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TIME VALUE OF MONEY
Net Present Value: What It Looks Like
ATM installation
Server consolidation
Discount
Present
Present
Year factor (at Cash flow value of Cash flow value of
10%)
cash flow
cash flow
0
1.000
-$1 million -$1 million -$1 million -$1 million
1
0.909
+$500,000 +$454,500
2
0.826
+$500,000 +$413,000 +$750,000 +$619,500
3
0.751
+$500,000 +$375,500 +$500,000 +$375,500
4
0.683
+$500,000 +$341,500
5
0.621
+$500,000 +$310,500
Total
+$1.5
million
+$895,000
+$1
million
+$1.25
million
+$909,000
+$904,000
NPV considers the time value of money. In this example, we
compare two $1 million projects with a minimum desired rate of
return of 10%. On the basis of simple cash flow, the ATM
installation looks better because it generates $250,000 more over
the life of the investment. But when the time value of money is
considered, the server consolidation project looks slightly better,
with an NPV higher by $9,000, because the returns occur earlier in
the project's life.
1. Compound Interest:
Suppose the Fosters invest $100,000 today in an investment that produces 5% interest per year. What will the
investment be worth in two years?
2. Compound vs. Simple Interest:
You are faced with a choice between two accounts, Account A and account B. Account A pays 5.00% interest
compounded annually. Account B pays 5.25% simple interest. Consider a deposit of $10,000 today. Which
account will provide the highest balance at the end of 4 years?
3. Frequency of Compounding
a) Suppose you invest $20,000 in an account that pays 6.5% interest, compounded monthly. How much will you
have at the end of 20 years?
b) What if you invest the same amount at the same interest but the compounding is done semi-annually. How
much will you have at the end of 20 years?
4. Discounting
Suppose you wish to have $20,000 saved by the end of 4 years, and you want to start depositing funds today.
You are getting 4% interest, compounded annually. How much to you need to deposit today to meet this goal?
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Q5. Assume you have 30 years to retire and you deposit $4,000 in an IRA each year earning an average of
7.5%. What will be the value at retirement? What if you start paying this year instead of next? What if you put
the money in stocks instead and estimate a 10% return?
Q6. What is the present value of 5 payments of $500 to be received annually at 10%?
Q7. Find the present value of $500 to be received in 5 years at 10%.
Q8. Find the future value of $1500 invested for 5 years at 6.75%.
Q9. A strategic mobile investment company in US buys a note for US $12,835,000 from a mobile operator in
your country. The funds received from the note will enable the local company to make new investments to
facilitate the expansion of mobile services in the rural areas. The local company is supposed to make ten equal
annual payments to the US based company of US $2,000,000. According to the signed contract, the first
payment should be made one year from the date of the receipt of the funds. You are required to calculate the rate
of return on the note offered.
Q10: Present Value with Quarterly Compounding
How much would you have to deposit today in an account that pays 4% annual interest, compounded quarterly,
if you wish to have a balance of $100,000 at the end of ten years?
Q11: Present Value with Monthly Compounding
How much would you have to deposit today in an account that pays 4% annual interest, compounded
continuously, if you wish to have a balance of $100,000 at the end of ten years?
Q12. Future value: Interest rate on a savings account
You put $10,000 in the bank for 4 years. The bank pays 3% interest per year, with semi-annual compounding.
Q13. Present value example - Payments for a loan
Loan balance = $100,000, 30 years, 6% interest per year, monthly payments (and monthly compounding).
Q14. Annuity Payment when FV is known
You want to purchase a house in 5 years and will need a down-payment of $90,000. How much will you need to
save each year if your savings will earn a rate of 4.25% a year?
Assume you inherited $10,000 that you will use to begin saving now toward the down-payment. What is your
new annual saving requirement?
Q15: Number of Annuity Payments when PV or FV is known
You need to get $25,000 payment for a car. You estimate an annual payment of $3000. The interest rate is 5%.
How many years do you need to pay?
TIME VALUE OF MONEY QUIZ
1.
Which of the following statements is (are) true?
(Note: more than one answer may be correct)
a. For a specific dollar amount today (the present value or PV), the associated future value (FV) will be
larger, given a positive rate of return (or a positive interest rate).
b. For a specific dollar amount at some point in the future (a future value or FV), the present value today
(or PV) will be larger, given a positive rate of return (or a positive interest rate).
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c. For a specific dollar amount at some point in the future (a future value or FV), the present value today
(or PV) will be smaller, given a positive rate of return (or a positive interest rate).
d. For a specific dollar amount today (the present value or PV), the associated future value (FV) will be
snaller, given a positive rate of return (or a positive interest rate).
e. none of the above
2.
A home mortgage loan and the related financial calculations are an example of _____.
a. a present value of a dollar problem
b. a future value of a dollar problem
c. a present value of an annuity problem
d. a future value of an annuity problem
e. none of the above
3.
All business investment decisions should be made on _____ .
a. a basis that maximizes profitability
b. a discounted cash flow basis
c. an accounting profit basis
d. a collaborative basis
e. none of the above
4.
Which of the following decisions can be made using time value of money problems?
a. personal investing decisions
b. small business investment decisions
c. home mortgage refinancing decisions
d. franchise investment decisions
e. retirement investment decisions
f. all of the above
5.
Which of the following statements is false?
a. A discount rate is nothing more than an interest rate that is used when calculating present values.
b. Compound Value Interest Factors are the same thing as Present Value Interest Factors.
c. When calculating compound interest the assumption is made that past interest earnings are reinvested.
d. Compound interest is the norm for time value of money calculations.
e. In simple interest calculations, it is assumed that past interest earned has not been reinvested.
6.
Which of the following statements is (are) false?
a. An annuity is a stream of equal payments.
b. An annuity due has the payments made at the beginning of each period.
c. An ordinary annuity has the payments made at the end of each period.
d. All annuities have the payments made in the middle of the payment period.
e. Annuity tables usually found in finance texts provide annuity interest rate factors for ordinary annuity
streams.
7.
If you invest $1,000 for 3 years at 7% simple interest, how much will you have at the end of the 3 years?
a. $1,000.00
b. $1,070.00
c. $1,210.00
d. $1,225.04
e. cannot calculate with given information
8. If you invest $1,000 for 3 years at 7% compound interest, how much will you have at the end of the 3
years?
a. $1,000.00
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b.
c.
d.
e.
$1,070.00
$1,210.00
$1,225.04
cannot calculate with given information
9. In a sinking fund, a firm makes a series of equal payments into a savings account in order to have a certain
dollar amount available at some point in the future. What type of time value problem is this?
a. a present value of a dollar problem
b. a future value of a dollar problem
c. a present value of an annuity problem
d. a future value of an annuity problem
e. none of the above
10. Assume you will work for the next 20 years and at the end of each year you will deposit $20,000 into a
savings account. At the end of that 20 year period you will start withdrawing your retirement living expenses
from that account at the beginning of every year. This financial plan involves a _____ problem while you are
working and a _____ problem while you are in retirement.
a. a present value of a dollar, future value of a dollar
b. a future value of an annuity due, a present value of an annuity due
c. a future value of an annuity due, a present value of an ordinary annuity
d. a future value of an ordinary annuity, a present value of an annuity due
e. a future value of an ordinary annuity, a present value of an ordinary annuity