SHOULD you buy a vehicle or should you lease it? In answering this question you need to consider whether you want to take the residual value risk, the tax effect if you buy rather than lease and balance sheet issues.
You will need also to carry out a financial evaluation of the lease versus buy decision. You are about to acquire a new car. It costs £10,000. You expect to sell it in three years’ time for £3,000. You had expected to buy it for cash but the salesman is offering you a non-maintenance contract hire deal at £2,800 per annum, payable annually in advance.
You had planned to buy it using your bank overdraft on which you currently pay interest at 10% per annum.
You have to decide whether to lease or buy. What are the thoughts that run through your mind?
‘Three times £2,800 is £8,400. The car will be worth, say, £3,000 at the end. Am I better off (a) paying three rentals at £2,800, or (b) paying £10,000 now, paying the interest on my overdraft and getting back £3,000 when I sell the car at the end of three years?’
You need a tool to be able to make these comparisons and the best tool that we have is called discounted cash flow analysis (DCF).
DCF is a method of comparing alternative business decisions based on the cash flows they will produce and expressing these in today’s money terms, also called present value (PV).
DCF is used in investment appraisal and analysis. You can use it for lease versus contract hire versus contract purchase vs hire purchase versus lease purchase versus buy decisions – in fact for any situation where you have choices to make that will involve different cash flows. An employee deciding whether to take a company car or a cash option can also use DCF to establish the cheapest option.
DCF uses the idea of the time value of money. This is the concept that says £1 received in one year’s time is worth less than £1 received today. This is 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’ (that is, to reduce) future cash flows to ‘today’s’ value (present value) so that they can be added up or deducted as if they were all happening today. Then the present value of all of the cash flows of two competing options is compared and the option showing the highest present value (or the lowest negative present value) is the winner. Let’s look again at the assumptions we made earlier:
Table 1 proves that this figure is correct
An easier way to do it would be 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 three.
The steps here are as follows: work out 1.1 to the power of 3 (ie 1.1 x 1.1 x 1.1 = 1.331).
Then divide 1.331 into 1 ie 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
This is the present value of £3,000 received in three years time at a discount rate of 10% per annum.
You need to work first with 1.1 because 0.1 is 10% and for the discounting arithmetic to work you have to place the 10% after the number 1 in DCF calculations.
So, for example, if you were about to work out the discount factor for 8% over four years, you would use 1 ÷ (1.08)4.
So, if you buy, 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.)
Option two is to lease the vehicle for three years.
As each rental falls due at a different time you have to do three discounting calculations; after one, two and three years. You will need different discount factors for each of these payments to reduce (that is, discount) the value of the rental to present value 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 and this is the date when the last rental would be payable under the leasing option.
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. Table 2 shows how we can then compare the two options.
So now we have our two options:
If you lease you will save £86.56 in present value terms. If there are no other factors that you need to consider, this analysis shows that you should opt for the lease and save £86.56.
This has been a very simple example. You can use DCF techniques to decide between any two series of cash flows, however complex.
You might wish to consider payments that are to be made monthly, on specific days of the month, or an irregular payment pattern, or you might include the tax effects of the options you are considering.
TABLE ONE
| Year | Start balance (£) | Interest (£) | End balance (£) | |||
| 1 | 2,253.94 | 225.39 | 2,479.34 | |||
| 2 | 2,479.33 | 247.93 | 2,727.27 | |||
| 3 | 2,727.27 | 272.73 | 3,000.00 | |||
TABLE 2
OPTION 1 purchase
Buy for £10,000 today, receive £3,000 in three years
Determine value of £3,000 in three years at today’s value
The discount is 1 ÷ (1.1)3 = 0.751315
£3,000 x 0.751315 = £2,253.94
Less outlay today = £10,000
Present value -£7,746.06
OPTION 2 lease
Pay £2,800 starting today for three years
1st rental (this occurs today so there is no need to discount this
-£2,800.00
Second rental £2,800 ÷ 1.1 0.909091 -£2,545.45
Third rental £2,800 ÷ 1.12 0.826446 -£2,314.05
-£7,659.50
So contract hire is cheaper than purchase by £86.56
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