More Than One Future Cash Flow?

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More Than One Future Cash Flow?
Yes
No
Single FV (4 parameters)
Even or Uneven Cash Flows
Even
Uneven
Annuity (5 parameters)
CF Worksheet
More Than One Pmt per year? Use Periodic Rate
More Than One Pmt per year?
Yes
No
Compute n
Draw Time Line
Draw Time Line
Add Cash Flows
Add Cash Flows
Ord. Annuity or An. Due?
Inventory What You Know To Identify What You
Dont Know Note Usually (but not always), One
of the Five Parameters Is Irrelevant
List Inputs
Know What You Need to Find?
Yes
No
Compute the Answer
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1. To complete your business school education,
you will need 10,000 a year for the next four
years, starting next year (that is, you will need
to pay for one years worth of schooling at the
beginning of the year, one year from today).
Your rich uncle offers to put you through school
and he will deposit a lump sum into a saving
account paying 7 p.a. sufficient to defray these
expenses. The deposit will be made today. How
large must the deposit be? (Assume your uncle is
rich because he won the lottery and he doesnt
know much about finance stuff.)
2. You are considering financing a new car which
cost 51,300 with an amortized loan. The nominal
rate is 2.9 p.a., the term of the loan is 6
years and you will make monthly payments. How
much will each payment be?
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3. How many years will it take for your savings
account to accumulate 1m if it pays 4 interest
p.a. compounded semiannually and you deposit 10k
every 6-months at the end of the 6-month period?
4. Today you deposited 1,300 in a bank that pays
5 p.a., compounded quarterly. How much money
would you have in this account 20 months from now?
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5. On 1 January 2008 you deposited 700 in a
mutual fund that has been yielding a constant 6
p.a. for the last several years. You plan to
deposit 700 every 3 months thereafter for the
next 4 years (i.e. the next deposit will be made
1 April, the subsequent deposit on 1 July, etc.)
How much money will have accumulated after 4
years?
6. On 1 January 2008 you deposited 700 in a
mutual fund that has been yielding a constant 6
p.a. for the last several years. You plan to
deposit 700 every 3 months thereafter for the
next 4 years (i.e. the next deposit will be made
1 April, the subsequent deposit on 1 July, etc.)
How much money will have accumulated after 4
years to include a payment to be made at the
beginning of the first quarter of the fifth year.
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TVM Sample Problems
6. (continued)
7. You are considering leasing a car that cost
46,000. The lease will be for 5 years and
requires monthly payments. Somewhere on the
lease paperwork you notice a statement to the
affect that you will be charged a nominal rate of
6.2850 p.a. Assume the car will be worth
20,000 at the end of the lease. What kind of
annuity is this?___________________ How much
will your payments be?
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TVM Sample Problems
8. What is the future value of an annuity due
yielding 9.6400 p.a. that pays quarterly
payments of 1,000 for 9 mos? (Do the math do
not use the financial functions on your
calculator. Draw a cash flow diagram)
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9. You are tasked with estimating the fair market
value of a security that promises uneven future
payments. The table below shows the monthly
payment schedule (each cash flow occurs at the
end of the month). You consider 6 p.a. to be
the appropriate opportunity cost. What is the
theoretical value of this security?
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10. Retirement Plan You plan to retire on your
65th birthday. You want to withdraw 100,000.00
each year at the beginning of each year. You plan
to live until your 88th birthday and you want
your account balance to be 0 on that day (this
is for planning purposes only). How much money
you must deposit annually into a retirement
account starting on your 25th birthday to fund
the above described retirement plan. You estimate
the average rate of return over the rest of your
life will be 7 p.a.
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TVM Sample Problems
11. Today you open a new investment account for
your company with a 30,000 deposit. The account
has had an average yield of 7.5600 p.a. over the
last three years and compounds every month. You
plan to deposit 30,000 into this account every
quarter, at the beginning of the quarter. Your
next deposit will be three months from now. How
much will you have in this account 3 years from
now?.
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12. A friend of yours is working as an unpaid
intern at a local brokerage firm and her boss is
selling some securities which pay 50 at the end
of each of the next 3 years and a final payment
of 1050 at the end of the 4th year. Your friend
says she can get you some of these securities at
a cost of 900 each. Your money is currently
invested in a bank that pays 8 p.a. with
quarterly compounding. You consider the
securities as being just as safe and as liquid as
your bank. What is the fair market value (the
theoretical value) of these securities?
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Another way
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13. You are considering buying one of the two
securities described below. What is the fair
market value of each security and which one is
priced closer to its fair market value? Security
A A 2-year investment period yielding 6.35
p.a. monthly payments of 75 priced at
1950. Security B A 2-year investment period
yielding 6.25 p.a. 3 payments of 62.50 at the
end of each of each successive 6-month period and
a final lump sum payment of 1,062.50 priced at
1300.
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TVM Sample Problems
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14. Martha Mills, manager of the Plaza Gold
Emporium, wants to allow her customers to buy on
credit, giving them 3 months in which to pay.
However, Martha will have to borrow from her bank
to establish the credit reserve. The bank will
charge 7 p.a. interest compounded monthly.
Martha wants to quote a simple rate to her
customers that will exactly cover her financing
cost. What simple (quoted, nominal) should
Martha quote to her customers. Assume that all
customers will take the full 3 months to pay.
(Hint the credit account compounds quarterly.)
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15. On 1 January you deposited 500 in a savings
account that pays 3 p.a.. You plan to deposit
500 every three months thereafter (i.e. the next
deposit will be on 1 April, the subsequent
deposit on 1 July, etc.) How much money will
have accumulated after 14 months? Wrong Ans
2,383.37
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16. If you save 500 each year for 2 years and
then 1,000 each for two years, how much must you
save in the 5th and 6th years to have 10,000 at
the end of 8 years if the interest rate is 5 p.
a.?
17. A football coach is leaving his current
school. In doing so, he is giving up an annuity
of 100,000 per year for 10 years that would
begin when he turns 60. The coach is 45. His
new school has offered to make up the loss of the
annuity with a lump sum payment when he moves.
How much should the new school pay if the
interest rate is 7 p.a.?