Finance

Chapter 18

Financial Mathematics

Learning Objectives

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Explain why a dollar today is worth more

than a dollar in the future.

Define future value and present value.

Explain the difference between an ordinary

annuity and an annuity due.

Calculate the future value and present value

of an annuity.

Decisions for Financial Managers

1. Where should we invest our funds?

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i.e. What types of equipment, buildings, services,

programs, or other opportunities should we

invest?

2. How will we finance our investment needs?

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Will we use debt, equity, or both?

Investment and Financing

• Investment decisions involve expending funds

today while expecting to realize returns in the

future

• Financing decisions involve the receipt of

funds today in return for a promise to make

payments in the future

• Therefore, manager’s major task is evaluating

the relative attractiveness of alternative

investment and financing opportunities

Time Value of Money

• Concept of time value money:

– Payment that is made or received in the first year

has a greater value than an identical payment made

or received in the tenth year

– “A dollar today is worth more than a dollar

tomorrow.”

• The idea that the value of money changes over

time is absolutely critical to investment and

financing decisions.

Time Value of Money

• If we accept that a dollar today is worth more

than a dollar received in the future, how can

we determine what that difference is?

– We must determine the cost for money

– e.g. the interest rate associated with borrowing, the

opportunity cost of investment, etc.

• Interest rate - the price for the commodity

called money (e.g. 10% per year)

Present Value & Future Value

• If the interest rate is 10%, a dollar received 1

year from now is only worth $0.9091 in

today’s dollar.

– This concept is called “Present Value”

• Conversely, if the interest rate is 10%, $0.9091

today will be worth exactly $1 one...