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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.

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basic time value concept
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
Accounting Applications
  • Notes
  • Leases
  • Pensions
  • Long-term assets
  • Sinking funds
  • Business combinations
  • Disclosures
  • Installment contracts
fundamental variables
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
Interest Rates
  • Specified in contracts
    • Stated
    • Coupon
    • Nominal
    • Face
  • Demanded by investors
    • Effective
    • Discount
    • Required rate of return
determining the effective rate
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 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    • the principal, and any interest accrued (earned and not withdrawn or paid).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
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
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
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
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
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
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
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
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
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
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.