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# cost of capital, optimal capital structure, Leverage, NPV

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Firms' weight average cost of capital and other questions:

1. A firm needs \$100 to start and expects:

Sales \$200
Expenses \$185
Tax rate 33% of earnings

a. What are earnings if the owners put up the \$100?
b. If the firm borrows \$40 of the initial at 10%, what are the profits received by the owner?
c. What is the return on the owners' investment in each case? Why do the returns differ?
d. If expenses rise to \$194, what will be the returns in each case?
e. In which case did the returns decline more?
f. What generalization can you draw form the above?

2. Given the following schedules:
Debt/Assets Cost of Debt Cost of Equity
0% 7% 14%
10 7 14
20 7 14
30 8 14
40 8 16
50 10 18
60 10 20

a. What is firm's cost of capital at the various combinations of debt and equity?
b. What is the firm's optimal capital structure? Construct a balance sheet showing that combination of debt and equity financing.

3. A firm has three investment opportunities. Each costs \$1,000, and the firm's cost of capital is 10 percent. The cash inflow of each investment is as follows:
Cash Inflow A B C
Year
1 300 500 100
2 300 400 200
3 300 200 400
4 300 100 500

a. If the net present value method is used, which investment(s) should the firm make?
b. What is the internal rate of return of investment A? The internal rate of return of investment B is 10.22% and 6.15% for investment C. Which investment(s) should the firm make?
c. What is the payback period for each investment?

4. Firm A had \$10,000 in assets entirely financed with equity. Firm B also has \$10,000, but these assets are financed by \$5,000 in debt (with a 10 percent rate of interest) and \$5,000 in equity. Both firms sell 10,000 units of output at \$2.50 per unit. The variable costs of production are \$1, and fixed production costs are \$12,000. (to ease the calculation, assume no income tax.)
A. What is the operating income (EBIT) for both firms?
B. What are the earnings after interest?
C. If sales increase by 10 percent to 11,000 units, by what percentage will each firm's earnings after interest income? To answer the question, determine the earnings after taxed and compute the percentage increase in these earnings from the answers you derived in part b.
D. Why are the percentage changes different?

5. A firm's current balance sheet is as follows:
Assets \$100 Debt \$10
Equity \$90

Debt/assets after-tax cost of debt cost of equity cost of capital
0% 8% 12% ?
10 8 12 ?
20 8 12 ?
30 8 13 ?
40 9 14 ?
50 10 15 ?
60 12 16 ?

B. Construct a pro forma balance sheet that indicates the firm's optimal capital structure. Compare this balance sheet with the firm's current balance sheet. What course of action should the firm take?
Assets \$100 Debt\$?
Equity\$?
C. As a firm initially substitutes debt for equity financing, what happens to the cost of capital, and why.
D. If a firm uses too much debt financing, why does the cost of capital rise?
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#### Solution Preview

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

1. A firm needs \$100 to start and expects:

Sales \$200
Expenses \$185
Tax rate 33% of earnings

a. What are earnings if the owners put up the \$100?
Profit Before Tax=\$200-\$185=\$15
Tax=33%*\$15=\$5
Earnings to owner =Profit after tax=\$15-\$5=\$10

b. If the firm borrows \$40 of the initial at 10%, what are the profits received by the owner?
Operating Income =\$200-\$185=\$15
Interest =40*10%=\$4
Profit Before Tax=\$11
Tax=33%*\$11=\$3.63
Earnings to owner =Profit after tax=\$11-\$3.63=\$7.37

c. What is the return on the owners' investment in each case? Why do the returns differ?
Return= Earning to owner / Investment by owner
Return in (a)=\$10/\$100=10%
Return in (b)=\$7.37/\$60=12.83%
The return differs as the firm is able to borrow at lower cost (interest is also tax deductible), hence the returns to owner increases.

d. If expenses rise to \$194, what will be the returns in each case?
a) Profit Before Tax=\$200-\$194=\$6
Tax=33%*\$6=\$2
Earnings to owner =Profit after tax=\$6-\$2=\$4

b) Operating Income =\$200-\$194=\$6
Interest =40*10%=\$4
Profit Before Tax=\$2
Tax=33%*\$2=\$0.66
Earnings to owner =Profit after tax=\$2-\$0.66=\$1.34

Return= Earning to owner / Investment by owner
Return in (a)=\$4/\$100=4%
Return in (b)=\$1.34/\$60=2.23%

e. In which case did the returns decline more?
The return declines more in case when firm borrows the capital.

f. What generalization can you draw form the above?
In case of borrowing by the firm, the returns to shareholders increase but the return also becomes more sensitive to the changes in profitability of the firm. With leverage, due to fixed payment of interest, the returns are more sensitive to profits so they increase more rapidly if ...

#### Solution Summary

This post answer several questions from corporate finance on Cost of capital, optimal capital structure, Leverage and capital investment decisions. This could be used as a good learning exercise to understand the capital structure and effect of advantage on profitability.

\$2.19

## Finance MC questions: optimal capital, risk types, leverage, NPV, 'real option', ROI

Question 1

The optimal capital structure is that structure which:

reduces overall leverage

reduces or eliminates only financial leverage

gives the highest stock price

provides the best risk versus return scenario for investors

carries extra options for timing and future events.

Question 2

Select the best combination below of risk as it relates to a company's sales and a company's profits.

foreign exchange risk / interest rate risk.

business risk / interest rate risk.

interest rate risk / investment risk.

Question 3

Operating leverage targets

the percent of costs that are fixed

the usage of labor.

outsourcing

variable costs

Question 4

Fill in the blank. Considering one industry, all firms must have _________ capital structures to be optimal.

identical

similar

dissimilar

any number of combinations of

Question 5

Capital rationing is:

the allocation of available capital to projects best suited to be undertaken, at the present time.

Applying an even distribution of capital; all departments get the same funding.

Applying a distribution of capital based on the % of profits generated by each department.

borrowing conservatively.

none of the above.

Question 6

As operating leverage increases, all things being equal,

the lower the break even point will be

variable costs per unit will decrease

the higher the sales volume needed to break even.

variable costs per unit will increse

all of the above.

Question 7

If the analytical results of projects "N" and "M" are:
M: NPV = \$450, IRR 12%
N: NPV = \$500, IRR = 12%
Which of the following would be correct?

Your company has an historical return for its shareholders at 15%; therefore, both projects are rejected.

If they are mutually exclusive, you would reject "N".

If they are not mutually exclusive, you can accept both because they have a positive NPV.

Reject both because there is no way both can have the same IRR with different NPV's.

"A" and "C" are correct answers.

Question 8

Which of the following is not considered a "real option"?.

flexibility

growth

timing

replacement

abandonment

Question 9

The concept of sunk costs is most associated with which of the following:

Baywatch

abandonment costs or options to abandon if you decide to do something else.

Working capital needed to start a business

Net after tax but before interest and principal payments.

none of these!

Question 10

Which of the following is not an example of a real option?

Quitting a job

Paying off a debt obligation early

dropping one quiz grade in this course

Question 11

What is the after-tax cost of debt for a firm in the 35% tax bracket that pays 15% on its debt?

5.25%

9.75%

12.17%

20.25%

Question 12

A project has the following projected outcomes in dollars: \$250, \$350, and \$500. The probabilities of their outcomes are 25%, 50%, and 25% respectively. What is the expected value of these outcomes?

\$362.5

\$89.4

\$94.5

\$178.3

Question 13

Financial risk refers to the:

risk of owning equity securities.

risk faced by equity holders when debt is used.

general business risk of the firm.

possibility that interest rates will increase.

Question 14

A firm's capital structure is represented by its mix of:

assets.

liabilities and equity.

assets and liabilities.

assets, liabilities and equity.

Question 15

Risk is usually measured as the :

potential loss.

variability of outcomes around some expected value.

probability of expected values.

potential expected loss.

Question 16

What is the return on equity for a firm with 15% return on assets, 10% return on debt, and a .75 debt/equity ratio?

18.75%

20.00%

23.75%

26.25%

Question 17

An increase in a firm's financial leverage will:

increase the variability in earnings per share.

reduce the operating risk of the firm.

increase the value of the firm in a non-MM world.

increase the WACC.

Question 18

Which of the following could SIGNAL to investors that the future prospects of the company are bright?

Borrow significantly more money (increase financial leverage).

Sell new equity shares in the open market.

Sell stock the company had listed as Treasury Stock.

Pay down debt.

all of the above.

Question 19

Trade off theory of leverage relates

returns to stock holders as bond leverage increases

returns to both owners and debt holders as leverage increases

operating versus financial aspects of leverage

tax benefits of debt versus increase chance of defaulting on debt.

Question 20

Which of the following is an example of restructuring the firm?

Dividends are increased from \$1 to \$2 per share.

A new investment increases the firm's business risk.

New equity is issued and the proceeds repay debt.

A new Board of Directors is elected to the firm.

Question 21

The stability of a firm's operating income is the focus of:

financial leverage.

weighted-average cost of capital.

capital structure.

Question 22

The capital asset pricing model (CAPM.:

uses the risk free rate

relates risk versus return

all of the above

none of the above

Question 23

Optimal Capital structure is:

easily attained; just plug in variables to the formula.

achieved through trial and error by leveraging financial assets.

static once the optimal point is reached.

a great academic discussion but cannot be determined in dynamic financial markets for any given period of time.

constant, but each industry, as defined by NAICS, has its own debt/equity mix.

Question 24

Asymmetric information occurs when:

all parties have complete information

one party has less information than the other.

all analysts agree about future earning predictions

No one has any information

none of the above

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