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# Calculating Present Values of future cash flows.

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I) Use Excel to perform the following calculations. Label each input and the output of your calculations. Highlight your final answer using the yellow highlighter on the top right menu bar. Assume for each part that the interest rate is 8% per year.
(1) What is the present value of \$8000 to be received in five years?
(2) What is the present value of \$8000 to be received in ten years? Why does this amount fall as the number of years increases? Why doesn't it fall in half as the number of years doubles?
(3) You are considering an investment which returns \$100 in year 1, \$100 in year 2, \$100 in year 3, and \$1,100 in year 4. What is the present value of this investment? What is the relationship between the present value and the price you would pay?
(4) How much is a share of preferred stock worth if it pays an annual dividend of \$3 per share forever?
(5) You deposit \$5,000 in a bank CD which matures in five years. What amount of money should you have when the CD matures?
(6) You have a brand new daughter in your house. You estimate she will require \$250,000 to attend a small, private college in the southwest. She will enroll in 18 years. How much money do you need to save each year to meet this goal?
(7) In 1987, the population of Maricopa County was 1.3 million people. Twenty years later, the population has increased to 3.6 million people. What is the annual rate of increase?
(8) You win the lottery, which advertises a jackpot of \$1 million. However, you learn that the \$1 million is to be paid in 20 equal annual installments over the next 20 years. If you want an immediate payout, you must settle for ½ the jackpot amount, or \$500,000. Which settlement is most valuable to you today?

#### Solution Preview

i) Use Excel to perform the following calculations.   Label each input and the output of your calculations.  Highlight your final answer using the yellow highlighter on the top right menu bar.  Assume for each part that the interest rate is 8% per year.

(1) What is the present value of \$8000 to be received in five years?

n= 5
r= 8.00%
PVIF (5 periods, 8.% rate ) = 0.680583

Future value= \$8,000
Therefore, present value= \$5,444.66 =8000x0.680583

(2) What is the present value of \$8000 to be received in ten years?  Why does this amount fall as the number of years increases?  Why doesn't it fall in half as the number of years doubles?

n= 10
r= 8.00%
PVIF (10 periods, 8.% rate ) = 0.463193

Future value= \$8,000
Therefore, present value= \$3,705.54 =8000x0.463193

This amount falls as as the number of years increases because the further in time the money is received the ...

#### Solution Summary

Answers time value of money questions.

\$2.19

## Calculating present/future values of given cash flows

Problem 1
Toadies, Inc., has identified an investment project with the following cash flows.

Year Cash Flow
1 \$ 1,400
2 1,520
3 1,605
4 1,655

If the discount rate is 9 percent, what is the future value of the cash flows in year 4?

If the discount rate is 10 percent, what is the future value of the cash flows in year 4?

If the discount rate is 25 percent, what is the future value of the cash flows in year 4?

Problem 2
Wainright Co. has identified an investment project with the following cash flows.

Year Cash Flow
1 \$ 780
2 1,050
3 1,310
4 1,425

If the discount rate is 8 percent, what is the present value of these cash flows?
What is the present value at 17 percent?

What is the present value at 25 percent?

Problem 3
The appropriate discount rate for the following cash flows is 7.48 percent per year.

Year Cash Flow
1 \$ 2,500
2 0
3 3,940
4 2,190

What is the present value of the cash flows?

Problem 4
You are planning to save for retirement over the next 25 years. To do this, you will invest \$880 a month in a stock account and \$480 a month in a bond account. The return of the stock account is expected to be 10.8 percent, and the bond account will pay 6.8 percent. When you retire, you will combine your money into an account with a 7.8 percent return.

How much can you withdraw each month from your account assuming a 20-year withdrawal period?

Problem 5
If you deposit \$5,600 at the end of each of the next 20 years into an account paying 10.80 percent interest, how much money will you have in the account in 20 years?

How much will you have if you make deposits for 40 years?

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