Module 8: Time Value of Money

The process of determining how much a future cash flow is worth today is called?

discounting. It is done for most major business transactions during investing decisions in capital budgeting.

Discount Rate

Discounting is the procedure of finding what a future sum of money is worth today.

Effective Annual Rate (EAR)

Finding the Effective Annual Rate (EAR) accounts for compounding during the year, and is easily adjusted to different period durations.

The interest rate and the number of periods must have consistent units.

If one period is one year, the interest rate must be X% per year, and vice versa.

Present Value, multiple flows

The PV of multiple cash flows is simply the sum of the present values of each individual cash flow

Compounding period

The length of time between the points at which interest is paid.

Principal:

The money originally invested or loaned, on which basis interest and returns are calculated.

Time value of money is a central concept to amortization

A dollar today, for example, is worth more than a dollar tomorrow due to the opportunity cost of other investments

Time period assumption

Business profit or losses are measured on a timely basis.

Another common name for finding present value (PV) is?

Discounting is the process of finding what a future sum of money is worth today.

The "present" can be moved based on whatever makes the problem easiest.

Just remember that moving the date of the present also changes the number of periods until the future for the FV.

Rule of 72 for Compound Interest

Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.

Multi-period investments

Multi-period investments require an understanding of compound interest, incorporating the time value of money over time.

Multi-period Investment

Multi-period investments take place over more than one period (usually multiple years). They can either accrue simple or compound interest

Present Value and Future Value

Present value (PV) and future value (FV) measure how much the value of money has changed over time

The discount rate represents some cost (or group of costs) to the investor or creditor.

Some costs to the investor or creditor are opportunity cost, liquidity cost, risk, and inflation. The discount rate is used by both the creditor and debtor to find the present value of an amount of money.

Future Value Multiple Flows

The FV of multiple cash flows is the sum of the FV of each cash flow. To sum the FV of each cash flow, each must be calculated to the same point in the future.

Fisher Equation

The nominal interest rate is approximately the sum of the real interest rate and inflation.

Perpetuity

The present value of a perpetuity is simply the payment size divided by the interest rate and there is no future value.

Time value of money:

The value of an asset accounting for a given amount of interest earned or inflation accrued over a given period.

Fractional time periods

The value of money and the balance of the account may be different when considering fractional time periods.

What is Time Value of Money?

Time value of money is integral in making the best use of a financial player's limited funds

The balance of an account only changes when interest is paid.

To find the balance, round the fractional time period down to the period when interest was last accrued.

In a single-period investment?

You only need to know two of the three variables Future Value , Present Value and interest rate. The number of periods is implied as one since it is a single-period.

Perpetuities are a special type of annuity

a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever.

Annuity

a specified income payable at stated intervals for a fixed or a contingent period, often for the recipient's life, in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.

he Fisher Equation approximates the amount of interest

accrued after accounting for inflation

Present Value:

also known as present discounted value, is the value on a given date of a payment or series of payments made at other times. If the payments are in the future, they are discounted to reflect the time value of money and other factors such as investment risk.

Repaying capital over time at an interest rate requires

an amortization schedule, which both parties agree to prior to the exchange of capital. This schedule determines the repayment period, as well as the amount of repayment per period.

Inflation

an increase in the general level of prices or in the cost of living

The equation in skips the step of solving for EAR

and is directly usable to find the present or future value of a sum.

To find Future Value , you must first identify Present Value , the interest rate,

and the number of periods from the present to the future.

A dollar today is worth more than a dollar tomorrow,

and the time value of money must take into account foregone opportunities

As a result of multiple periods, it is usually a good idea to calculate the

average rate of return (cumulatively) over the lifetime of the investment.

Variables, such as compounding, inflation, and the cost of capital must?

be considered before comparing interest rates.

A nominal interest rate that compounds has a different effective rate (EAR)

because interest is accrued on interest.

Amortization

borrowing money to be paid back via a number of installments over time, it is important to understand the time value of money and how to build an amortization schedule.

The Future Value can be?

calculated by knowing the present value, interest rate, and number of periods, and plugging them into an equation.

To find the PV of multiple cash flows

each cash flow must be discounted to a specific point in time and then added to the others. To discount annuities to a time prior to their start date, they must be discounted to the start date, and then discounted to the present as a single cash flow.

The future value is the value of a

given amount of money at a certain point in the future if it earns a rate of interest.

Investments that accrue simple interest

have interest paid based on the amount of the principal, not the balance in the account.

Investments that accrue compound interest

have interest paid on the balance of the account. This means that interest is paid on interest earned in previous periods.

Compound interest

interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.

A company will theoretically only invest if the expected return

is higher than their cost of capital, even if the return has a high nominal value.

FV future value

is stand for future value, money in the future has a value

PV present value

is stand for present value, Money today has a value

Time Value of Money

is the concept that money is worth more today that it is in the future.

Compound Interest

is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is the interest on interest, and it can result in exponential growth of the original principal.

Loans, investments, and any other deal?

must be compared at a single point in time to determine if it's a good deal or not.

Single period investments are relatively simple to calculate in terms

of future value, applying the interest rate to a present value a single time.

Amortization is the process

of scheduling intervals of payment over time to pay back an existing debt, taking into account the time value of money

Single-period investments take place over?

one period (usually one year)

Incremental cash flows:

the additional money flowing in or out of a business due to a project.

When interest compounds more than once a year,

the effective interest rate (EAR) is different from the nominal interest rate.

Perpetuities with growing payments are called Growing Perpetuities

the growth rate is subtracted from the interest rate in the present value equation.

The amount that the value of the money changes after one year is called?

the interest rate (i). For example, if money today is worth 10% more in one year, the interest rate is 10%.

Discount rate:

the interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value

Interest rate

the percentage of an amount of money charged for its use per some period of time. It can also be thought of as the cost of not having money for one period, or the amount paid on an investment per year.

The future value of a present value is calculated by plugging

the present value, interest rate, and number of periods into one of two equations.

Discounting

the process of determining how much money paid/received in the future is worth today. You discount future values of cash back to the present using the discount rate.

Amortization of a loan is

the process of identifying a payment amount for each period of repayment on a given outstanding debt.

Money today is worth more than?

the same quantity of money in the future. You can invest a dollar today and receive a return on your investment.

Cash flow

the sum of cash revenues and expenditures over a period of time.

Future Value

the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future, assuming a certain interest rate, or more generally, rate of return, it is the present value multiplied by the accumulation function

Multiple cash flow investments that are not annuities

unfortunately cannot be discounted by any other method but by discounting each cash flow and summing them together.

Single-period investments

use a specified way of calculating future and present value. Since the number of periods (n or t) is one, Future Value = Present Value X 1 + interest rate

Multi-period investments require a slightly more complex equation,

where interest gets compounded based on the number of periods the investment spans

To find the future value of a perpetuity requires having a future date

which effectively converts the perpetuity to an ordinary annuity until that point.

Simple interest increases the balance linearly,

while compound interest increases it exponentially.