the outset and then worse in every single later year. That is the whole economics of the choice in one column — leasing buys you cash today and charges you for it later — and it is why the discount rate matters so much to the answer.

  6. The rental that would make it a dead heat

    Worth computing, because it converts the answer from a verdict into a negotiating position. Let the annual rental be P. The lease is then worth

    −P(1 + a3) + 0.25P × a4 = −3.6730119P + 0.8662764P = −2.8067355P

    Setting that equal to the cost of buying:

    −2.8067355P = −7,83,430.90, so P = ₹2,79,125.30

    Check it: −2,79,125.30 × 2.8067355 = −₹7,83,430.90, equal to the buy case. So the lessor would have to come down from ₹3,00,000 to about ₹2,79,125 a year — a cut of nearly 7% — before leasing became the better deal. That is a far more useful sentence to hand a finance director than "do not lease".

Where this fits in CB1

This page explains one idea from CB1 Business Finance. The full CB1 syllabus, with what each part is examined on, sits on the course page, and past-paper style mock exams with full solutions are where you find out whether the idea has stuck under time pressure.

Other CB1 topics explained

Stuck on a term rather than the idea? The actuarial glossary defines the notation used above. If something here is wrong or unclear, tell us — these pages get corrected.