Discounted Cash Flow Techniques
 

Discounted cash flow (DCF) techniques will save you money! It is worth taking time out to understand them because they are an invaluable asset for decision making.

When you invest in anything you have to spend money, using DCF appraisals will help you choose the cheapest or most profitable method. Specifically for an investment in a fleet of cars you may need to make a decision between leasing or buying the cars. DCF methods are the only sure way of knowing you have made the right choice.

The time value of money

This approach takes into account the time value of money. Over time the value of the same amount of money changes. For example if you were offered £100 today or £100 in a year, the prudent amongst us should want the £100 today.
The three reasons for this are that firstly there is a risk you may not receive the money in a year. Secondly and more importantly you can take the £100 and put it in the bank and earn interest on it. Hence the £100 today could be worth about £106 in a year. Compare this to the £100 you were offered one year from now and you would rather have the £100 today. Thirdly because of inflation £100 will buy you more now than in a year.
These are the bases for using DCFs and in using them you can properly compare a choice of investments. For example the decision may be between purchasing the cars outright today in one lump sum payment, versus leasing the cars and making payments over a period of time. Only by using DCFs can this decision be made by expressing each of the patterns of payments in today’s money.

How do I calculate the DCF?

Using the example of purchasing cars outright against leasing them I may be offered the choice of spending £10,000 today or spending £40 per month for the next 30 months. Which is the cheapest investment?
To answer this question I need to know three things:

  1. All the future incremental cash flows associated with each investment.
  2. When they will occur.
  3. The discount rate.
1. Future incremental cash flows are those cash flows which would occur only if the investment was undertaken i.e. they would not occur if the investment was not undertaken. They should not be accounting adjustments e.g. depreciation (a non-cash flow) but could include capital allowances which would reduce any tax actually payable by a company or sole trader.

2. Their timing is important because this will help the pattern of payments to be expressed in today’s money i.e. their present value.

3. The discount rate should consider the pool of money from which the investment is funded, alternative uses for the money, inflation and risk of investment. For example was a loan taken out to fund the fleet? What else could the loan have been spent on? Could the money have been invested in machinery thus creating a return on it? What could this return have been? Would the money have been paid out as a dividend instead? If so what return were the shareholders expecting? Many areas have to be considered when determining the discount rate. Finance Directors of companies should know the discount rate for their company.

The Discount Factor

Returning to the earlier example, if £100 of today’s investment was worth £106 in a year, it would follow that the discount rate of this investment would be 6%. This is because £106 in a year discounted back at a rate of 6% into today’s money (its present value) would be worth £100.

To get a future incremental cash flow into present value terms a discount factor is applied to it. The discount factor is related to the discount rate by the following formula:

Discount factor = 1/(1 + r)n

r = discount rate
n = number of years

Applying this to the earlier example the discount factor on £106 is as follows:

Discount rate = 6%
Number of years = 1

Thus discount factor = 1/(1 + 0.06)1 = 0.943

Thus the present value of £106 = £106 * 0.943 = £100, as we suspected.

 

An example

Now choose between outright purchasing a car today for £10,000 and getting a residual value of £5,000 at the end of 2 years or leasing a car for 2 years at £3,000 per year assuming the lease payments are made at the end of the year. The discount rate is 10%.

Outright purchase

Cashflow in/(out)

Discount Factor

Present Value

 

 

 

(10,000)

1

(10,000)

5000

1/(1 + 0.1)2

4,132

 

 

 

Total

 

(5,868)

Leasing

Cashflow in/(out)

Discount Factor

Present Value

 

 

 

(3,000)

1/(1 + 0.1)1

(2,727)

(3,000)

1/(1 + 0.1)2

(2,479)

 

 

 

Total

 

(5,206)

Hence, because leasing is the lowest cash out that is the option which would be chosen for lowest cost. However, now you have the exact figures to compare you can also value the non-quantifiable benefits. For example if leasing had come out at a slightly higher cost you could quantify whether the differential was worth having the cars off balance sheet.

If the costs saved by choosing the correct way of funding the car fleet are multiplied over all the cars, the saving can run into thousands of pounds.

Catherine Bowden
Manager
Deloitte & Touche

     
 
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