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1 Time Value of Money Concepts Sid Glandon, DBA, CPA Associate Professor of Accounting

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2 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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3 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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4 Components of Interest Pure (risk free) rate (2%-4%) Credit risk rate (0%-5%) Expected inflation (0%-?)

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5 Simple Interest Interest = p * i * n p=principal i=rate of interest for a single period n=number of periods

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6 Example: Simple Interest

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7 Compound Interest Computed on Principal balance, plus Accumulated interest not withdrawn

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8 Example: Compound Interest

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9 Interest Rates Frequency 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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10 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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11 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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12 Ordinary Annuities Payments or receipts are always made at the end of the period Use the FVOA or PVOA tables

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13 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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14 Future Value of $1

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15 Present Value of $1

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16 Future Value of Ordinary Annuity

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17 Present Value of Ordinary Annuity

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18 Future Value of Annuity Due

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19 Present Value of Annuity Due

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20 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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21 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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22 Issue Price of Bonds

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Bellringer Calculate the Simple Interest for #s 1 and 3 and the Total cost for #2. 1.$1800 at 3.2% for 4 years. 2. $17250 at 7.5% for 6 years. 3. $3,650.

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