## Page 5: Discounted cash flows

This problem is tackled using discounted cash flows. This is a method of determining what *future * cash inflows are actually worth today. This depends on the opportunity cost of money. One way of putting a value on the opportunity cost of money is to use interest rates. This is what could be earned by simply keeping the money in a bank account gaining interest.

Suppose interest rates for the next year are estimated to be 10% on average. Then, in a year’s time an investment of £1 would be worth:

Put another way, £1.10 in a year’s time is worth £1 today. A formula can similarly be applied to find out what any sum in the future would be worth today. Assuming opportunity costs of 10%, a £1 in one year’s time is worth:

And £1.00 in two years' time is worth:

This sequence can be extended for years into the future producing factors that can be used to convert future cash flows into their present values (PV). For example, with a discounting rate of 10%, the discount factor is 100/110 or 0.91 applied to the value of a sum received after one year; for two years it is (100/110)2 or 0.83; for three years it is (100/110)3 or 0.75. Table 2 shows factors for discount rates of 10% and 20%.

We can now look again at the Grangemouth expansion project and calculate the expected return on a discounted cash flow basis. Typically, a company such as Syngenta uses a discount rate that reflects the minimum return expected on capital employed. This is likely to be a good deal higher than average interest rates. Table 3 shows the discount cash flow for the Grangemouth project using a discount factor of 20%. Again this is illustrative data to show the basic principles of the method.

#### Present value

The present value of all the projected cash flows can be aggregated to give the net present value (NPV) for the whole project. In this illustrative example, the net present value is £569.1m. If this value is positive, then the project is expected to achieve earnings with a value greater than the opportunity cost of the funds committed.