Chapter 8: Time Value of Money

Annuity

Annuity is a stream of fixed payments over fixed periodic intervals of time: for example, a payment of $100 for a ten-year period. The formula for annuity is on p. 150

Capitalization rate

Capitalization rate is the discount rate used to calculate the perpetuity value of an income or earnings into a single present value. It is used to calculate the value of some asset upon the assumption that the asset will produce a perpetual stream of income. For example, if a building produces 10 in profit from leasing and the capitalization rate is 10%, the capitalized present value of the building is 100.

Growth perpetuity formula

Growth perpetuity formula calculates the value of a perpetual, growing stream of income, and it is calculated as the annual income capitalized by the discount rate minus the growth rate. PV = A/(R-g) where g is growth rate

Inflation

Inflation is the phenomenon where money depreciates in value over time as prices of goods and services increase over time.

Nominal price or value

Nominal price or value is the price or value of a thing unadjusted for changes in price due to inflation. It is the stated price that has not been adjusted for inflation or time value.

Time value of money

Time value of money is the idea that money changes value with different time periods. Since the value of money in the future is always less than the value of the same money in the present, a future value must be discounted to present value.

Money has a time value: a dollar today is always worth more than a dollar tomorrow.

Why? Because of 1) inflation and 2) opportunity cost of delaying consumption to the future

Discount factor

Discount factor is the multiple applied to a future value to calculate its present value, and it is calculated as: discount factor = 1/(1+R)^T.

Discount rate

Discount rate is rate at which a future value is discounted to present value. As the discount rate increases, the present value decreases, and vice versa.

Future value

Future value is the nominal value (undiscounted value) of an expected return in the future. (value of money in some future time) FV = PV X (1 + R)^T pv = present value r = rate of return t = time

Perpetuity formula

Perpetuity formula calculates the value of a perpetual stream of income, and it is calculated as the annual income capitalized by the discount rate. PV = A/R (if R = 0 then PV = infinity)

Present value

Present value is a future value discounted by an appropriate discount rate and time, which is the value equivalent in today's money of a future sum. (aka the value of a future sum of money expressed as a present dollar equivalent). PV = FV/(1 + R)^T

Real price or value

Real price or value is the price or value of a thing adjusted for changes in price due to inflation.