Finance - Investment
Theory 3 - Discounted cash flow - what's it worth in the future?
Discounted cash flow (DCF) is the most complex of the three methods we are looking at here, but has the main advantage that it takes account of the fact that returns in the future may be worth less than the same return now. This would seem obvious to you if you were offered either £5,000 now or £5,000 in three years time - which would you accept? Of course you'd want the money now, because if you took the £5,000 and put it in the bank for three years (if you could stop yourself spending it!), then it would be worth a lot more - £6,655 at an interest rate of 10%. Discounting future returns is the same in principle, but in reverse. We say that if you have a return of £6,655 in three years time, then this will be worth £5,000 now - we discount the future returns by the amount of the interest rate, which we call the discount rate. Another way of looking at it is to ask how much you would need to put into a bank today to earn a specific amount in x years time.
We can work this out mathematically, but generally you would be given discount tables that tell you how much less a return is worth each year. Below is an example of a discount table for three different interest rates:
| Years in future | 8% | 10% | 12% |
|---|---|---|---|
| Year 1 | 0.926 | 0.909 | 0.893 |
| Year 2 | 0.857 | 0.826 | 0.797 |
| Year 3 | 0.794 | 0.751 | 0.712 |
| Year 4 | 0.735 | 0.683 | 0.636 |
| Year 5 | 0.681 | 0.621 | 0.567 |
As an example, at a rate of 8% you would need to invest just over 68p now to earn £1 in five years time. So, for example, to get the discounted value of £20,000 in 4 years time at a discount rate of 10%, we would multiply the £20,000 by 0.683, giving us a present value of £13,660.
To use this to value an investment project, we would go through the following steps:
- Choose an appropriate discount rate (this may depend on expected future interest rates in the market).
- Multiply the expected net cash flows over the lifetime of the project by their discount factor (as in the table above).
- Add together all the present values from step 2 and subtract the capital cost to give us the net present value.
Let's do an example to see how this works. A firm is thinking of buying a machine costing £200,000 and the expected net cash flows are:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Net cash flow (£) | 50,000 | 55,000 | 65,000 | 75,000 | 75,000 |
If we follow the three steps above, we will get:
Step 1
Let's choose a discount rate of 10%. This means that our discount factors are:
| Years in future | 10% |
|---|---|
| Year 1 | 0.909 |
| Year 2 | 0.826 |
| Year 3 | 0.751 |
| Year 4 | 0.683 |
| Year 5 | 0.621 |
Step 2
If we multiply the expected net cash flow by the discount factor, we get:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Net cash flow (£) | 50,000 | 55,000 | 65,000 | 75,000 | 75,000 |
| Discount factor | 0.909 | 0.826 | 0.751 | 0.683 | 0.621 |
| Present value (£) | 45,450 | 45,430 | 48,815 | 51,225 | 46,575 |
Step 3
If we add all these present values together and subtract the capital cost, we get:
£237,495 - £200,000 = Net present value of £37,495
This represents quite a small return of 18.7% over 5 years on the original investment. The average rate of return calculation gives us a result of 12% per annum on these same figures and so discounting the future value of returns does give a very different picture.
Why not now have a look at the case study and practice using this technique?
