4. ) The promised cash flows of three securities are listed below. If the cash flows are risk-free, and the risk-free interest rate is
3.5 %3.5%,
determine the no-a
itrage price of each security before the first cash flow is paid:
Security
Cash Flow Today ($)
Cash Flow in One Year ($)
A
500500
500500
B
00
1 comma 0001,000
C
1 comma 0001,000
00
The no-a
itrage price of security A is?
$
(Round to the nearest cent.)
5.) An Exchange Traded Fund (ETF) is a security that represents a portfolio of individual stocks. Consider an ETF for which each share represents a portfolio of 1 shareshare of Hewlett-Packard (HPQ), 33 sharesshares of Sears (SHLD), and 33 shares of General Electric (GE). Suppose the cu
ent stock prices of each individual stock are as shown here:
Stock
Cu
ent Market Price
HPQ
$ 29$29
SHLD
$ 35$35
GE
$ 12$12
a. What is the price per share of the ETF in a normal market?
. If the ETF cu
ently trades for $ 152$152, what a
itrage opportunity is available? What trades would you make? (Ignore any transaction costs.)
c. If the EFT cu
ently trades for $ 182$182, what a
itrage opportunity is available? What trades would you make? (Ignore any transaction costs.)
8.) Your grandfather put some money in an account for you on the day you were born. You are now
1818
years old and are allowed to withdraw the money for the first time. The account cu
ently has
$ 9 comma 838$9,838
in it and pays a(n)
5 %5%
interest rate.
a. How much money would be in the account if you left the money there until your 25th birthday?
. How much would be in your account if you left the money in the account until your 65th birthday?
c. How much money did your grandfather originally put in the account?
9. You have just received a windfall from an investment you made in a friend's business. He will be paying you $10,525 at the end of this year, $21,050 at the end of the following year, and $31,575
at the end of the year after that (three years from today). The interest rate is 14.8% per year.
a. What is the present value of your windfall?
. What is the future value of your windfall in three years (on the date of the last payment)?
10.) Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $700.
However, once built, the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $7,000 to build. Your buddy wants to know if he should invest the money to construct it. If the interest rate is 15.0% per year, what should your buddy do?
The NPV of the machine is
$.
(Round to the nearest dollar.)
11.)
What is the present value of $10,000
paid at the end of each of the next
5454 years if the interest rate is 8% per year?
The present value is
$
(Round to the nearest dollar.)
12.) When you purchased your house, you took out a 30-year annual-payment mortgage with an interest rate of 8% per year. The annual payment on the mortgage is $11,549. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance.
a. What is the payoff amount if you have lived in the house for 14
years (so there are 16 years left on the mortgage)?
. What is the payoff amount if you have lived in the house for 24
years (so there are 66 years left on the mortgage)?
c. What is the payoff amount if you have lived in the house for 14 years (so there are 16
years left on the mortgage) and you decide to pay off the mortgage immediately before the 14th
payment is due?
13.) A rich relative has bequeathed you a growing perpetuity. The first payment will occur in one year and will be $2,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 5% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 16% per year,
a. What is today's value of the bequest?
. What is the value of the bequest immediately after the first payment is made?
14.) Your oldest daughter is about to start kindergarten in a private school. Tuition is $20,000
per year, payable at the beginning of the school year. You expect to keep your daughter in private school through high school. You expect tuition to increase at a rate of 3% per year over the 13
years of her schooling. What is the present value of your tuition payments if the interest rate is
3% per year? How much would you need to have in the bank now to fund all 13 years of tuition?
The present value is
$
(Round to the nearest dollar.)
15.) Your
other has offered to give you $130, starting next year, and after that growing at 2.6%
per year for the next 20 years. You would like to calculate the value of this offer by calculating how much money you would need to deposit in a local bank so that the amount will generate the same cash flows as he is offering you. Your local bank will guarantee a 6.4% annual interest rate so long as you have money in the account.
a. How much money will you need to deposit into the account today?
. Assuming you deposited the amount of money in part
(a), and then withdrew the required payments each year, calculate the remaining balance at the end of years 1, 2, 10 and 19. (Hint: To solve this problem it is best to use an excel spreadsheet.)
16.) Your firm spends
$4,500 every month on printing and mailing costs, sending statements to customers. If the interest rate is 0.52% per month, what is the present value of eliminating this cost by sending the statements electronically?
This cost has a present value of
$
(Round to the nearest dollar.)
17.) You have just made an offer on a new home and are seeking a mortgage. You need to bo
ow
$631,000.
a. The bank offers a 30-year
mortgage with fixed monthly payments and an interest rate of
0.51% per month. What is the amount of your monthly payment if you take this loan?
. Suppose you take the 30-year
mortgage described in part (a). How much will you still owe on the mortgage after
15 years?
18.) You have an investment opportunity that requires an initial investment of $8,000
today and will pay $8,000 in one year. What is the IRR of this opportunity?
The internal rate of return (IRR) is
%.
(Round to the nearest whole percentage.)