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# Present and Future Values of cash flows

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Problem:

Use the future value interest factors in Appendix Table A-1 in each fo the cases shown below to estimate, to the nearest year, how long it would take an initial deposit, assuming no withdrawals.
a.To double
Case Interest rate
A 7%
B 40%
C 20%
D 10%

Problem : As part of your financial planning, you wish to purchase a new car exactly 5 years from today. The car you wish to purchase costs \$14,000 today, and your research indicates that its price will increase by 2% to 4% per year over the next 5 years.
a. Estimate the price of the car at the end of 5 years if inflation is (1) 2% per year and (2) 4% per year.

Problem : You can deposit \$10,000into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today?

Problem : A person borrows \$200 to be repaid in 8 years with 14% annually compounded interest. The loan may be repaid at the end of any earlier year with no prepayment penalty.
a. What amount will be due if the loan is repaid at the end of year 1?
b. What is the repayment at the end of year 4?
c. What amount is due at the end of the eighth year?

Problem:
Answer each of the following questions:
a.What single investment made today, earning 12% annual interest, will be worth \$6,000 at the end of 6 years?
b.What is the present value of \$6,000 to be received at the end of 6 years if the discount rate is 12%
c.What is the most you would pay today for a promise to repay you \$6,000 at the end of 6 years if your opportunity cost is 12%
d.Compare, contrast, and discuss your findings in parts a through c.

Problem :
An Iowa state savings bond can be converted to \$100 at maturity 6 years from purchase. If the state bonds are to be competitive with U.S savings bonds, which pay 8% annual interest (compounded annually), at what price must the state sell its bonds? Assume no cash payments on saving bonds prior to redemption.

Problem :
Time Value-Annuities Marian Kirk wishes to select the better of two 10-years annuities, C and D Annuity C is an ordinary annuity of \$2,500 per year for 10 years. Annuity D is an annuity due of \$2,200 per year for 10 years.
a.Find the future value of both annuities at the end of year 10, assuming that Marian can ear (1) 10% annual interest and (2) @0% annual interest.
b.Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates.
c.Find the present value of both annuities, assuming that Marian can earn (1) !0% annual interest and (2) 20% annual interest/
d.Use your finding in part c to indicate which annuity has the greater present value for both (1) 10% and (2) 20% interest rates.
e.Briefly compare, contrast and explain any differences between your findings using the 10% and 20% interest rates in parts b and d.

Problem :
Value of retirement annuity An insurance agent is trying to sell you an immediate-retirement annuity, which for a single amount paid today will provide you with \$12,000 at the end of the year for the next 25 years. You currently earn 9% on low-risk investment comparable to the retirement annuity. Ignoring taxes, what is the most you would pay for this annuity?

Problem :
Perpetuities : Consider the data in the following table

Perpetuity Annual amount Discount rate
A \$20, 000 8%
B 1000,000 10
C 3,000 6
D 60,000 5
Determine, for each of the perpetuities
a.The appropriate present value interest factor.
b.The present value.

Problem:
Value of a mixed stream For each of the mixed streams of cash flows shown in the following table, determine the future value at the end of the final year if deposits are made into an account paying annual interest of 12%, assuming that no withdrawals are made during the period and that the deposits are made:
a.At the end of each year.
b.At the beginning of each year.
Year Cash flows stream
A B C
1 \$ 900 \$30,000 \$1,200
2 1, 000 25,000 1,200
3 1,000 20,000 1,000
4 10,000 1,900
5 5,000

#### Solution Preview

Solutions are attached herewith for better clarity. Please refer solution below for last question.

Problem :

Use the future value interest factors in Appendix Table A-1 in each for the cases shown below to estimate, to the nearest year, how long it would take an initial deposit, assuming no withdrawals.
a.To double
Case Interest rate
A 7%
Since we have to use tables, we can only get nearest year. Use formula to get exact time as discussed in part (b)
For amount to double, Refer "Future Value of \$1 at the end of n periods" and look for factor=2 in the column of 7%, we get FV factor of 2.1049 for n=11. We can say that amount will be doubled in 11th year.
For amount to quadruple, Refer "Future Value of \$1 at the end of n periods" and look for factor=4 in the column of 7%, we get FV factor of 4.1406 for n=21. We can say that amount will be quadruple in 21th year.

B 40%
I don't have tables for 40%
Here i=40% and FVn/PV=2
2=(1.40)^n
n=ln(2)/ln(1.40)= 2.06004
Similarly for amount to be quadruple,
Here i=40% and FVn/PV=4
4=(1.40)^n
n=ln(4)/ln(1.4)= 4.12009

C 20%
For amount to double, Refer "Future Value of \$1 at the end of n periods" and look for factor=2 in the column of 20%, we get FV factor of 2.0736 for n=4. We can say that amount will be doubled in 4th year.
For amount to quadruple, Refer "Future Value of \$1 at the end of n periods" and look for factor=4 in the column of 20%, we get FV factor of 4.2998 for n=8. We can say that amount will be quadruple in 8th year.
D 10%
For amount to double, Refer "Future Value of \$1 at the end of n periods" and look for factor=2 in the column of 10%, we get FV factor of 2.1436 for n=8. We can say that amount will be doubled in 8th year.
For amount to quadruple, Refer "Future Value of \$1 at the end of n periods" and look for factor=4 in the column of 10%, we get FV factor of 4.1772 for n=15. We can say that amount will be quadruple in 15th year.

Problem : As part of your financial planning, you wish to purchase a new car exactly 5 years from today. The car you wish to purchase costs \$14,000 today, and your research indicates that its price will increase by 2% to 4% per year over the next 5 years.
a.Estimate the price of the car at the end of 5 years if inflation is (1) 2% per year and (2) 4% per year.

For inflation rate =2%
Price of Car after 5 years =14000*(1+0.02)^5=\$15457.13
For inflation rate =4%
Price of Car after 5 years =14000*(1+0.04)^5=\$17033.14

Problem : You can deposit \$10,000into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today?
Future Value of \$10000 if deposit today ...

#### Solution Summary

Solutions to various problems explains the steps to find out present and future values of single cash flows, annuities and perpetuity. At last future values of mixed stream of cash flows are calculated.

\$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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