# Time Value of Money

## Definition

Time Value of Money is a concept that recognizes the relevant worth of future cash flows arising as a result of financial decisions by considering the opportunity cost of funds.

Topic Contents:

## Concept

Money loses its value over time which makes it more desirable to have it now rather than later.

There are several reasons why money loses value over time. Most obviously, there is inflation which reduces the buying power of money.

But quite often, the cost of receiving money in the future *rather than now* will be greater than just the loss in its real value on account of inflation. The opportunity cost of not having the money right now also includes the loss of additional income that you could have earned simply by having received the cash earlier. Moreover, receiving money in the future rather than now may involve some risk and uncertainty regarding its recovery. For these reasons, future cash flows are worth less than the present cash flows.

Time Value of Money concept attempts to incorporate the above considerations into financial decisions by facilitating an objective evaluation of cash flows from different time periods by converting them into present value or future value equivalents. This ensures the comparison of 'like with like'.

The present or future value of cash flows are calculated using a discount rate *(also known as cost of capital, WACC and required rate of return)* that is determined on the basis of several factors such as:

● Rate of inflation | Higher the rate of inflation, higher the return that investors would require on their investment. |

● Interest Rates | Higher the interest rates on deposits and debt securities, greater the loss of interest income on future cash inflows causing investors to demand a higher return on investment. |

● Risk Premium | Greater the risk associated with future cash flows of an investment, higher the rate of return required by an investors to compensate for the additional risk. |

Consider a simple example of a financial decision below that illustrates the use of time value of money.

## Example

Suppose that you have earned a cash bonus for an outstanding performance at your job during the last year.

Your pleased boss gives you 2 options to choose from:

● Option A: Receive $10,000 bonus now

● Option B: Receive $10,800 bonus after one year

Further information which you may consider in your decision:

- Inflation rate is 5% per annum.

- Interest rate on bank deposits is 12% per annum.

**Which option would you choose?**

## Solution

Although in absolute terms Option B offer the higher amount of bonus, Option A gives you the choice of receiving bonus one year earlier than Option B. This can be beneficial for the following reasons:

- To start with, you can buy more with $10,000 now than with $10,800 in one year's time due to the 5% inflation.
- Secondly, if you receive the bonus now, you could invest the cash in a bank deposit and earn a safe annual return of 12%. in contrast, you stand to lose this interest income if you choose Option B.
- Thirdly, future is uncertain. In worst case scenario, the company you work for could become bankrupt during the next year which would significantly reduce your chances of receiving any bonus. The probability of this happening might be remote, but there would be a slim chance none the less.

The above considerations must be incorporated into the decision analysis by factoring them into a discount rate which will then be used to calculate the future values and present values as illustrated below.

## Discount Rates

As the interest rate on bank deposits is higher than the rate of inflation, we should set the discount rate at 12% for our analysis because it represents the highest opportunity cost for receiving the bonus in one year's time rather than today.

For this example, we may assume that the risk of not getting the bonus after one year (e.g. due to the company becoming bankrupt) is minimal and is therefore ignored. If such a risk is considered significant, we would have to increase the discount rate to reflect that risk.

Using the 12% discount rate, we could either calculate future value or present value of the 2 options to assess which option is better in financial terms. Both are included here for completeness sake although they shall lead to the same conclusion.

## Future Values

The future value of Option A will be the amount of bonus plus the interest income of 12% which could be earned for one year.

Option A | ||

Bonus | $10,000 | |

Interest Income | $ 1,200 | ($10,000 x 12%) |

Future Value | $11,200 after 1 year | ($10,000 + $1,200) |

Option B | ||

Bonus | $10,800 | |

Interest Income | - * | |

Future Value | $10,800 after 1 year |

** No interest income shall accrue on $10,800 as it shall be received after one year.*

Based on the future values, Option A is preferable as it has the highest future value.

## Present Values

The present value of Option B will be the amount required today that shall equal to $10,800 in one year's time after having accrued an interest income of 12%.

Option A | ||

Bonus | $10,000 | |

Interest Income | 1.0 * | |

Present Value | $10,000 | ($10,000 x 1.0) |

**No need to discount as $10,000 is already stated in its present value terms.*

Option B | ||

Bonus | $10,800 | |

Interest Income | 0.8928 | (1 ÷ [1 + 0.12] ) |

Present Value | $9,642* | ($10,800 x 0.8928) |

**The present value of $9,642 represents the amount of cash that, if invested in a bank deposit @ 12% p.a., shall equal to $10,800 in one year. This can be confirmed as follows:*

**$9,642 x 1.12 ≈ $10,800**

Based on the present values, Option A is preferable as it has the highest present value.

**Note**

Both present and future value analysis lead to the same conclusion (i.e. Option A is preferable over Option B). This is because both methods are a mirror image of the other.

You may wonder why the difference between the 2 future values (i.e. $400) and the 2 present values ($358) is not the same. The difference is just a timing difference similar to that of other cash flows (i.e. future value is calculated 1 year ahead of present value). The difference can be reconciled by calculating either the future value of $358 (i.e. $358 x 1.12 ≈ $400) or the present value of $400 (i.e. $400 x 0.8928 ≈ $358).

## Calculation

Time Value of Money principle is used extensively in financial management to incorporate the financial impact of the timing of cash flows in business decisions.

In order to apply the time value of money principle in complex financial decisions, you need to familiarize yourself with the detailed understanding and calculation of the following key topics:

- Cost of capital (also referred to as WACC and required rate of return);
- Present value of cash flows
- Future value of cash flows

These topics will be covered in detail later.