5.2 Time Value of Money Present Value

Present Value

The current value of future cash flows discounted at the appropriate discount rate.

Discount Rate

The rate used to calculate the present value of future cash flows.

Which one of the following variables is the exponent in the present value formula? present value. future value. interest rate. time. There is no exponent in the present value formula.

Time

Discount

To "discount" a value means to calculate the present value of some future cash flow.

**** if the discount number is zero what is the value?

you raise it to the 0 power and it equals the value

** Ceteris Paribas (all else equal):

As interest rates increase → PV decreases

***** Ceteris Paribas (all else equal):

As the time period increases → PV decreases

The process of determining the present value of future cash flows in order to know their worth today is called which one of the following? compound interest valuation interest on interest computation discounted cash flow valuation present value interest factoring complex factoring

discounted cash flow valuation

Steve invested $100 two years ago at 10 percent interest. The first year, he earned $10 interest on his $100 investment. He reinvested the $10. The second year, he earned $11 interest on his $110 investment. The extra $1 he earned in interest the second year is referred to as: free interest. bonus income. simple interest. interest on interest. present value interest.

interest on interest

You want to purchase a new car, and you are willing to pay $20,000. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?

ln(FV_t/PV_00/ln(1+r) PV = -15000, FV = 20000 PMT = 0, I/Y = 10%, CPT N = 3.02

What is the relationship between present value and future value interest factors? The present value and future value factors are equal to each other. The present value factor is the exponent of the future value factor. The future value factor is the exponent of the present value factor. The factors are reciprocals of each other. There is no relationship between these two factors.

reciprocals of each other

• 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?

10,000/(1.07)^1 = $9,345.79

Example: You want to begin saving for your 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?

150,000/(1.08)^17

Example: Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest?

19,671.51/(1.07)^10= $10,000 N = 10, I/Y = 7, FV = 19671.51, PMT = 0,

You are planning to propose to your girlfriend in 3 years. Since she is the love of your life, you want to buy her a $20,000 diamond ring in 3 years. How much do you need to save today in an account that earns 6.25% annually? A. $16,674.13 B. $19,674.13 C. $20,000.00 D. $20,989.26 E. $23,989.26

A. $16,674.13 Solving for present value

What is the future value of $6,200 invested for 23 years at 9.25 percent compounded annually? $22,483.60 $27,890.87 $38,991.07 $41,009.13 $47,433.47

$47,433.47

You are investing $100 today in a savings account at your local bank. Which one of the following terms refers to the value of this investment one year from now?

Future Value

Present Value VS. Future Value

Future Value is Compounding Present Value is Discounting

Discounted Cash Flow

calculating the present value of a future cash flow to determine its value.

Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?

20,000/10,000^(1/6) − 1 = 12.2462%

Interest earned on both the initial principal and the interest reinvested from prior periods is called: free interest. dual interest. simple interest. interest on interest. compound interest.

Compound Interest

Your grandmother has promised to give you $5,000 when you graduate from college. She is expecting you to graduate two years from now. What happens to the present value of this gift if you delay your graduation by one year and graduate three years from now? remains constant increases decreases becomes negative cannot be determined from the information provided

Decreases

Terry is calculating the present value of a bonus he will receive next year. The process he is using is called: growth analysis. discounting. accumulating. compounding. reducing.

Discounting

Present Value Formula

FV_t/(1+r)^t

Compound Interest *** will be on Exam

Interest earned on both the initial principal and the interest reinvested from prior periods.

If you keep the interest you earned in an account, you should expect that interest to make interest. This is called

Interest on Interest

Steve just computed the present value of a $10,000 bonus he will receive in the future. The interest rate he used in this process is referred to as which one of the following? current yield effective rate compound rate simple rate discount rate

discount rate