Business Finance Ch. 5 - Introduction to Valuation: The Time Value of Money

Suppose present value is $100, future value is $1,000, and N is 10 years. Which formula below is used to find the (decimal) interest rate?

r = (1000/100)(1/10) - 1

Interest earned only on the original principal amount invested is called ___ interest.

simple

Interest earned on the original principal amount invested is called _____.

simple interest

The difference between _______ interest and compound interest is that the amount of compound interest earned gets (bigger or smaller) ___________ every year.

simple; bigger

What is the future value of $1,000 invested for 8 years at 6%?

$1,593.85 $1,000 x (1 + .06)^8

If $100 earns compound interest for 2 years at 10 percent per year, the future value will be ____.

$121.00

If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years?

$133.10

If you invest for a single period at an interest rate of r, your money will grow to ______ per dollar invested.

(1+r)

Using a time value of money table, what is the future value interest factor for 10 percent for 2 years?

1.21

True or false: The multi-period formula for future value using compounding is FV = (1 + r)t.

False

True or false: When using the time value of money features of a financial calculator, you should key in the interest rate as a decimal.

False Reason: The calculator is programmed to interpret 10 as 10%, and 0.1 as 0.1%.

___ value is the cash value of an investment at some time in the ___.

Future future

Future value is the Blank______ value of an investment at some time in the future.

cash

Discounting is the opposite of

compounding

The idea behind ______ is that interest is earned on interest.

compounding

The process of leaving your money and any accumulated interest in an investment for more than one period, thereby reinvesting the interest, is called ___ . (Enter one word per blank.)

compounding or compound

The equation that results in the Blank______ value interest factor for a single deposit is as follows: (1 + r)t

future Reason: This is the equation for the future value.

A dollar received one year from today has _____ value than a dollar received today.

less

All else equal, the longer time period you have before you will need the money, the __ (less/more) you will need to deposit today to have the same amount in the future.

less

In general, if you invest for one period at an interest rate of r, your investment will grow to 1 ___ (minus/plus) r.

plus or +

If you want to know how much you need to invest today at 12 percent compounded annually in order to have $4,000 in five years, you will need to find a(n) _______ value.

present

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

present

The equation that results in the ______ value interest factor for a single deposit is as follows: 1(1+r)t

present

If we know the interest rate is 10 percent per year and the money is invested for 10 years, then we can use the _____ to find the present value.

present value factor

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

discount or discounted

The basic present value equation underlies many of the _____.

most important ideas in corporate finance

When the future value formula is used to calculate growth rates, the assumption is that _____ growth rate is achieved each year.

the same

The greater the number of time periods, ___ the (smaller/greater) the impact of compounding.

greater

The discount rate is also called the rate of

return

Which formula below represents a present value factor?

1/(1 + r)t

Assuming the interest rate offered for a 10-year investment plan is same as for a 4-year investment plan. For an investor to achieve the same future value, which of these two plans would require a smaller savings amount to be deposited today?

10-year investment

Suppose you want to save $10,000 to buy a car. You have $6,000 to deposit today and you can earn 6% on your investments. You want to know when you'll have enough to buy the car. Which of the following spreadsheet functions will solve the problem?

=NPER(0.06,0,−6000,10000)

Which formula will you enter into a spreadsheet cell to determine how long it will take $40 to grow to $240 at an interest rate of 6.53% compounded annually?

=NPER(0.0653,0,−40,240)

Which of the following methods can be used to calculate present value?

A time value of money table An algebraic formula A financial calculator

The basic present value equation is:

PV = FVt(1+r)t

Why is a dollar received today worth more than a dollar received in the future?

Today's dollar can be reinvested, yielding a greater amount in the future.

True or false: Discounting is the opposite of compounding.

True

True or false: The correct future value interest factor in a time value of money table for $1 in 10 years at 10 percent per year is 2.5937.

True Reason: On Table A.1 in the back of the text, read the interest rate across the top and the time periods along the side. This is the correct FV factor for 10 percent for 10 years.

The formula for a present value factor is 1/(1+r)^t.

True Reason: This is the present value interest factor, not the present value itself. In order to get PV, you need to multiply FV by this factor. Notice how as the denominator becomes larger due to higher interest or longer periods, it reduces the factor.

You invest $500 at 10 percent interest. At the end of 2 years with simple interest you will have ____ and with compound interest you will have ____.

$600; $605 Reason: With simple interest you will earn $500 X 0.10 = $50 each year. Your total will be $500+100=$600. With compound interest, you will have $500(1.10)2 = $605 at the end of the two years. Given the same rate of interest, the FV will always be higher with compound interest.

True or false: Small changes in the interest rate affect the future value of a small-term investment more than they would affect the value of a long-term investment.

False Reason: Small rate differences can be worth thousands of dollars, especially when either the amount or the time period is large.

True or false: Given the same rate of interest, more money can be earned with compound interest than with simple interest.

True Reason: With compound interest, you earn interest on interest as well as interest on the principal.

Calculating the present value of a future cash flow to determine its value today is called _____.

discounted cash flow valuation

Which of the following can be determined using the future value approach to compound growth developed in this chapter?

Dividend growth Sales growth

Which of the following is the correct mathematical formula for calculation of the future value of $100 invested today for 3 years at 10% per year?

FV = $100 × (1.10)3

The ___ (smaller/greater) the interest rate changes, the greater the impact to the future value of an amount invested.

greater