The Time Value of Money Future Amounts and Present Values:

The Time Value of Money Future Amounts and Present Values Appendix B

Chapter 26 & Appendix B Outcomes: Capital Budgeting:

Chapter 26 & Appendix B Outcomes: Capital Budgeting Explain the concept of time value of money. Describe the difference between present value and future value of money. Describe the process of capital budgeting. Use the Payback Period method of capital budgeting to determine length of time needed to recover investment. Use the Average Rate of Return to make long-term business decisions. Use Discounted Cash Flows (Net Present Value) to make long-term business decisions.

Time Value of Money:

Time Value of Money An amount of money available today can be safely invested to accumulate to a larger amount in the future.

The growing value of money over time:

The growing value of money over time 0 1 2 3 4 Assume you invest $500 in a savings account that earns interest at the rate of 8% per year. This graph illustrates the growth in your savings account balance at the end of each of the next four years. $500 × 1.08 $540 × 1.08 $583 × 1.08 $630 × 1.08

Relationships between Present Values and Future Amounts:

Relationships between Present Values and Future Amounts In this example, your initial investment of $500 is the present value . It is invested for four years at 8% interest. Over the four years, the value of your investment increases to $680 , the future amount . 0 1 2 3 4 $500 × 1.08 $540 × 1.08 $583 × 1.08 $630 × 1.08

Future Amounts:

Future Amounts Present Value Future Amount A future amount is simply the dollar amount to which a present value will accumulate over time.

Future Amounts:

Future Amounts Assume you invest $500 in a savings account that earns interest at the rate of 8% per year. What will be the future amount at the end of 4 years? $500 Present Value × 1.360 Factor = $680 Future Amount

Computing the Required Investment:

Computing the Required Investment Assume you need $680 at the end of 4 years. If you can invest at 8% per year, what is the present value? $680 Future Amount 1.360 Factor $500 Present Value =

The Future Amount of an Annuity:

The Future Amount of an Annuity Future Amount Annuity Payment Annuity Payment Annuity Payment Annuity Payment Annuity Payment An annuity is a series of equal periodic payments.

The Future Amount of an Annuity:

Assume you invest $500 in a savings account at the end of each of the next 4 years. The account earns interest at the rate of 8% per year. What will be the balance in your account at the end of 4 years? $500 Periodic Payment × 4.506 Factor = $2,253 Future Amount of an Annuity The Future Amount of an Annuity

The Future Amount of an Annuity:

Assume you need $2,253 at the end of 4 years. If you can invest at 8% per year, what is the amount of required periodic payment? $2,253 Future Amount of an Annuity 4.506 Factor $500 Periodic Payment = The Future Amount of an Annuity

Present Values:

Present Values Present Value Future Amount The present value is today’s value of funds to be received in the future.

Using Present Value Tables:

Using Present Value Tables What would you pay today for the opportunity to receive $680 in 4 years, assuming an 8% interest rate? $680 Future Amount × .735 Factor = $500 Present Value (rounded)

What is the Appropriate Discount Rate?:

What is the Appropriate Discount Rate? All investments involve some degree of risk that actual future cash flows may turn out to be less than expected. Investors will require a rate of return that justifies taking this risk.

The Present Value of an Annuity:

The Present Value of an Annuity Annuity Payment Annuity Payment Annuity Payment Annuity Payment Annuity Payment Present Value

The Present Value of an Annuity:

The Present Value of an Annuity Assume you need cash flows of $500 at the end of each of the next 4 years. If your investment earns interest at the rate of 8% per year, what amount do you need to invest today to achieve your cash flow needs? $500 Periodic Payment × 3.312 Factor = $1,656 Present Value of an Annuity

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