Chap006

# Chap006 - Chapter 6 Discounted Cash Flow Valuation using M...

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Chapter 6 Discounted Cash Flow Valuation using Multiple Cash Flows

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Example of Multiple Cash Flows You are considering an investment that will pay you \$1000 per year for 3 years. If you want to earn 10% on your money, how much would you be willing to pay? We could deal with each cash flow individually: PV = 1000 / (1.1) 1 = 909.09 N = 1; I/Y = 10; FV = 1000; CPT PV = -909.09 PV = 1000 / (1.1) 2 = 826.45 N = 2; I/Y = 10; FV = 1000; CPT PV = -826.45 PV = 1000 / (1.1) 3 = 751.31 N = 3; I/Y = 10; FV = 1000; CPT PV = -751.31 PV = 909.09 + 826.45 + 751.31 = 2,486.85 We can keep doing this with more and more cash flows, but it quickly gets tedious.
3 types of multiple cash flow streams Annuity: cash flows are all the same amount, and spread out equally over a finite period of time. \$1000 per year for 5 years, e.g. We can handle annuities using the Time Value of Money keys on the BA-II Plus, specifically the PMT key. Perpetuity: cash flows are same amount, over regular intervals, but forever. Two perpetuity formulas. Multiple, uneven cash flows: use the cash flow (CF) function

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Ordinary Annuity versus Annuity Due If the first payment occurs at the end of the period, it is called an ordinary annuity We assume all problems are solved in this way unless told otherwise; default calculator setting If the first payment occurs at the beginning of the period, it is called an annuity due
Annuities and Perpetuities Basic Formulas Perpetuity: PV = C / r Ordinary Annuities: [ ] [ ] periods. of number the is t and rate interest the is r flow, cash annuity the is C where 1 FVIF 1 ) 1 ( r PVIF 1 ) 1 ( 1 1 , , - = = - + = - = = + - = r C FVIFA C r r C FVA C PVIFA C r r C PVA t r t t r t

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Annuity Notation The term in brackets is sometimes called the PVIFA— Present Value Interest Factor for Annuities, and written as PVIFA(r,t). Think of it as the present value of \$1 each period discounted back to t=0 at a rate r. Example: The present value of \$500 per year for three years if r=10% is: I will not use the PVIFA notation in class, but the solutions manual uses it occasionally. \$1387.55 3) , 04 (. * 500 04 . ) 04 . 1 ( 1 1 500 3 = = + - PVIFA
Annuities and the Calculator You can use the PMT key on the calculator for the annuity payment The sign convention still holds Ordinary annuity versus annuity due You can switch your calculator between the two types by hitting <2 nd > <PMT>, then <2 nd > <ENTER> on the TI BA-II Plus If you see “BGN” in the upper right corner of your calculator display, you have it set for an annuity due Don’t forget to switch back to “END” when finished by repeating the above process.

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Annuity – Using the PMT key Going back to the previous example:
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## This note was uploaded on 09/24/2011 for the course HADM 2225 taught by Professor Wellman, j during the Spring '08 term at Cornell.

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Chap006 - Chapter 6 Discounted Cash Flow Valuation using M...

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