Chapter 5 Introduction to Valuation: The Time Value of Money
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 financial calculator An algebraic formula A time value of money table
what is compounding? what is discounting?
Compounding refers to the growth of a dollar amount through time via reinvestment of interest earned. It is also the process of determining the future value of an investment. Discounting is the process of determining the value today of an amount to be received in the future.
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
If $100 earns compound interest for 2 years at 10 percent per year, the future value will be ____.
FV = $100 × 1.10 2 = $121
what happens to a future value if you increase the rate r? what happens to a present value?
FV as the rate of interest r increases (1+r)^(1+r)^t increases, thus the future value increases as the rate increases. PV as the rate of interest r increases (1+r)^(1+r)^t increases, as the rate increases (1+r)^t increases and thus the present value decreases
as you increase the length of time involved, what happens to future values? what happens to present values?
FV, as the length of time involved increases (1+r)^(1+r)^t increase, thus the future value increases as the time period increases. This reason this happens is the at the amount earns interest for an additional period which increases the future value. PV, as the length of time involved increases (1+r)^(1+r)^t. increase as the length of time involved increases (1+r)^t increases and the present value decreases.
the basic present value equation has four parts. what are they?
FV, future value t, time period r, cost of capital (interest) PV, present value
If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years?
FV= 100(1+.0.10)^3 $133.10
The multi-period formula for future value using compounding is FV = (1 + r)t.
False
When using the time value of money features of a financial calculator, you should key in the interest rate as a decimal.
False
Simple Interest
Interest earned only on the original principal amount invested
Which of the following investments would result in a higher future value? Investment A - 12% APR for 10 years Investment B - 12% APR for 12 years
Investment B
Which of the following investments would result in a higher future value? Investment A - 12% APR for 10 years Investment B - 12% APR for 12 years
Investment B
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)
in general what is the present value of $1 to be received in t periods, assuming a discount rate of r per period?
PV=FV/(1+r)^t
what is the basic present value equation?
PV=FV/(1+r)^t
Which of the following are correct spreadsheet functions?
Present value = PV(rate,nper,pmt,fv) Discount rate = RATE(nper,pmt,pv,fv) Future value = FV(rate,nper,pmt,pv)
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.
Discounting is the opposite of compounding.
True
discount
calculate the present value of some future amount
discount cash flow (DCF) valuation
calculating the present value of a future cash flow to determine its value today
what do we mean by discounted cash flow (DCF) valuation?
calculating the present value of future cash flow to determine its worth today.
Future value is the ________ 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 ___ .
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 ___.
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 ____?
compounding
The ___ rate is the rate used to calculate the present value of the future cash flows.
discount
Calculating the present value of a future cash flow to determine its value today is called _____.
discounted cash flow valuation
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
The equation that results in the _______ value interest factor for a single deposit is as follows: (1 + r)t
future
_______ value is the cash value of an investment at some time in the _____.
future ; future
The ___ the interest rate changes, the greater the impact to the future value of an amount invested.
greater
The greater the number of time periods, the ___ the impact of compounding.
greater
Longer-term bonds have ___ interest rate sensitivity because a ___ portion of a bond's value comes from the face amount.
greater ; larger
Compound Interest
interest earned on both the initial principal and the interest reinvested from prior periods.
Interest on Interest
interest earned on the reinvestment of previous interest payments
What do we mean by future vale of an investment:
is the cash value of an investment at some time in the future.
the process of discounting a future amount back to the present is the opposite of doing what?
it is the opposite of compounding the money forward
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 ___ you will need to deposit today to have the same amount in the future.
less
The reason that interest rate risk is greater for ____ term bonds than for ____ term bonds is that the change in rates has a greater effect on the present value of the ____ than on the present value of the ____.
long; short; face value; coupon payments
The basic present value equation underlies many of the _____.
most important ideas in corporate finance
In general, if you invest for one period at an interest rate of r, your investment will grow to 1 ___ r.
plus
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
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
What are the two major forms of long-term debt?
public issue and privately placed
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
The discount rate is also called the rate of ___.
return
Which of the following can be determined using the future value approach to compound growth developed in this chapter?
sales growth ; dividends growth
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
Future Value (FV)
the amount an investment is worth after one or more periods
present value (PV)
the current value of future cash flows discounted at the appropriate discount rate
future value interest factor (FVIF)
the expression (1 + r)^t
what does we mean by the present value of an investment?
the present value we invest today
Compounding
the process of accumulating interest on an investment over time to earn more interest
discount rate
the rate used to calculate the present value of future cash flows
When the future value formula is used to calculate growth rates, the assumption is that _____ growth rate is achieved each year.
the same
Given the same rate of interest, more money can be earned with compound interest than with simple interest.
true
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
The formula for a present value factor is 1/(1+r)^t.
true
What is the future value of $1,000 invested for 8 years at 6%?
$1,593.85
What is the future value of $100 compounded for 50 years at 10 percent annual interest?
$11,739.09
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
If you invest for a single period at an interest rate of r, your money will grow to ______ per dollar invested.
(1+r)
In general, what is the future value of $1 invested at r per periods for t periods?
(1+r)^t
Using a time value of money table, what is the future value interest factor for 10 percent for 2 years?
1.21
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
