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# Capital, risk, profit, pension planning and maturity

See attached file with 15 problems.

1. A firm wants to expand its business and to do so it must issue new capital (debt, common stock, or preferred stock) since its internal cash flow is not sufficient to pay for the expansion. The firm wants to issue the cheapest type of capital. Given the following information, what type of capital will the firm prefer to issue first, second, and third?

11% Before-tax cost of debt
20% Tax rate
0.8 Beta of common stock
5% Risk free rate
10% Expected return of the stock (common) market
\$100 Preferred stock price
\$80 Par value of preferred stock
\$10 Preferred stock dividend
5% Floatation cost for new preferred stock

a) 1st common stock, 2nd preferred stock, 3rd debt
b) 1st common stock, 2nd debt, 3rd preferred stock
c) 1st preferred stock, 2nd debt, 3rd, common stock
d) 1st preferred stock, 2nd common stock, 3rd debt
e) 1st debt, 2nd, common stock, 3rd preferred stock
f) 1st debt, 2nd preferred stock, 3rd common stock

#### Solution Preview

See the attached file.

1. A firm wants to expand its business and to do so it must issue new capital (debt, common stock, or preferred stock) since its internal cash flow is not sufficient to pay for the expansion. The firm wants to issue the cheapest type of capital. Given the following information, what type of capital will the firm prefer to issue first, second, and third?

11% Before-tax cost of debt
20% Tax rate
0.8 Beta of common stock
5% Risk free rate
10% Expected return of the stock (common) market
\$100 Preferred stock price
\$80 Par value of preferred stock
\$10 Preferred stock dividend
5% Floatation cost for new preferred stock

a) 1st common stock, 2nd preferred stock, 3rd debt
b) 1st common stock, 2nd debt, 3rd preferred stock
c) 1st preferred stock, 2nd debt, 3rd, common stock
d) 1st preferred stock, 2nd common stock, 3rd debt
e) 1st debt, 2nd, common stock, 3rd preferred stock
f) 1st debt, 2nd preferred stock, 3rd common stock

Answer (e) 1st debt, 2nd, common stock, 3rd preferred stock

After tax cost of debt = rd*(1-tax)=11*(1-20%)=8.8%
Required return on common stock = rf+beta*(rm-rf) = 5%+0.8*(10%-5%)=9%
Cost of preferred stock = Dividend / (Market price*(1-floatation cost)
= 10/(100*(1-5%)=10.53%
Cost of debt is least, then common equity and then preferred equity.

2. Management of a firm is trying to determine an optimal capital structure - the one that yields the lowest WACC. Management realizes that, in general, debt is a cheaper source of capital than equity; however, it also knows that as it raises the amount of debt in its capital structure that the cost of debt and equity will rise. Which of the capital structures below yields the lowest WACC?

Capital Structure A: 10% debt; 40% tax rate; 4% before tax cost of debt, 8% cost of equity
Capital Structure B: 25% debt; 40% tax rate; 5% before tax cost of debt, 9% cost of equity
Capital Structure C: 40% debt; 40% tax rate; 6% before tax cost of debt, 10% cost of equity
Capital Structure D: 55% debt; 40% tax rate; 7% before tax cost of debt, 11% cost of equity
Capital Structure E: 70% debt; 40% tax rate; 8% before tax cost of debt, 12% cost of equity

Note: assume that there is only debt and equity in the capital structure.

a) A
b) B
c) C
d) D
e) E

WACC for A = 10%*4%*(1-40%)+90%*8%=7.44%
WACC for B = 25%*5%*(1-40%)+75%*9%=7.50%
WACC for C = 40%*6%*(1-40%)+60%*10%=7.44%
WACC for D = 55%*7%*(1-40%)+45%*11%=7.26%
WACC for E = 70%*8%*(1-40%)+30%*12%=6.96%
Lowest WACC is for capital structure E.

3. Oftentimes, firms use the same or a very similar WACC to value all projects for a firm. This is convenient, but it may not be appropriate if different projects have different risk profiles. What will result if the company uses one WACC - the WACC for the overall firm - as the minimum rate of return that all projects must make in order to be accepted?

a) Risk of the overall firm will rise
b) Risk of the overall firm will fall
c) Risk of the overall firm will probably not be impacted
d) Projects that are accepted will all have returns less than the firm-level WACC

Answer (a) Risk of the overall firm will rise
Project with higher risk are more likely to provide higher return and hence these are more likely to qualify the WACC criteria. On the other hand, projects with lower risk will have lower return and hence will not qualify the same WACC criteria. Thus, we are selecting more projects with high risk resulting in overall increase in the risk of the firm.

4. An analyst has determined that the required rate of return, using the Fama and French three factor model, for a stock is 11.0%. The analyst used the following information to make this determination:

rrf = 5%
rm = 10%
rSMB = 4%
rHML = 5%
beta to market ...

#### Solution Summary

This post addresses multiple questions of type of capital, risk, profit, pension planning and maturity

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