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Accounting and the Time Value of MoneyPowerPoint Presentation

Accounting and the Time Value of Money

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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
- Business combinations
- 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- the principal, and any interest accrued (earned and not withdrawn or paid).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 rate 8%
- 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.

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