Accounting and the Time Value of Money

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• the principal, and any interest accrued (earned and not withdrawn or paid).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