ActSc371_Lecture 9_Chapter 5 (Ross)

ActSc371_Lecture 9_Chapter 5 (Ross) - ActSc 371 Corporate...

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Lecture 9 Sections 5.4 and 5.5 Chapter 5: Time Value of Money (Corporate Finance by Ross et al.) ActSc 371 – Corporate Finance 1 Instructor: Dr. Lysa Porth 1
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Introduction Introduction to Corporate Finance 5.4 Simplifications 5.5 What is a firm worth? 2
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3 5.4 Simplifications Perpetuity A constant stream of cash flows that lasts forever. Growing perpetuity A stream of cash flows that grows at a constant rate forever. Annuity A stream of constant cash flows that lasts for a fixed number of periods. Growing annuity A stream of cash flows that grows at a constant rate for a fixed number of periods.
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Perpetuity A constant stream of cash flows that lasts forever. 0 1 C 2 C 3 C The formula for the present value of a perpetuity is: + + + + + + = 3 2 ) 1 ( ) 1 ( ) 1 ( r C r C r C PV r C PV =
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Perpetuity: Example What is the value of a British consol that promises to pay £15 each year, every year indefinately? The interest rate is 10-percent. 0 1 £15 2 £15 3 £15 £150 10 . £15 = = PV
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Growing Perpetuity A growing stream of cash flows that lasts forever. 0 1 C 2 C ×(1+ g ) 3 C ×(1+ g )2 The formula for the present value of a growing perpetuity is: + + + × + + + × + + = 3 2 2 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( r g C r g C r C PV g r C PV - =
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Growing Perpetuity: Example The expected dividend next year is $1.30 and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream? 0 1 $1.30 2 $1.30 ×(1.05) 3 $1.30 ×(1.05)2 00 . 26 $ 05 . 10 . 30 . 1 $ = - = PV
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Annuity A constant stream of cash flows with a fixed maturity. 0 1 C 2 C 3 C The formula for the present value of an annuity is: T C T r C r C r C r C PV ) 1 ( ) 1 ( ) 1 ( ) 1 ( 3 2 + + + + + + + = + - = T r r C PV ) 1 ( 1 1
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Annuity Intuition An annuity is valued as the difference between two perpetuities: one perpetuity that starts at time 1 less a perpetuity that starts at time T + 1 0 1 C 2 C 3 C T C T r r C r C PV ) 1 ( + - =
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Annuity: Example If you can afford a $400 monthly car payment, how much car can you afford if interest rates are 7% on 36-month loans? 0 1 $400 2 $400 3 $400 36 $400 59 . 954 , 12 $ ) 12 07 . 1 ( 1 1 12 / 07 . 400 $ 36 = + - = PV
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How to Value Annuities with a Calculator First, set your calculator to 12 payments per year. PMT I/Y FV PV N –400 7 0 12,954.59 36 Then enter what you know and solve for what you want.
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0 1 2 3 4 5 $100 $100 $100 $100 $327.9 7 $297.2 2 What is the present value of a four-year annuity of $100 per year that makes its first payment two years from today if the discount rate is 9%? Annuity: Example for “Lumpy” Cash Flows 97 . 327 $ ) 09 . 1 ( 100 $ ) 09 . 1 ( 100 $ ) 09 . 1 ( 100 $ ) 09 . 1 ( 100 $ ) 09 . 1 ( 100 $ 4 3 2 1 4 1 1 = + + + = = = t t PV 22 . 297 $ 09 . 1 97 . 327 $ 0 = = PV
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How to Value “Lumpy” Cash Flows First, set your calculator to 1 payment per year.
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