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# Future value tables

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

2) Time value 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. b. How much more expensive will the car be if the rate of inflation is 4% rather than 2%?

3) Time value You can deposit \$ 10,000 into 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?

4) Single- payment loan repayment 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?

6) Present value concept 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.

7) Time value 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 savings bonds prior to redemption.

10) Time value Annuities Marian Kirk wishes to select the better of two 10- year 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 earn ( 1) 10% annual interest and ( 2) 20% 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) 10% annual interest and ( 2) 20% annual interest. d. Use your findings 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.

11) Value of a 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 each year for the next 25 years. You currently earn 9% on low- risk investments comparable to the retirement annuity. Ignoring taxes, what is the most you would pay for this annuity?

14) Changing compounding frequency Using annual, semiannual, and quarterly com-pounding periods, for each of the following, ( 1) calculate the future value if \$ 5,000 is deposited initially, and ( 2) determine the effective annual rate ( EAR). a. At 12% annual interest for 5 years. b. At 16% annual interest for 6 years. c. At 20% annual interest for 10 years.

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#### Solution Summary

Future value tables are scrutinized.

\$2.19

## PV calculations: single cash flow, mixed stream, FV, annuities, EBIT, leverage

See attached file.

P4-4 For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today that will be available at the end of the deposit period if the interest is compounded annually at the rate specified over the given period.

Case Signgle Cash Flow Interest Rate Deposit Period
A \$200.00 5% 20
B 4,500 8 7
C 10,000 9 10
D 25,000 10 12
E 37,000 11 5
F 40,000 12 9

P4-9 Present value calculation
Without referring to tables or to the preprogrammed function on your financial calculator, use the basic formula for present value, along with the given opportunity cost, i, and the number of periods, n, to calculate the present value interest factor in each of the cases shown in the accompanying table. Compare the calculated value to the table value.
Case Opportunity cost, i Number of periods, n
A 2% 4
B 10% 2
C 5 3
D 13 2

P4-25 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 at the beginning of each year into an account paying annual interest of 12%, assuming that no withdrawals are made during the period.
Cash flow stream
Year A B C
1 \$ 900 \$30,000 \$1,200
2 1,000 25,000 1,200
3 1,200 20,000 1,000
4 10,000 1,900
5 5,000

P4-31 Relationship between future value and present value?Mixed stream
Using only the information in the accompanying table, answer the questions that follow.
Year (t) Cash flow Future value interest factor at 5% (FVIF5%,n)
1 \$ 800 1.050
2 900 1.102
3 1,000 1.158
4 1,500 1.216
5 2,000 1.276
A) Determine the present value of the mixed stream of cash flows using a 5% discount rate.
B) How much would you be willing to pay for an opportunity to buy this stream, assuming that you can at best earn 5% on your investments?
C) What effect, if any, would a 7% rather than a 5% opportunity cost have on your analysis? (Explain verbally.)

P4-37 Annuities and compounding
Janet Boyle intends to deposit \$300 per year in a credit union for the next 10 years, and the credit union pays an annual interest rate of 8%.
A) Determine the future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn, if
a. \$300 is deposited annually and the credit union pays interest annually.
b. \$150 is deposited semiannually and the credit union pays interest semiannually.
c. \$75 is deposited quarterly and the credit union pays interest quarterly.
B) Use your finding in part a to discuss the effect of more frequent deposits and compounding of interest on the future value of an annuity.

P4-43 Loan amortization schedule
Joan Messineo borrowed \$15,000 at a 14% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments.
A) Calculate the annual, end-of-year loan payment.
B) Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.
C) Explain why the interest portion of each payment declines with the passage of time.

P4-51 Interest rate for an annuity
Anna Waldheim was seriously injured in an industrial accident. She sued the responsible parties and was awarded a judgment of \$2,000,000. Today, she and her attorney are attending a settlement conference with the defendants. The defendants have made an initial offer of \$156,000 per year for 25 years. Anna plans to counteroffer at \$255,000 per year for 25 years. Both the offer and the counteroffer have a present value of \$2,000,000, the amount of the judgment. Both assume payments at the end of each year.
A) What interest rate assumption have the defendants used in their offer (rounded to the nearest whole percent)?
B) What interest rate assumption have Anna and her lawyer used in their counteroffer (rounded to the nearest whole percent)?
C) Anna is willing to settle for an annuity that carries an interest rate assumption of 9%. What annual payment would be acceptable to her?

Chapter 11:

P11-6 EBIT sensitivity
Stewart Industries sells its finished product for \$9 per unit. Its fixed operating costs are \$20,000, and the variable operating cost per unit is \$5.
A) Calculate the firm's earnings before interest and taxes (EBIT) for sales of 10,000 units.
B) Calculate the firm's EBIT for sales of 8,000 and 12,000 units, respectively
C) Calculate the percentage changes in sales (from the 10,000-unit base level) and associated percentage changes in EBIT for the shifts in sales indicated in part b.
D) On the basis of your findings in part c, comment on the sensitivity of changes in EBIT in response to changes in sales.

P11-7 Degree of operating leverage
Grey Products has fixed operating costs of \$380,000, variable operating costs of \$16 per unit, and a selling price of \$63.50 per unit.
1. Calculate the operating breakeven point in units.
2. Calculate the firm's EBIT at 9,000, 10,000, and 11,000 units, respectively.
3. With 10,000 units as a base, what are the percentage changes in units sold and EBIT as sales move from the base to the other sales levels used in part b?
4. Use the percentages computed in part c to determine the degree of operating leverage (DOL).
5. Use the formula for degree of operating leverage to determine the DOL at 10,000 units.

P11-10 Degree of financial leverage
Northwestern Savings and Loan has a current capital structure consisting of \$250,000 of 16% (annual interest) debt and 2,000 shares of common stock. The firm pays taxes at the rate of 40%.
A) Using EBIT values of \$80,000 and \$120,000, determine the associated earnings per share (EPS).
B) Using \$80,000 of EBIT as a base, calculate the degree of financial leverage (DFL).
C) Rework parts a and b assuming that the firm has \$100,000 of 16% (annual interest) debt and 3,000 shares of common stock.

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