IE 8_ Current vs Future Consumption.pdf - Page 1 of 13 Present(current vs future consumption and the PDV Charles Staelin Class Notes Present(current vs

IE 8_ Current vs Future Consumption.pdf - Page 1 of 13...

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Page 1 of 13 Present (current) vs. future consumption and the PDV Charles Staelin Class Notes - Present (current) vs. future consumption and the PDV We’re going to start backwards, with the result. We’ll then look at the consumer choice theory behind it. x Let’s say you are given the choice of two streams of income, starting today and g oing out four years. Date: 01/01/2019 01/01/2020 01/01/2021 01/01/2022 01/01/2023 Total Period 0 1 2 3 4 Stream 1 $800 $700 $600 $500 $400 $3,000 Stream 2 $400 $500 $600 $700 $900 $3.100 o Which stream would you chose? Stream 2 gives you more in total, but your satisfaction is delayed, relative to stream 1. x There are two ways that we could compare them: o Which one gives you the biggest nest egg at the end of the stream? This is called the “future value”. o Which one could you borrow the most against to day? This is called the “present value”, or often the “net present value” or “present discounted value” . o We’ll look at both. x Future value: o Look first at the first stream. The $800 you get “now” could be put in the bank at interest. H ow much would you have on 1/1/23? x On 1/1/20 you’d have $800 plus interest: $800*(1+r) x On 1/1/21 , you’d have that plus interest: [$800*(1+r)](1+r) = $800*(1+r) 2 x On 1/1/22 you’d have that plus interest: $800*(1+r) 3 x And on 1/1/23 you’d have that plus interest: $800*(1+r) 4 The $700 you get next year would have 3 years to collect interest: $700 *(1+r) 3 The $600 would have two years: $600*(1+r) 2 The $500 would have one year: $500*(1+r) 1 And that last $400 would have no years: $400*(1+r) 0 So, in total you’d have $800*(1+r) 4 + $700*(1+r) 3 + $600*(1+r) 2 + $500*(1+r) 1 + $400*(1+r) 0
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Page 2 of 13 Present (current) vs. future consumption and the PDV 2/21/2019 12:20 PM Page 2 of 13 The Excel spreadsheet (page 6). Let’s say that r was 10%, that would be: 1171.28 + 931.70 + 726.00 + 550.00 + 400.00 = $3,778.98 You’d have saved a nest egg of almost $3,779, earning a total of $779 in interest. This is called the future value . o Now let’s look at the second stream. In total you’d have $400*(1+r) 4 + $500*(1+r) 3 +$600*(1+r) 2 +$700*(1+r) 1 +$900*(1+r) 0 At 10%, that would be: 585.64 + 665.50 + 726.00 + 770.00 + 900.00 = $3,647.14 Your nest egg would be only about $3,647, even though you received $3,100 rather than only $3,000. Why? Because you ’d have earned less interest, $547.14 rather than $778.98, more than offsetting the extra $100. o But what if the interest rate were lower? Would the rank ing change? Let’s see. As r falls, the two streams get closer until finally the extra $100 of stream 2 overwhelms the higher interest earned on stream 1and stream 2 has a higher FV. x If r = 0 x Approx. equal at r = 4.9% o Back to the board. o How can we write FV symbolically? FV = ∑ Y i (1 + r) (T−t) T t=0 Where Y i is the income in year t (counting from zero, “now”) and T is the year of the last payment. o But, you say. That is well and good, but I need that money now! Well, you can. x Present Value: o You could borrow NOW against all that income, and pay off the loan as the money came in.
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