The concept of Time Value of Money is a principle financial theory that underlies the fields of business valuation, damages quantification and corporate finance. A solid understanding and comprehension of the practical workings of time value of money is critical to any financial practitioner as well as those involved in commercial litigation, financial advisory and corporate disputes. Although a central tenant of financial theory, the idea of time value of money is often one that is misunderstood by the general population. This article seeks to provide a high level overview of the time value of money concept, debunk some of the financial jargon used and highlight some of its applications.

### The Basic Concept

From a practical standpoint, the time value of money concept can be explained by a simple example. Would you rather have \$100 today or \$100 a year from now?

Most people would be correct in taking the \$100 today, but why? Consider that history has generally shown us that prices typically inflate over time. For example, the same bag of groceries purchased today for \$100 will likely cost more than \$100 in a year. Therefore your purchasing ability is improved by taking the \$100 today as opposed to waiting. Considered another way, you could take the \$100 today and invest in a risk free Canada Savings Bond or Guaranteed Investment Certificate and earn a return (interest) such that your \$100 today is worth more than \$100 in a year's time.

The example becomes more difficult when the question is changed to; would you rather have \$100 today or \$110 a year from now?

The correct answer is now made more difficult as we are comparing different amounts. The correct answer may also be different for different individuals. The ultimate decision is dependent on what you plan on doing with the money received and your expected rate of return. Investing the \$100 today requires a rate of return of 10% [\$100 + (\$100 x 10%) = \$110] to achieve \$110 in a year. Therefore, if you cannot invest the \$100 in a project that will at least earn 10% you are in a better off taking the \$110 a year from now.

Consider a risk adverse investor who plans on investing the \$100 in his/her savings account paying a guaranteed 2% interest per annum. If the investor takes the \$100 today, the future value of this \$100 is only \$102 in one year [\$100 + (\$100 x 2%)]. This investor would be better off taking the \$110 in one year.

### Terms & Definitions

Financial practitioners and theorists use a variety of terms in their consideration of the time value of money and to assess financial projects. Some of the most common terms are defined below:

• Present value (PV) – represents the current value of a future cash flow or stream of cash flows at a specified rate of return. Consider the example in the previous section. The present value of \$110 received a year from now at a 10% rate of return is \$100.
• Future value – represents the value of a cash flow at a specified future date that is equal to a given sum today. Considering the earlier example, the future value of the \$100 invested at a rate of 10% is \$110.
• Annuity – an annuity is a series of recurring cash flows at evenly spaced intervals. For example, a mortgage payment or lease payment. Many financial problems require the calculation of the present value of annuity cash flows.
• Simple interest – represents a basic return on the principal investment. If you invest \$100 at 5%, simple interest is calculated as \$100 x 5% or \$5.
• Compound interest – process by which the interest you earn on your principal investment is reinvested and added to the principal investment and earns interest itself. For example, \$100 invested at 5% per year earns \$5 in year 1, in year 2 the interest of 5% is calculated on a base of \$105 (\$100 principal + \$5 year 1 interest) resulting in a return for year 2 of \$5.25.
• Net Present Value (NPV) – commonly used in assessing capital projects, the NPV is the sum of the present values of all future cash inflows and outflows discounted at an appropriate rate of return. A positive NPV implies a favourable project while a negative NPV is unfavourable. Consider the construction of a new factory. The present value of the future cash inflows from production must be sufficient to cover the initial cash outflows to build the factory.

### Mathematics

The formulas used to account for the time value of money are not overly complex and the basic formulas can be manipulated to solve a variety of problems and a range of different cash flow streams.

The basic present value formula is summarized as below:

 PV = Future Value x [1 / (1 + i)n]
 Where i = discount rate n = number of years/periods

This formula can be used to value a variety of patterns of future cash flows. Consider a period of 5 years whereby an individual is paid \$1,000 at the end of year 1, \$2,000 in year 2, \$500 in year 3, \$750 in year 5 and \$3,000 in year 5 and an assumed 10% discount rate. The calculation of the present value of this uneven stream of cash flows is summarized as follows and employs the above formula:

Rearranging the above present value formula, the future value is simply:

 FV = PV x (1 + i)n

Understanding this basic formula is integral to understanding the concept of time value of money and is used significantly in business valuation, damages quantification and other financial reports.

### Determining the Appropriate Discount Rate

The discount rate used in the present value formulas identified above has a strong bearing on the result of such calculations and as such determining an appropriate discount rate is subjective and complex requiring a high degree of professional judgment. Having said this, the selection of a discount rate should consider:

• the risks and returns associated with the projected cash flows, whereby higher risk, less stable cash flows are generally discounted at a higher discount rate;
• an assessment of the prevailing industry, economic and credit market conditions and any company/individual specific factors;
• target rates of return for the company and the threshold rates required for certain projects;
• the discount rate should reflect both operating risk and financial risk; and
• that there must be consistency between the rate of return selected and the cash flows to which it is applied.

### Applications

Time value of money must be considered in a variety of applications and business owners and managers must be cognizant of the theory when evaluating different business opportunities and projects. The following are some of the key applications of time value of money:

• Evaluating Offers for Sale and Purchase – sellers of a business must be aware of the terms of sale and consider the risks inherent in future payments. A sale agreement that provides for payment of the sales price over a future period of time must be discounted at an appropriate rate reflecting the risk of the future payment being received and the opportunity cost of not having the capital upfront.
• Damages Quantification – in calculating damages, future projected cash flows are often discounted to a present value amount that is paid to the injured party as a onetime settlement. For example, personal injury cases typically involve a onetime payment amount where the injured individual is compensated at a current date based on projected future income earning potential.
• Capital Investment Opportunities – when selecting between different capital projects, business owners must appropriately weigh the net cash flows to be received while factoring in risk considerations and opportunity costs. Timing of cash flows is a critical component of evaluating capital investments.
• Personal Financial Planning – in assessing personal investments, mortgage payments, lease agreements etc. individuals should be aware and consider the time value of money.

### Conclusion

The concept of time value of money and present value is a central component of financial theory and modeling. Having a basic understanding of these concepts and being able to question and apply the basic formulas is critical to the effective interpretation of business valuation, damages quantification and other financial reports.