Time Value of Money Concepts

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Time Value of Money Concepts

• Sid Glandon, DBA, CPA
• Associate Professor of Accounting

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Accounting Measurements using Present Value
Concepts

• Notes
• Leases
• Amortization of premiums and discounts
• Pensions and other postretirement benefits
• Long-term assets
• Sinking funds
• Business combinations
• Disclosures
• Installment contracts

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Variables in Interest Computation

• Principal
• Amount borrowed or invested
• Interest rate
• Percentage applied to outstanding principal
• Time
• Number of periods that the principal is
  outstanding

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Components of Interest

• Pure (risk free) rate (2-4)
• Credit risk rate (0-5)
• Expected inflation (0-?)

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Simple Interest

• Interest p i n
• pprincipal
• irate of interest for a single period
• nnumber of periods

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Example Simple Interest
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Compound Interest

• Computed on
• Principal balance, plus
• Accumulated interest not withdrawn

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Example Compound Interest
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Interest RatesFrequency of Compounding

• Interest rate of 12 per year
• Annual
• Compounded once per year at 12
• Semi-annual
• Compounded twice per year at 6
• Quarterly
• Compounded four times per year at 3
• Monthly
• Compounded twelve times per year at 1

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Compound Interest Tables

• Future value of 1
• Present value of 1
• Future value of ordinary annuity of 1
• Present value of ordinary annuity of 1
• Future value of annuity due of 1
• Present value of annuity due of 1

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Annuity Computations

• Requires that
• Periodic payments or receipts always be of the
  same amount
• Interval between payments or receipts be the same
• Interest be compounded once each interval

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Ordinary Annuities

• Payments or receipts are always made at the end
  of the period
• Use the FVOA or PVOA tables

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Annuity Due

• Payments or receipts are always made at the
  beginning of the period
• Multiply 1 plus the interest rate times the table
  value of an ordinary annuity

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Future Value of 1
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Present Value of 1
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Future Value of Ordinary Annuity
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Present Value of Ordinary Annuity
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Future Value of Annuity Due
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Present Value of Annuity Due
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Issue Price of Bonds

• PV of Principal
• Using market rate of interest
• PV of Annuity
• Annuity Principal times stated interest rate
• Using market rate of interest
• Equals Issue Price of Bonds

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Fact Pattern Issue Price of Bonds

• Face Amount, 100,000
• Stated interest rate, 8
• Length of bonds, 10 years
• Interest payments, semi-annual
• Market interest rate, 10

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Issue Price of Bonds