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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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Accounting and the Time Value of Money

Chapter 6


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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.


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Accounting Applications

  • Notes

  • Leases

  • Pensions

  • Long-term assets

  • Sinking funds

  • Business combinations

  • Disclosures

  • Installment contracts


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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).



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Interest Rates

  • Specified in contracts

    • Stated

    • Coupon

    • Nominal

    • Face

  • Demanded by investors

    • Effective

    • Discount

    • Required rate of return


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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.


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    • the principal, and any interest accrued (earned and not withdrawn or paid).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


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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


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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


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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?


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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?


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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.


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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.


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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?


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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?


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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


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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.