Class #1 Assignment

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```					                               Time Value of Money
Practice Problems

Objective: Practice Calculator Skills

1. Compound a Single Amount to a Future Value:
An investory pays 125,000 today to purchase land for future development.
The property is expected to increase in value by 9.5% per year. What will the
investment be worth at the end of the tenth year?

2. Compound an Annuity to a Future Value
If \$15,000 is invested at the end of each year for the next 10 years, earning 8%
compounded annually, how much money will be in the account at the end of
the tenth year?

3. Sinking Fund Payments:
An office building’s roof will need to be “re-roofed” 10 years from now. The
estimated cost is \$60,000. How much must be invested at the end of each
month for 10 years, into an account earning a 10% annual rate, to have the
\$60,000 at the end of year 10?

Compounding Using Three Functions of the Dollar:

4. What will \$1,500 accumulate to in 8 years if compounded at 8%?

5. If \$75 is deposited in a savings account at theend of each month for 5 years
earning 6%, how much money would be in that account at the end of year 5?

6. If an invesotr deposits \$500 per year in an investment paying 10% interest,
how long will it take to reach an accumulated amount of \$5,000?

7. How much will have to be deposited monthly in an investment earning 7% for
10 years to accumulate \$30,000?

8. What will \$250 accumulate to in 12 years at 12% interest compounded
monthly?

9. If \$8,000 is invested today earning 9% annual interest that is compounded
monthly, what is the investment worth at the end of 6 years?

10. Discounting a Single Future Amount to a Present Value:
You are considering buying a tract of land that you anticipate selling for
\$750,000 three years from now. What would you pay today for this property
to achieve a 13% annual yield?

11. Discounting an Annuity to a Present Value:
What is the value today of a series of \$500 payments, to be received at the end
of each month for 3 years, when discounted at 9% annually?

12. Determining a Series of Equal Payments Necessary to Amortize a Present
Value:
What is the monthly payment on a \$350,000 loan for 30 years at 6% interest?

Discounting Using 3 Functions of the Dollar:

13. An insurance policy requiring no premiums matures in 15 years and will be
worth \$1,000,000. What is that policyworth today assuming a 10% discount
rate, discounted annually?

14. What are the monthly payents for a 20-year, 7% loan for \$175,000?

15. You have just won \$1,200,000 in the Texas Lottery. You will receive \$42,500
per year (at the end of each year) for the next 25 years. If the discount rate is
12%, what are your winnings worth today?

16. What is the present valueof \$1,000 received at the end of each month for 4
years when discounted at 8.5%?

17. A zero coupon bond has a redemption value of \$1,000 15 years from today.
What would an investor who has an annual yield requirement of 7% pay for
this bond today?

18. Calculating the IRR of a Single Amount Received:
If an investment requiring a \$15,000 initial investment is forecasted to produce
income of \$2,500 per year for five years and will be sold at the end of year 5
for \$15,000, what is its projected IRR?

19. Calculating the IRR of an Annuity Plus Single Amount Received:
If an investment requiring a \$15,000 initial investment is forecasting to
produce income of \$2,500 per year for five years and will be sold at the end of
year 5 for \$12,000, what is its projected IRR?

20. Calculating the IRR of an Annuity Plus Single Amount Received:
If an investment requiring a \$15,000 initial investment is forecasting to
produce income of \$2,500 per year for five years and will be sold at the end of
year 5 for \$20,000, what is its projected IRR?
EOY                    \$
0
1                20,000
2                19,000
3                18,000
4                17,000
5                16,000
6                15,000
7                14,000
8                13,000
9                12,000
10                11,000

21. Calculating the IRR with Variable Cash Flows: (use CF’s from above)
If an investment requiring a \$70,000 initial investment, is forecasted to
produce variable cash flows each year over a 10-year holding period, and will
be sold at the end of period 10 for \$50,000, what is the projected IRR?

22. Recalculating the IRR with Variable Cash Flows (Use same CF’s from
above:
If an investment requiring a \$70,000 initial investment, is forecasted to
produce variable cash flows each year over a 10-year holding period, and will
be sold at the end of period 10 for \$75,000 (instead of \$50,000), what is the
projected IRR?

23. IRR for Investment A:
A buyer makes an initial investment of \$15,000 that produces cash flows of \$0
at the end of period one, \$0 at the end of period two, \$0 at the end of period
three, and \$20,000 at the end of period four. What is the IRR of this
investment?

24. IRR for Investment B:
A buyer makes an initial investment of \$15,000 that produces cash flows of
\$1,500 at the end of period one, \$1,500 at the end of period two, \$1,500 at the
end of period three, and \$15,000 at the end of period four. What is the IRR of
this investment?

25. IRR for Investment C:
A buyer makes an initial investment of \$15,000 that produces cash flows of \$0
at the end of period one, \$1,500 at the end of period two, \$7,000 at the end of
period three, and \$10,000 at the end of period four. What is the IRR of this
investment?

26. Measuring Investment Performance Using NPV with a Target Yield of
13%:
An investor wishes to purchase an investment for \$15,000 that produces cash
flows of \$0 at the end of year one, \$1,500 at the end of year two, \$7,000 at the
end of year three, and \$10,000 at the end of year four. If the investor’s target
yield for this investment is 13%, what price could theinvestor pay for the
property to earn the desired return?
27. Measuring Investment Performance Using NPV with a Target Yield of
10%:
An investor wishes to purchase an investment for \$15,000 that produces cash
flows of \$0 at the end of year one, \$1,500 at the end of year two, \$7,000 at the
end of year three, and \$10,000 at the end of year four. If theinvestor’s target
yield for this investment is 10%, what price could theinvestor pay for the
property to earn the desired return?

28. Calculating IRR and NPV:
An investor is analyzing two parcels of vacant land to determine which is the
better investment to purchase and hold for future appreciation in value. The
following are the analysis assumptions for the two parcels:

Parcel "A"      Parcel "B"
Purchase price                \$150,000        \$200,000
Carrying costs per year       \$2,000          \$3,000
Projected sale price          \$200,000        \$400,000
Anticipated holding          5 years         7 years
period

What is the projected IRR for each of the parcels?

Parcel “A” IRR =

Parcel “B” IRR =

29. Using the information from the previous question, what could the investor
pay for each of the parcels to achieve a 13% yield?

Parcel “A” purchase price =

Parcel “B” purchase price =
30. An investment is expected to produce specified variable cash flows
eachyear over a 10-year holding period (see T-bar below) and is projected
to sell for \$100,000 at the end of year 10. Assuming the investor has a 9%
investment to achieve the desired yield?

EOY                 \$
0                 0
1              20,000
2              19,000
3              18,000
4              17,000
5              16,000
6              15,000
7              14,000
8              13,000
9              12,000
10         11,000 + 100,000

Price =

31. An investor is considering the purchase of an investment whose cash flows
are reflected in the T-bar below. Using NPV as the investment
performance measure, would theinvestor achieve or exceed the target
yield of 12%?

EOY                 \$
0             (200,000)
1               20,000
2               21,000
3               20,500
4               21,200
5         22,000 + 110,000

a. Would the investment achieve or exceed the target yield?

b. Explain the rationale for your response.

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