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# Various Finacne Problems

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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future value that Janet will have at the end of 10 years, given that end-of-period deposits are made and no interest is withdrawn, if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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#### Solution Preview

Please refer attached document for complete solution, tables and work done with the help of equation writer may not print properly here.

Solutions

Values in dollars
Case Single Cash Flow Interest Rate Deposit Period Future Value
A \$200.00 5 20 200(1.05)^20=200*2.6533 531
B 4,500 8 7 4500(1.08)^7= 4500*1.7138 7712
C 10,000 9 10 10000(1.09)^10= 10000*2.3674 23674
D 25,000 10 12 25000(1.10)^12=25000*3.1384 78461
E 37,000 11 5 37000(1.11)^5=37000*1.6851 62347
F 40,000 12 9 40000(1.12)^9=40000*2.7731 110923

P4-9 Present value calculation
Solution

Case Opportunity cost, i Number of periods, n (1+i)^n PV=1/(1+i)^n Table Value
A 2 4 1.08243216 0.92385 0.924
B 10 2 1.21 0.82645 0.826
C 5 3 1.157625 0.86384 0.864
D 13 2 1.2769 0.78315 0.783

P4-25 Value of a mixed stream

For calculating Future Value of any deposit we use following formula

In stream A, \$900 is deposited at the beginning of year and it remains invested for 5 years. It will get interest for five years. Future value of this deposit will be . Similarly for deposit of \$1000, deposit period will be 4 years only. FV of this investment will be
Calculations will be repeated for every deposit and at the end we can add these values to find the total FV of stream.
Cash flow stream Future Value
Year A B C A B C
1 \$900 \$30,000 \$1,200 1586 52870 2115
2 1,000 25,000 1,200 1574 39338 1888
3 1,200 20,000 1,000 1686 28099 1405
4 10,000 1,900 12544 2383
5 5,000 5600 0
Total FV 4846 138451 7791

P4-31 Relationship between future ...

#### Solution Summary

There are 10 problems. First 4 problems are about finding present value of single cash flow, present value factor, future value and present value of mixed cash flows.
Next three problems are about future value of annuity, amortization schedule and finding interest rates for annuity.
Remaining problems are about finding operational and financial leverarge.
All the problems have step by step explaination sothat concept becomes clear and easier to understand.

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