Module 24
May 2015
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A dollar today is worth more than a dollar a
year from now…if you know you are going to
receive $1000 a year from now, you can
borrow money today to be paid back when
you receive your $1000…however, you must
borrow less than $1000 because you must
factor in the amount borrowed plus interest
Scenario 2: Get $1000 now and put in the
bank…one year from now it will be more than
$1000 because it will have earned interest
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Present value – of $1 realized one year from
now is equal to $1/(1+r): the amount of
money you must lend out today in order to
have $1 in one year. It is the value to you
today of $1 realized one year from now.
If the interest rate is 10%, then r=0.10. If you
lend out $X at the end of the year you will
receive $X plus interest which is $X x r or
$X(1+ r)
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If $X(1 +r) = $1 then $X=$1/(1+r)
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$X=$1/(1+0.10)=$1/$1.10=$0.91
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In order to have $1 a year from now at an
interest rate of 10%, you must invest $0.91
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$V is the amount of money you’ll lend today
in order to have $1 in two years
$Vx(1+r) in one year and if you re-lend you
will receive $Vx(1+r) x (1+r) = $𝑉 × (1 + 𝑟)2
Solve if we want $1 in two years
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$0.83
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A project is the present value of current and
future benefits minus the present value of
current and future costs.