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# Corporate Finance : Present and Future Values, Annuity Future Values, EAR vs APR, Amortization with Equal Payments, Break-Even EBIT and Leverage

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The Problem is for a Corporate Finance Course. The author is Ross-Westerfield-Jordan: Essentials of Corporate Finance. Fourth Edition.

I have circled the questions that I need help answering. If you would, please show all work and or fomulas. (this is what always throws me off)

I need the following questions answered:
CH 4: 2, 3, 4, 6, 7
CH 5: 3, 4, 7, 19, 20, 24, 55
CH 13: 4, 6

Please see the attached file for the fully formatted problems.

Calculating interest 'Rates. Assume the total cost of a college education will be \$300,000 when your child enters college in 18years. You presently have \$40,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

Calculating the Number of Periods. At 9 percent. interest, how long does it take to double your money? To quadruple it?

Future Value and Multiple Cash Flows. ? . Qffiçer, me., has identified an investment project with the following cash flows. If the discount rate is 8. pc\$teflt,

Calculating Annuitty Present Value. An investment offers \$6,000 per year for
15 years, with the first payment occurring 1 year from now. If the required return is
8 percent, what is the value of the investment? What would the value be if the
payments occurred for 40 years? For 75 years? Forever?
Calculating Annuity Values. If you deposit \$2,000 at the end of each of the next 20 years into an account paying 7.5 percent ñterest how much money will y&i have in the account in 20 years? How much will you have if you make deposits for 40years?

EAR versus APR. RickyRipovs Pawn Shop chargesa.interest rate of 20 percent
per month on loans to its customers. Like all lenders, Ricky rnust report an APR to consumers. What rate should the shop report? What is the effective annual rate?

Calculating Loan Payments. You want to buy a new sports coupe for \$52,350, and the finance office at the dealership has quoted you an 86 percent APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual. rate on this loan?

Calculating Annuity Future Values, You are to make monthly deposits of \$200 into a retirement account that pays 1.1 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement
Account be in 30 years?

Amortization with Equal Payments. Prepare an amortization schedule for a three-year loan of \$60,000. The interest rate is 11 percent per year, and the loan calls for equal annual payments. How much Interest is paid in the third year? How much total interest is paid over the life of the loan?

Break-Even EBIT. Duval Corporation is comparing two different capital structures, an all-equity plan (Plan I) and a levered plan Plan II). Under Plan I, Duval would have 600,000 sharesof stock outstanding; Under Plan 11,there would be 300,000 shares of stock outstanding and \$10 million in debt outstanding. The interest rate on the debt is 10 percent, and there are taxes.
a. If EBIT is \$1 .5 million, which plan will result in the higher EPS?
b. If EBIT is \$11 million, which plan will result in the higher EPS?
c. What is the break-even EBIT?
Break-Even EBIT and Leverage. Hoobastank Co. is comparing two different capital structures. Plan I would result in.1.,000 shares of stock and \$30,000 in debt. Plan II would result in 2,000 shares of stock and \$15,000 in debt. The interest rate on the debt is 10 percent. .

#### Solution Preview

Chapter 4

Q.No 2:

Solution:

Here we have to calculate the future value.

Given : Present value, rate , and number of years.

We need to find the Future value (ie) Amount after n-th year.

We know the formula A = P (1+ r/100)^n (Compound interest formula)

A - Amount (ie) Future value

P - Principle (ie) present value

r -is the rate of interest

n- is the number of years.

Let me explain the first one.

Given P= \$ 2250, r= 18%= 18/100 =0.18
and n= 3

Plugin these values in the formula, we get

A = 2250 (1+0.18)^3

A = 2250 (1.18)^3

A = \$ 3696.82

Similarly , we have to do for other 3 problems in this question.

(ii)Given P= \$9310 , r= 0.06% and n= 10.

Plugin these values in the given formula and find A (ie) future value.

______________________________________________________________________________

3. Here we have to find the present value (ie) Principle value.

(i) Given : A= 15,415 , r= 4% =4/100= 0.04
and n= 4

Plugin these values in the formula A= P (1+ r/100)^n

P(1+ 0.04)^4 = 15,415

P( 1.04)^4= 15,415

P(1.17) = 15,415

P = 15,415/ 1.17

P = 13205.98 ( Round off the nearest tenths place)

Similarly we can do remaining problems.

Let me give you the last two steps :)

(ii) P (2.77) = 51, 557

(iii) P ( 16.18) = 886, 073

Ans: P = \$54763.79

(iv) P ( 26.62) = 550,164

Ans: P = \$20667.32
______________________________________________________________________________

4. Here we have to find the Interest rate.

(i) Given : A = \$307 , P= 221 and n= 4

Plug in these values into the given formula P (1+ r/100)^n= A

221(1+r/100) ^4 = 307

(1+ r/100)^4 = 307/221

(1+r/100)^4 = 1.39 ( Rounded ...

#### Solution Summary

Present and Future Values, Annuity Future Values, EAR vs APR, Amortization with Equal Payments, Break-Even EBIT and Leverage are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

\$2.19