Unformatted text preview: • The value of 10 dollars received in the next time period is • Discounting is a central concept in natural resource economics. • So, if $10 received at the beginning of the next period is only worth $10/(1 + r) at the beginning of the current period, how much is $10 received two periods from now worth? 2 Present Value Present Value
• In general, the value today of $B received t periods from now is $B/(1 + r)t. • The value today of an amount received in the future is called the Present Value of the amount. well as to amounts received. r) . • The concept of present value applies to amounts paid in the future as • For example, the value today of $B paid t periods from now is $B/(1 + t • Note that if the interest rate increases, the value today of an amount received in the future declines. • Similarly, if the interest rate increases, then the value today of an amount paid in the future declines. You Win the Lottery! You Win the Lottery!
• You are awarded aftertax income of $1M. However, this is not handed to you all at once, but at $100K/year for 10 years. If the interest rate is, r = 10%, net present value: • NPV = 100K+(1/1.1)100K+(1/1.1)2100K + (1/1.1)3100K + … + (1/1.1)9100K. = $675,900 • The value of the last payment received is: NPV = (1/1.1)9100K = $42,410. would be indifferent between receiving the flow of $1M over 10 years and $675,900 today or between receiving a one time payment of $100K 10 years from now and $42,410 today. • That is, if you are able to invest money at r = 10%, you The value of time :discounting The value of time :discounting
interest rate Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.05 0.1 Future Discou Future Discou earning nting earning nting 100 100 100 100 105 95.24 110 90.91 110.25 90.7 121 82.64 115.76 86.38 133.1 75.13 121.55 82.27 146.41 68.3 127.63 78.35 161.05 62.09 134.01 74.62 177.16 56.45 140.71 71.07 194.87 51.32 147.75 67.68 214.36 46.65 155.13 64.46 235.79 42.41 162.89 61.39 259.37 38.55 171.03 58.47 285.31 35.05 179.59 55.68 313.84 31.86 188.56 53.03 345.23 28.97 197.99 50.51 379.75 26.33 The Present Value of an The Present Value of an Annuity
• An annuity is a type of financial property (in the same way that stocks and bonds are financial property) that specifies that some individual or firm will pay the owner of the annuity a specified amount of money at each time period in the future, forever! • Although it may seem as if the holder of an annuity will receive an infinite amount of money, the Present Value of the stream of payments received over time is actually finite. rate r (this is the sum of an infinite geometric series). • In fact, it is equal to the periodic payment divided by the interest Annuity Cont. Annuity Cont.
• Let’s consider an example where you own an annuity that specifies that Megafirm will pay you $1000 per year for...
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 Spring '09
 ZELBERMAN
 Economics, Environmental Economics, Interest Rates

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