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Microeconomics

Lecture 11Capital market

Institute of Economic Theories - University of Miskolc

Mónika Orloczki

Assistant lecturer

Andrea Gubik Safrany, PhD

Assistant professor

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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 rateInterest 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.

ti

FVPV

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Future value (FV) - the present value plus interest.

Discounting refers to the method used to calculate the present value of a stream of payments over time.

Compound interest interest that is paid both on the original amount of money saved and on the interest that has been added to it (interest on interest)

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Present Value of a Dollar in the Future

Pre

sen

t val

ue,PV

20¢

10¢

40¢

50¢

60¢

70¢

80¢

90¢

$1

t, Years0 10 20 30 40 50 60 70 80 90 100

i = 0%

i = 5%i = 10%i = 20%

30¢

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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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ExampleSuppose 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:

87.24$1.1

10$

1.1

10$

1.1

10$32PV

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

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10years

$

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Payments Forever (perpetuity)

i

fPV

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:

Value of land

i

rentlandPVland

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Net Present Value ApproachA 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 investment.

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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.

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C

FVtIRR t