Published in Business Car Manager March 2011
Everyone has an opinion on whether it is best to lease or buy.
Pop into your local dealership and the salesperson will be happy to sell you a car. Ask them if you’d be better off buying or leasing it and my guess is they’ll say buying it. As several dealer salespeople have told me over the year “leasing complicates the sale”. Which of course, it does. More paperwork to be filled in (by you and the salesperson), a credit check and then, horror of horrors, the embarrassing moment that does happen occasionally, where the customer is turned down for finance and turns on his heel and walks out of the showroom. Which means the salesperson hasn’t just lost the chance to arrange the finance, they’ve also lost the chance to sell the car.
Ask a business colleague and they may tell they’ll never lease a car again because last time their leasing company charged them £75 for a scratch on the bonnet when they handed back the car at the end of the lease.
Ask your accountant whether you should lease or buy and he’ll think about whether you have enough spare cash to buy outright, the tax advantages, your tax position and so on, and will then, hopefully, give you a nice wellconsidered answer taking all the financial issues into consideration.
The fact is there are lots of reasons why people choose to lease, and lots of reasons why others adamantly stay away from it. But this article isn’t about opinions, it’s about doing a detailed financial analysis when you choose your next car, to help you decide whether to lease or buy. You can in fact ask your leasing company to do a financial evaluation for you to help you to make this decision. That evaluation will compare every relevant financial consequence of buying the car or leasing it, and will tailor the answer to your personal circumstances.
In this article I simply want to explain the fundamentals of that evaluation.
Let’s take a very simple example. (I’ve greatly oversimplified this to try to make the basic concepts more obvious).
You are about to buy a new car for £10,000 and plan to sell it in three years for £3,000. You would normally buy your cars by borrowing the money from the bank (current rate 10% pa) but the salesman offers you a nonmaintenance contract hire lease for £2,800 pa payable annually in advance, and you find this option interesting.
You need to decide whether to lease or buy. You might be thinking “Why change? I’ve always used bank loans. I bet he earns more commission on contract hire. Jack down the road tells me he hates leasing: why exactly was that? I can’t remember.”
I’d like to focus on just one point which you would start thinking about: is it better for you to pay three £2,800 rentals, or to pay £10,000 now, pay the loan interest then get back £3,000 in three years?”
You need a tool to be able to make these comparisons and the best tool that we have is discounted cash flow analysis.
DCF uses the idea of the time value of money. £1 received in a year is worth less than £1 received today, because you could invest £1 today to generate more over the year and also because inflation will reduce the value of that £1 over the year.
It uses interest rates to ‘discount’ (ie, to reduce) future cash flows to ‘today’s’ value (present value, or PV). Then the PVs of all of the cash flows of each option are totalled and the option with the highest PV (or the lowest negative PV) is the winner.
So now we need to evaluate the options:
1. You could buy the car and sell it in three years.
£10,000 paid today is £10,000 in today’s money (PV).
Next you need to determine the PV of the £3,000 receivable in three years. We do this by discounting (adjusting) the £3,000 by an interest rate, 10% per annum, using compound interest.
A simple way to think of this is to ask ‘how much would I have to invest today to give me £3,000 in three years if I earn 10% per annum interest? The answer is £2,253.94
This spreadsheet proves that this figure is correct.
Year 
Start balance 
Interest at 10% pa 
End balance 
£ 
£ 
£ 

1 
2,253.94 
225.39 
2,479.34 
2 
2,479.34 
247.93 
2,727.27 
3 
2,727.27 
272.73 
3,000.00 
You could calculate this using trial and error or using Excel’s ‘goal seek’ function.
An easier way to do it is to use a calculator to work out the value of the formula: 1 ÷ (1.1)^{3}.
That is, one divided by 1.1 and raised to the power of 3.
The steps here are as follows: Work out 1.1 to the power of 3. i.e. 1.1 x 1.1 x 1.1 = 1.331. Then divide 1.331 into 1, i.e. 1 ÷ 1.331. The answer is 0.751315. This is called the discount factor. Then multiply the discount factor by £3,000. The answer is £2,253.94 (£2,253.944 before rounding)
This is the PV of £3,000 received in three years time at a discount rate of 10% per annum.
The reason you needed to work first with 1.1 is that 0.1 is 10% and for the DCF arithmetic to work you have to place the 10% after the number 1 in DCF. (So if you wanted to work out the discount factor for 8% over 4 years, you would use 1 ÷ (1.08)^{4}).
So, if you buy the car you will pay out £10,000 and receive £2,253.94 in “today’s money”, so the net cost to you today is £7,746.06. (This is the net cost to you but not necessarily to someone else. If their borrowing rate is 12% they will arrive at a different answer.)
2. Or you could lease the vehicle for three years.
As each rental falls due at a different time you now have to do three discounting calculations; after one, two and three years. You will need different discount factors for each of these payments to discount the value of the rental to PV terms.
We saw that solving 1 ÷ (1.1)^{3} gave us the discount factor for a cash flow arising in three years’ time. Similarly, 1 ÷ (1.1)^{2} is the discount factor for a cash flow arising in two years’ time, which is the date the last rental would be payable under the lease.
1 ÷ (1.1)^{1}, that is, 1 ÷ 1.1, is the discount factor for the first rental and 1 ÷ (1.1)^{0} is the discount factor for any payment on day one. However, 1 ÷ (1.1)^{0} = 1, reflecting the fact that there is no need to discount a cash flow that occurs on day one.
We then add up the three present values of the three discounted rentals and see that they total £7,659.50.
The chart shows how we can then compare the two options.
Option 1 PURCHASE 
Buy for 10k today 
Receive £3,000 in three years  
Step 1; determine value of £3,000 in three years at today’s value (present value)  
The discount rate is  1 ÷ (1.1)^{3} = 0.751315^{ }^{ }  
So  £3,000 x  0.751315 =  £ 2,253.94  
Less. Outlay today  £10,000.00  
Present value  £ 7,746.06  
Option 2LEASE  
Pay £2,800pa starting today, for three years  
First rental  (Payable today, so there is no need to discount this)  £2,800.00  
2^{nd} rental  £2,800  ÷ 1.1  0.909091 =  £2,545.45  
3^{rd} rental  £2,800  ÷ 1.1^{2}  0.826446 =  £2,314.05  
£7,659.50  
So leasing is cheaper than buying by 
£86.55 
So now we have our two options:
Buy for a PV of £7,746.06 or lease for a PV of £7,659.50
If you lease you will save £86.55 in present value terms. If there are no other factors that you need to consider, this proves you should opt for the lease and save £86.55.
This has been a very simple example. Normally the payments would be more frequent and you’d want to include the tax effects. If you ask a leasing company they will be happy to do this sort of evaluation for you, and the printout you get back will include tax, VAT, national insurance, etc. These evaluations can also look at whether you would be better off taking a company car or taking a cash allowance and buying your own car.
DCF underlies all such evaluations. You can also use DCF to select between contract hire, contract purchase, hire purchase, lease purchase, salary sacrifice and outright purchase decisions, in fact any time you have to choose between alternatives that involve different cash flows.
Opinions are everywhere. Everyone has them. The best opinion is one that’s come from a proper evaluation of all the facts, and DCF is a great tool for carrying out financial evaluations. It probably won’t make Jack change his mind though!
Professor Colin Tourick