Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options

Appendix A. Financial Calculations

TIME VALUE OF MONEY

Time value of money (TVM) is a key concept in modern finance. It tells us two things:

• A dollar received today is worth more than a dollar to be received in the future.

• A dollar to be received in the future is worth less than a dollar received today.

The reason for this is because a dollar today can be invested at a rate of interest and will grow to a larger sum of money in the future. The cost of money for a specific period of time (its time value) is measured by the interest rate for the period. Interest rates in the financial markets are normally quoted on a nominal per annum basis. A nominal interest rate has two components:

• Real rate. This compensates the lender for the use of the funds over the period.

• Inflation rate. This compensates the lender for the predicted erosion in the value of money over the period.

Normally the inflation element is more subject to change than the real or underlying rate. The relationship between the two can be expressed mathematically (with the rates inserted in the formulae as decimals):

1+ Nominal rate = (1 + Inflation rate) × (1 + Real rate)

Real rate = [(1 + Nominal rate)/(1 + Inflation rate)] – 1

If the nominal interest rate for one year is 5% p.a. (0.05 as a decimal) and the predicted rate of inflation over the period is 3% p.a. (0.03 as a decimal) then the real interest rate is calculated as:

Real rate = (1.05/1.03) – 1 = 0.0194 = 1.94% p.a.

By convention, interest rates are usually expressed per ...