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# Accounting and the Time Value of Money PowerPoint PPT Presentation

Accounting and the Time Value of Money Chapter 6 Basic Time Value Concept The time value of money is the relationship between time and money. According to the present value of money concept, a dollar today is worth more than a dollar in the future.

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## Accounting and the Time Value of Money

Chapter 6

### Basic Time Value Concept

• The time value of money is the relationship between time and money.

• According to the present value of money concept, a dollar today is worth more than a dollar in the future.

• This concept is used extensively to choose among alternative investment proposals.

### Accounting Applications

• Notes

• Leases

• Pensions

• Long-term assets

• Sinking funds

• Disclosures

• Installment contracts

### Fundamental Variables

• Interest rate: A percentage rate usually expressed as an annual rate of return.

• Time: the number of years or fractional portion of a year (periods) that amounts compound.

• Present Value: The value now (present) of a set of future cash flows.

• Future Value: The value at a given future date of cash invested (may be multiple FV’s).

### Interest Rates

• Specified in contracts

• Stated

• Coupon

• Nominal

• Face

• Demanded by investors

• Effective

• Discount

• Required rate of return

### Determining the effective rate

The appropriate interest rate depends on:

• the pure rate of interest

• expected inflation rate of interest

• credit risk rate of interest

The higher the credit risk, the higher the interest rate.

### Simple vs. Compound interest

• Simple interest is determined using only the original principal amount.

principal x interest rate (%) x time

• Compound interest is determined using:

• the principal, and any interest accrued (earned and not withdrawn or paid).

• Compound interest is used in virtually all time value applications.

### The basic calculations

• Future value of \$1

• Present value of \$1

• Future value of an ordinary annuity of \$1

• Present value of an ordinary annuity of \$1

• Future value of an annuity due of \$1

• Present value of an annuity due of \$1

### Single cash flow problems

Typically one of two types:

• Computing a future value of a known single sum present value.

• Computing a present value of a known single sum future value.

• FV = PV*(1+i)^n or PV = FV/(1+i)^n

i = interest rate per period

n = the number of periods

### Single cash flow FV example

Given:

• Amount of deposit today (PV):\$50,000

• Interest rate8%

• Frequency of compounding: Quarterly

• Time outstanding:5 years

What is the future value of this single sum?

### Single cash flow PV example

Given:

• Amount of deposit end of 3 years: \$100,000

• Interest rate (discount) rate:12%

• Frequency of compounding: Quarterly

• Time outstanding: 3 years

What is the present value of this single sum?

### Annuity Calculations

An annuity requires that:

• the periodic payments or receipts (rents) always be of the same amount,

• the interval between such payments or receipts be the same, and

• the interest be compounded once each interval.

### Types of annuities

Annuities may be broadly classified as:

• Ordinary annuities: where the rents occur at the end of the period.

• Annuities due: where rents occur at the beginning of the period.

### Future Value of an Ordinary Annuity

Given:

• Deposit made at the end of each period: \$5,000

• Compounding:Annual

• Number of periods:Five

• Interest rate:12%

• What is future value of these deposits?

### Present Value of an Ordinary Annuity

Given:

• Rental receipts at the end of each period: \$6,000

• Compounding:Annual

• Number of periods (years):5

• Interest rate:12%

• What is the present value of these receipts?

### Complex Situations

Deferred Annuities:

• Rents begin after a specified number of periods.

Valuation of Long-term Bonds:

• Two cash flows: principal paid at maturity and periodic interest payments

### Expected Cash Flows

• Introduced by SFAC No. 7

• Uses a range of cash flows.

• Incorporates the probabilities of those cash flows to arrive at a more relevant measurement of present value.