What is the present value of 110 paid one year from now if the interest rate is 10%?

Discounted cash flow (DCF) and net present value (NPV)

Discounted cash flow (DCF) analysis is a method of valuing a project, company or asset using the concepts of the time value of money. DCF is used to calculate the value of future cash flows in terms of an equivalent value today. All future cash flows are estimated and discounted to give their present values (PVs).

What is the time value of money?

You have probably looked at compound interest in mathematics and asked simple questions such as:

If you had $100 and put it in the bank at 10% interest how much would you have at the end of:

Year 1 $110 ($100 + $100 x 10 per cent) or ($100 x 1.1).

Year 2 $121 ($110 + $110 x 10 per cent) or ($110 x 1.1).

Year 3 $133.1 ($110 + $110 x 10 per cent) or ($110 x 1.1).

N.B. Multiplying by 1.1 is the same as calculating 110%.

This is called compound interest, because you receive 10% interest on your original $100 deposit (the principal) plus 10% interest on any previous interest. So, in the case of year 2 to year 3, you receive 10% on your original $100 (which is $10) plus an additional 10% on your $21 interest (which is $2.1), receiving $12.1 interest added to your $121 to give $133.1.

Compound interest is calculated not only on the initial principal, but also on the accumulated interest of prior periods.

So, what is $110 earned in one year’s time worth today (the Present Value or PV) if the interest rate is 10%? One way of thinking of this is reverse compound interest. The answer is obviously $100, as this could have been invested a year ago at 10% to earn $10 in interest giving $110. Therefore $100 is worth the same as $110 received in a year’s time or $121 received in two years’ time. This indicates the time value of money.

Discounted cash flow (DCF) deals with both interest rates and time. The return on an investment project is always in the future. Money paid in the future is worth less today, because of reversecompound interest.

$100 is worth the same as $110 received in a year’s time or $121 received in two years’ time, indicating the time value of money. So the Present Value orPV of $110 received in a year’s time is $100, as this could have been invested today at 10% to earn $10 in interest giving $110 at the end of the year. $100 today is therefore exactly the same in financial terms, as $110 received at the end of the year.

If a business wishes to compare two possible investments, which deliver different returns in the future, it is impossible to compare the relative merits unless the business can compare ‘like with like’. To achieve this, future returns are converted into present values (PV) by discounting.

To evaluate the worth of an investment we calculate Net Present Value:

The Net Present Value (NPV) of a project is the return on the investment (the sum of the discounted cash flows), less thecost of the investment.

If the NPV is larger than the initial cost (positive NPV), then the firm sees a return on its money. If it is less than the initial cost (negative NPV) the project is not worth pursuing.

An investment project costing $100,000 yields an expected stream of income over a three year period of:

If the interest rate is 10%, the discount values (present values) can be found using a discount table. The extract of a table below shows the present value of $1 receivable for a 6 year period at an interest rate of 5% per cent (to two decimal places).

Present value of $1 receivable at the end of 6 years at 5 per cent

It is possible to calculate the present values of the yields using the correct discount factor:

This investment is now viable as the Total Present Value ($107,500) is greater than the cost ($100,000). The NPV, therefore, is $7,500.

Benefits of discounting/NPV:

• accounts for the time value of money and considers the opportunity cost

• NPV will be wrong if the estimates of cost or net cash inflows are incorrect

• selection of the discount factor is crucial, but is mostly guesswork

• NPVs look deceptively accurate

• ignores non-financial factors

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