Managerial Finance Chapter 5
How much is $100 at the end of each year forever at 10% interest worth today?
$1,000 Reason: $100/.10 = $1,000
What is the future value of $100 invested for 4 years at 10% interest?
$146.41 Reason: FV = $100 x (1+r)t = $100 x (1+.1)4=$146.41
You will receive $100 in 1 year, $200 in 2 years and $300 in 3 years. If you can earn a 7.5% rate of interest, what is the present value of this stream of cash flows? (Please note that you receive nothing immediately - there is no initial payment).
$507.58 Reason: $100/(1.075)1 + $200/(1.075)2 + $300/(1.075)3 = $507.58
What is the present value of an annuity consisting of 100 end of year payments of $50,000 when the interest rate is 6 percent? Use your financial calculator.
$830,877.31 Reason: n=100,i=6,PMT=50000,fv FV=0, compute FV=830877.31
If a bank quotes a loan with an APR of 15 percent, compounded monthly, what is the periodic rate on this loan?
1.25 percent Reason: 15/12 = 1.25 percent
Which of the following is the correct formula for the discount factor?
1/(1+r)t Reason: 1/(1+r)t
If a bank account pays a monthly interest rate on deposits of 0.5 percent, what is the APR the bank will quote for this account?
6 percent Reason: 12 x 0.5 = 6 percent
Which of the following is a perpetuity?
A constant stream of cash flows forever
future value
FV
constant recurring payment
PMT
present value
PV
Which of the following is the correct equation for the present value of an annuity with regular payment C for t periods at interest rate r?
PV = C[1/r - 1/r(1+r)t]
True or false: The time value of money functions that are provided by your financial calculator are also available as functions in an Excel spreadsheet.
True Reason: Excel supports financial calculator functions.
The effective annual interest rate is also known as the ______________.
annually compounded rate
The present value of an annuity of $1 per period is called the ______________.
annuity factor
Joseph signs a contract with a company that will pay him $25,000. Following the principles of the time value of money, Joseph would be best off if he received payment:
at the beginning of the project Reason: The time value of money states that a dollar today is worth more than a dollar tomorrow. Therefore, if he received the $25,000 at the beginning of the project, he would have 3 months to invest his money and have it grow.
An ordinary annuity is a series of level payments that begin ____.
at the end of one payment period
A traditional (non-growing) annuity consists of a(n) ________ stream of cash flows for a fixed period of time.
fixed
A perpetuity is a constant stream of cash flows for a(n) ______ period of time.
infinite Reason: A perpetuity is a constant stream of cash flows for an infinite time period.
If you are promised $100 in one year, $200 in two years, and $300 in 3 years, then those promises combined equal ______ $600 today.
less than Reason: This relates to the time value of money concept - $1 is worth more today than it is in the future. Therefore, any funds that you receive in the future will be worth less than they are if you received them today.
The time value of money concept states that a dollar today is worth _______ a dollar tomorrow.
more than
number of periods
n
A stream of cash flows means that ________.
payments are made over time
The interest rate on the financial calculator is expressed as a
percentage.
Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2 and 3 you will deposit $100 in that account. What is the present value of that stream of cash flows?
$1,267.30 Reason: $1000 + $100/(1.06)1 + $100/(1.06)2 + $100/(1.06)3 = $1,267.30
Find the future value of an annuity of $100 per year for 10 years at 10 percent per year.
$1,593.75 Reason: First, find the PV by using the 10 year annuity factor: PV = $100 x 10 year annuity factor = $100 x [1/.1 - 1/.1x(1.1)10]= $614.46 To find the future value, multiply $614.46 x (1.1)10= $1,593.75.
Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2 and 3 you will deposit $100 in that account. How much will you have at the end of year 4?
$1,599.94 Reason: $1000(1.06)4 + $100(1.06)3 + $100(1.06)2 + $100(1.06)1 = $1,599.94
A dollar invested today at 7.5 percent interest compounded annually will be worth _______ one year from now.
$1.075 Reason: FV=$1.00(1+0.075)1
$200 at the end of each year forever at 10% per year is worth how much today?
$2,000.00 Reason: $200/0.10 = $2,000
You put $100 in the bank now, $200 in the bank a year from now, and $300 in the bank in two years. How much money will you have available 3 years from now if you earn a 7.5% rate of interest? (Calculate the future value of this stream of cash flows. Refer to Example 5.6.)
$677.85 Reason: $100 x (1.075)3 + $200 x (1.075)2 + $300 x (1.075) = $677.85
If the interest rate is 10% per year, then what is the present value (PV) of $100 received one year from today?
$90.91 Reason: PV = $100/1.10 = $90.91
A fixed stream of cash flows that ends after a specified number of years is called a(n):
annuity
A series of level payments that begins immediately for a specified period of time is called a(n):
annuity due
The value in t years of an investment made today at interest rate r is called the ___________ of your investment.
future value
interest rate expressed as a percentage
i
To use your financial calculator to solve annuity problems, you use the _____ key for entry of the constant payment C.
pmt
In Excel, cash inflows are recognized as ______ values and cash outflows are recognized as ______ values. Interest rates should be entered as ______.
positive, negative, decimals
Real-world investments often involve many payments received or paid over time. Managers refer to this as a ___________________.
stream of cash flows
Which of the following is a proper definition for the effective annual interest rate?
the interest rate that is annualized using compound interest
The future value of an annuity that lasts n years is equal to
the present value allowed to grow n years.