FIN504_PowerPoint_Slides_04

FIN504_PowerPoint_Slides_04 - FIN 504: Financial Management...

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FIN 504: Financial Management Lecture 4: Time Value of Money II
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2 FIN 504: Financial Management Time Value of Money II Time Lines Annuities Perpetuities
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3 FIN 504: Financial Management Time Lines The Use of Time Lines Temporal Indices: t T 1, 2, 3,… 0 1 2 3 4 5 T 6 C 0 C 1 C 2 C 4 C 3 C 5 C 6 C T
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Annuities
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5 FIN 504: Financial Management Annuities Annuities A finite series of constant cash flows, e.g., $100 per year for 5 years $10 per month for 7 months Variables Cash Flow Amount The Date of the First Payment The Period (weekly, quarterly, annually) The Length (or Number) of Payments
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6 FIN 504: Financial Management Annuities A 5 year annual, annuity of $500 beginning in year 1: TECHNICAL NOTE: When we use the term ‘annuity’ we mean an ‘annuity in arrears’, i.e., an annuity whose first payment begins next (not this) period. An annuity that begins this period is called an ‘annuity due’ and will be considered toward the end of the lecture. 0 1 2 3 4 5 6 0 50 50 50 50 50 0
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7 FIN 504: Financial Management Annuities Annuities can always be valued as a series of one time cash flow (r = 7%): 0 1 2 3 4 5 6 0 50 50 50 50 50 0 2 3 4 5 50 50 50 50 50 $205.01 1.07 1.07 1.07 1.07 1.07 + + + + =
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8 FIN 504: Financial Management Annuities But there is a general present value formula that is often more convenient: NOTE: The formula assumes that the first payment begins next period! ( 29 1 1 1 Annuity t C PV r r = - +
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9 FIN 504: Financial Management Annuities Thus: ( 29 5 50 1 1 $205.01 0.07 1.07 Annuity PV = - = 0 1 2 3 4 5 6 0 50 50 50 50 50 0
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10 FIN 504: Financial Management Annuities And there is a general future value formula : NOTE: The formula assumes that the first payment begins next period and it give the future value in year T! ( 29 ( 29 1 1 t Annuity C FV r r = + -
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11 FIN 504: Financial Management Annuities Thus: 0 1 2 3 4 5 6 0 50 50 50 50 50 0 ( 29 ( 29 5 50 1.07 1 $287.54 .07 Annuity FV = - =
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12 FIN 504: Financial Management Annuities We can check our calculations to make sure that the future value of the annuity (properly discounted) gives its present value: 5 287.54 $205.01 (1.07) =
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Delayed Annuities
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14 FIN 504: Financial Management Delayed Annuities Annuities may not begin in the next period. What if the annuity begins in two or three years, not next year. I call these ‘delayed annuities’.
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This note was uploaded on 06/29/2011 for the course FIN 525 taught by Professor Dloncar during the Spring '11 term at University of Baltimore.

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FIN504_PowerPoint_Slides_04 - FIN 504: Financial Management...

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