Revise Discounted cash flow method: net present value (NPV) for Cambridge 9609 (10.3.3)

The entire principle of discounted cash flow is built upon the concept of the time value of money. This fundamental idea states that a sum of money received today is worth more than the identical sum received in the future. There are two primary reasons for this. Firstly, money available now can be invested to earn a return, meaning it can grow over time – this is its opportunity cost. Secondly, inflation erodes the purchasing power of money, so £100 in five years will buy fewer goods and services than £100 today. Therefore, to make a valid comparison between an initial investment cost (a present value) and future earnings (future values), we must first discount the future cash flows to find their equivalent value in today's terms.

Discounting is the process of calculating the present value of a future cash flow. It is essentially the reverse of calculating compound interest. To do this, we use a discount rate, which represents the minimum required rate of return on an investment, often reflecting the business's cost of capital or the return available from alternative investments of similar risk. The formula for a discount factor is 1 ÷ (1 + r)^n, where 'r' is the discount rate and 'n' is the number of years. In an exam, you will typically be provided with a table of discount factors. To find the present value of a future cash flow, you simply multiply the cash flow by the appropriate discount factor for that year and that rate. A higher discount rate signifies greater risk or higher opportunity cost, leading to a lower present value.

Calculating the Net Present Value involves a clear, methodical process. First, identify the initial investment cost, which is the cash outflow at Year 0. Next, forecast the net cash flows (inflows minus outflows) for each year of the project's life. Then, using the given discount rate and a discount factor table, calculate the present value of each year's net cash flow by multiplying the cash flow by its corresponding discount factor. Remember, the Year 0 outflow is already a present value and is not discounted. After discounting all future cash flows, sum these present values together. Finally, subtract the initial investment (the Year 0 outflow) from the total sum of the discounted future cash flows. The resulting figure is the Net Present Value.

The NPV calculation provides a clear, financially-grounded decision rule. If the NPV is positive, the project is forecast to generate returns that exceed the required rate of return (the discount rate). This means it is expected to add value to the business and increase shareholder wealth, and should therefore be accepted. If the NPV is negative, the project is forecast to earn less than the required rate of return, effectively destroying business value, and should be rejected. An NPV of zero indicates the project will earn exactly the required rate of return, making it financially acceptable but not adding any extra value. When comparing two or more mutually exclusive projects, the one with the highest positive NPV should be chosen, as it is expected to generate the most value for the business.

Discount factor (year $n$) = $\frac{1}{(1 + r)^n}$

Present value = Net cash flow × Discount factor

NPV = $\sum PV\text{ of inflows} - \text{Initial outlay}$

The cost of capital (discount rate) reflects the firm's required return given risk and financing costs. Cash flows in Year 0 are usually not discounted (initial investment). Years 1, 2, 3… each have their own factor.