BA103-F04-class03-annuities(4slides)

BA103-F04-class03-annuities(4slides) - Todays plan How to...

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1 class #03 page 1 How to calculate present values class #03 class #03 page 2 Class rep The class rep is ?? If you have constructive suggestions that will help the course, could you: come see me in office hours see the class rep if you don’t want to see me directly In the past some students waited until the final evaluation to offer suggestions (which, of course, didn’t help them out) class #03 page 3 Today’s plan What do we still need to value projects, financial assets, firms? We need to learn how to value streams of cash flows … this is what we will do today Compute FV and PV of multiple cash flows: annuities and perpetuities Compound interest class #03 page 4 Valuation of multiple cash flows There are two ways to calculate future values of multiple cash flows: Calculate the future value of each cash flow first and then add them up Compound the accumulated balance forward one year at a time Therefore, there are two ways to calculate present values of multiple cash flows: Calculate the present values of each individual cash flow first and then add them up Discount back the balance one period at a time
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2 class #03 page 5 Multiple cash flows: present value Suppose we expect to receive $1000 at the end of each of the next 5 years. Interest rate is 6%. What is the value today of this set of cash flows? 1. PV 0 = 1,000 / (1.06) 5 + 1,000 / (1.06) 4 + 1,000 / (1.06) 3 + 1,000 / (1.06) 2 + 1,000 / (1.06) = $4212.37 2. 1,000 / (1.06) = 943.4; 1,943.40 / (1.06) = 1,833.40; 2,833.40 / (1.06) = 2,673.01; 3,673.01 / (1.06) = 3,465.11; 4465.11 / (1.06) = $4,212.37 01 2 3 5 PV 0 = ? +1,000 +1,000 +1,000 +1,000 +1,000 4 class #03 page 6 Multiple cash flows: present value Present value calculated by discounting each cash flow separately 0 1 2 3 4 5 $1,000 $1,000 $1,000 $1,000 $ 943.40 890.00 839.62 792.09 747.26 $4,212.37 x 1/1.06 5 Total present value Time (years) $1,000 r = 6% x 1/1.06 4 x 1/1.06 3 x 1/1.062 x 1/1.06 0 1 2 3 4 5 $4,212.37 0.00 $4,212.37 $3,465.11 1,000.00 $4,465.11 $2,673.01 1,000.00 $3,673.01 $1,833.40 1,000.00 $2,833.40 $ 943.40 1,000.00 $1,943.40 $ 0.00 1,000.00 $1,000.00 Present value calculated by discounting back one period at a time Time (years) Total present value = $4,212.37 r = 6% class #03 page 7 Multiple cash flows: future value We invest $2,000 for 5 years at 10% per year. What is the FV in five years? Future value calculated by compounding forward one period at a time Time (years) 0 1 2 3 4 5 $0 0 $0 $ 0 2,000 $2,000 $2,200 2,000 $4,200 $4,620 2,000 $6,620 $7,282 2,000 $9,282 $10,210.2 2,000 $12,210.2 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 Time (years) 0 1 2 3 4 5 $2,000 $2,000 $2,000 $2,000 $2,000.0 2,200.0 2,420.0 2,662.0 2.928.2 $12,210.20 x 1.14 x 1.1 3 x 1.1 2 x 1.1 Total future value Future value calculated by compounding each cash flow separately class #03 page 8 Types of multiple cash flows Annuities Ordinary annuity : a series of identical cash flows occurring at the end of each period for some fixed number of periods Examples: consumer loans (e.g. car loans), home mortgages, etc.
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BA103-F04-class03-annuities(4slides) - Todays plan How to...

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