Institute of Economic Theories - University of Miskolc
Microeconomics
Lecture 11
Capital market
Andrea Gubik Safrany, PhD
Assistant professor
Mónika Orloczki
Assistant lecturer
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Time Value of Money
Money today is more valuable than the same
amount of money at some point in the future.
– Money has a time value because it can be invested
to make more money.
Money makes money. And the money that money
makes, makes more money.
Benjamin Franklin
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• Interest The payments made for the use of
money.
Interest is an important part of the investment
decisions for two reasons:
– Interest must be paid to borrow funds.
– Interest is the opportunity cost of using money to
pay for an investment project. (Money used to
purchase capital could have been deposited in a
bank to earn interest.)
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Lenders charge interest
• To compensate themselves for not being
able to use their own money to buy the
things they want
• To compensate themselves for the risk
they assume when they make a loan
• Because rising prices will reduce the
purchasing power of the money when it
is repaid
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Interest rate
Interest rate A fee paid annually expressed as a
percentage of the loan or deposit.
Interest rate’s determinants
• Demand and supply of money
• Risk level
• Length of maturity
• Transaction costs
• Inflation rate (a given amount of money buys
fewer goods in the future than it will now)
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Present value and future value
Present value (PV) - The current value of a future sum
of money.
FV
PV 
t
1  i 
Discounting refers to the method used to calculate the present
value of a stream of payments over time.
Future value (FV) - the present value plus interest.
Compound interest interest that is paid both on the original
amount of money saved and on the interest that has been added
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to it (interest on interest)
Present Value of a Dollar in the
Future
Present value, PV
$1
i = 0%
90¢
80¢
70¢
60¢
50¢
40¢
30¢
20¢
10¢
i = 20%
i = 10%
i = 5%
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0
10
20
30
40
50
60
70
80
90
100
t, Years
Example
Suppose the interest rate is 5%.
– What is the future value of $10,000 one year from
now?
• FV = $10,000 x (1 +.05) = $10,500
– What is the present value of $10,000 received one
year from now?
• PV = $10,000 / (1 +.05) = $9,524
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Example
Suppose that you agree to pay $10 at the end of each
year for three years to repay a debt. If the interest rate is
10%, the present value of this series of payments is:
$10 $10 $10
PV 
 2  3  $24.87
1.1 1.1 1.1
Find the future value of compound interest where the
amount is $100 and interest is 10% for 10 years.
FV = $100 * (1 + 0.1)10 = $259.37
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Example
$
300
250
200
150
100
50
0
1
2
3
4
5
6
7
8
9
10
years
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Payments Forever (perpetuity)
If you put PV dollars into a bank account earning an
interest rate of i,
you can get an interest or future payment of
f = i × PV at the end of the year.
To get a payment of f each year forever, you’d have
to put in the bank:
f
PV 
i
Value of land
land  rent
PVland 
i
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Net Present Value Approach
A firm should make an investment only if the present
value of the expected return exceeds the present
value of the costs
• If
– R = the present value of the expected returns to an
investment and
– C = the present value of the costs of the investment,
– the firm should make the investment if
R > C.
• A firm should make an investment only if the net
present value is positive:
NPV = R − C > 0.
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Net Present Value Approach
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Example
Suppose a firm is considering investing $8,000 in new
equipment. As a result of the new equipment, the firm
expects to earn revenues of $10,000 in each of
the next 2 years.
NPV   $8,000  $10,000 / (1 .05)  $10,000 / (1 .05)2
  $8,000  $9,524  $9,070  $10,594
Since NPV is positive, the firm should undertake the
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investment.
Internal rate of return (IRR)
The internal rate of
return on an
investment or project
is the discount rate
that makes the net
present value of all
cash flows (both
positive and negative)
from a particular
investment equal to
zero.
FVt
IRR  t
1
C0
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