141208M first summarized and advance-posted on FB Summarized from Greg Mankiw’s Principles of Economics PART 9 The Real Economy in the Long Run Chapter 27 of 36 – The Basic Tools of Finance … section 3 … The present value formula: • if r is the interest rate • then an amount X to be received in N years • has a present value of X / (1 + r)ᴺ • with an interest rate of 5%, the present value of $100 received in ten years is • $100 / (1.05)¹⁰ = $61 Because earning interest • reduces the present value below the amount X • the finding of the present value of a future sum of money • is called “discounting” The present value formula shows how much future sums should be discounted. The previous section question was: would you choose to receive $100 today or $200 in 10 years? If the interest rate is 5 percent, you should prefer $200 in 10 years • the present value of $200 in 10 years is • $200 / (1.05)¹⁰ = $123, which is more than $100 Note the answer to the question depends on the interest rate. If the interest rate were 8 percent • the $200 in 10 years would have a present value of $93 • $200 / (1.08)¹⁰ = $93 • here, you should take the $100 today Why does the interest rate matter for your choice? The higher the interest rate • the more you can earn by depositing your money in a bank • so, the more attractive getting $100 today becomes • future value of $100 at 5% interest ten years later is = $100 x (1.05)¹⁰ = $163 • future value of $100 at 8% interest ten years later is = $100 x (1.08)¹⁰ = $216 The concept of present value is useful in many applications, including investment decisions of companies. For example, General Motors consideration of building a new factory • the factory will cost $100 million today • and will yield $200 million in 10 years • should GM commence the project? GM compares the present value of the $200 million return to the $100 million cost • if the interest rate is 5 percent • the present value of the $200 million return from the factory is $123 million • present value of receiving $200 in 10 years = $200 / (1.05)¹⁰ = $123 • GM chooses to make the $100 million investment But, if the interest rate is 8 percent • the present value of the $200 million return from the factory is $93 million • present value of receiving $200 in 10 years = $200 / (1.08)¹⁰ = $93 • GM chooses not to make the $100 million investment The concept of present value • helps explain why investment • thus the quantity of loanable funds demanded • declines when the interest rate rises Suppose you win a million dollar lottery and are given a choice between • $20,000 a year for 50 years totaling $1,000,000 • or an immediate payment of $400,000 • which would you choose? To make this choice, you must calculate the present value of a stream of payments • suppose the interest rate is 7% • after doing 50 present value calculations and adding up the results • you would learn the present value of this million-dollar prize • at a 7% interest rate is only $276,000 Here, you are better off choosing the immediate payment of $400,000. You can confirm this calculation and see the formula for present value of a stream of payments at this website: ultimatecalculators/present_value_annuity_calculator.html
Posted on: Mon, 08 Dec 2014 13:53:39 +0000
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