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Unformatted text preview: rowth Suppose your company expects to
Suppose increase unit sales of widgets by 15% per
year for the next 5 years. If you currently
sell 3 million widgets in one year, how
many widgets do you expect to sell in 5
years? FV = 3,000,000(1.15)5 = 6,034,072 11 Quick Quiz – Part I What is the difference between simple interest
and compound interest?
Suppose you have $500 to invest and you
believe that you can earn 8% per year over the
next 15 years.
next How much would you have at the end of 15 years
using compound interest?
How much would you have using simple interest? 12 Present Values How much do I have to invest today to have some
amount in the future?
amount FV = PV(1 + r)t
Rearrange to solve for PV = FV / (1 + r)t When we talk about discounting, we mean finding the
present value of some future amount.
When we talk about the “value” of something, we are
talking about the present value unless we specifically
indicate that we want the future value.
indicate 13 Present Value – One Period
Example Suppose you need $10,000 in one year for the down
payment on a new car. If you can earn 7% annually,
how much do you need to invest today?
PV = 10,000 / (1.07)1 = 9,345.79
CPT PV = -9,345.79 14 Present Values – Example 2 You want to begin saving for your
You daughter’s college education and you
estimate that she will need $150,000 in 17
years. If you feel confident that you can
earn 8% per year, how much do you need
to invest today?
to PV = 150,000 / (1.08)17 = 40,540.34 15 Present Values – Example 3 Your parents set up a trust fund for you 10
Your years ago that is now worth $19,671.51. If
the fund earned 7% per year, how much
did your parents invest?
did PV = 19,671.51 / (1.07)10 = 10,000 16 Present Value – Important
Relationship For a given interest rate – the longer the
For time period, the lower the present value
time What is the present value of $500 to be
received in 5 years? 10 years? The discount
rate is 10%
5 years: PV = 500 / (1.1)5 = 310.46
10 years: PV = 500 / (1.1)10 = 192.77 17 Present Value – Important
Relationship For a given time period – the higher the
For interest rate, the smaller the present
value What is the present value of $500 received
in 5 years if the interest rate is 10%? 15%?
• Rate = 10%: PV = 500 / (1.1)5 = 310.46
• Rate = 15%; PV = 500 / (1.15)5 = 248.59 18 Quick Quiz – Part II What is the relationship between present value
and future value?
Suppose you need $15,000 in 3 years. If you
can earn 6% annually, how much do you need to
If you could invest the money at 8%, would you
have to invest more or less than at 6%? How
much? 19 The Basic PV Equation The
Refresher PV = FV / (1 + r)t
There are four parts to this equation PV, FV, r and t
If we know any three, we c...
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