Chapter 10 Problem Solution
Problem #12
A cash dividend increase is viewed as a positive signal by the market because the firm is generally committing to higher cash out flow to the shareholders. To understand this one must appreciate to basic concepts about cash dividends. First and foremost, cash dividends are “costly” to the firm. Second, firms do not want to reduce cash dividends as the market views this action as a negative signal about a firm’s ability to generate future cash flow. So when a firm increases dividends it is making a commitment to shareholders that it will have sufficient future cash flow to sustain this higher level of cash out flow, thus a positive signal about future prospects of the firm.
If one takes market reaction as a belief then in general the market believes the signal. On average stock prices increase with dividend increase announcements but the increase is anticipated trading volume and asymmetric information among traders does not change at the announcement of a dividend increase. The reason the increase in dividends is associated with the increase in price is because it is a costly signal. It is a costly signal because to replicate this signal a competing firm must raise its dividend, increasing cash out flow. See Figure 10.15 (page 476) for the average reaction to the dividend decrease and increase announcement.
Chapter 11 Problem Solutions
Problem #12
Facts – Firm has beta of 1.25, risk-free rate is 8% and expected return on the market is 16%,
Required Return on Equity = 8% + 1.25 (16% - 8%) = 18%
The cost of debt (marginal) is 12% before tax.
Equity Value is $15 x 100,000,000 = $1,500,000,000
Debt Value is $500,000,000
Corporate Tax Rate is 50%
WACC = $1,500 /($1,500+$500) x 18% + $500 / ($1,500+$500) x 12% x 0.5
WACC = 13.5% + 1.5% = 15%
Decision #1 – Which projects have positive NPV and how much do they required in terms of initial investment? Those with IRRs greater than 15%, Projects A, B, and C.
Positive NPVs Initial Investment
A $15 million
B $10 million
C $25 million
Total Investment $50 million
With the current D/E ratio of 1/3 it means that 25% of the financing for these projects should come from debt (to keep the same debt/equity ratio) and 75% from equtiy. Therefore debt and equity will finance,
Debt Financing = $50 million x 0.25 = $12.5 million
Equity Financing Requirement = $50 million x 0.75 = $37.5 million
Available Equity Financing is $100 million
Return to Equity Holders (Dividend) = $100 million - $37.5 million = $62.5 million
Dividend = $62.5 million / 100 million = $0.625 per share
Problem #13
First Step is to find WACC and see what projects have positive NPVs
Cost of Debt = 10% (pre-tax)
Cost of Equity = 22%
Debt Value = $100 million
Equity Value = $10 x 50,000,000 = $500 million
Corporate Tax Rate = 40%
WACC = (5/6) x 22% + (1/6) (10%) (1 -0.4) = 19.33%
Second Step find the NPV of the projects:
Project #1 OCF = EBIT x (1 – 0.4) + Depreciation = $1 (0.6) + $0.5 = $1.1
NPV Project #1 = $-10 + $1.1 (3.0352) + $2.5 / (1.1933)5 = -$5.63
Project #2 OCF = $5 x (0.6) + $1 = $4
NPV Project #2 = $-40 + $4.0 (4.2896) + $10 / (1.1933)10 = -$21.13
Project #3 OCF = $5 x (0.6) + $1 = $4
NPV Project #3 = $-50 + $4.0 (4.2896) + $10 / (1.1933)10 = -$31.13
All projects are rejected.
What can it pay in dividends, look at the Free Cash Flow to Equity:
FCFE = Net Income - (1 - % debt financing) x (Capital Expenditures – Depreciation)
Here we have zero Capital expenditure and $10 million in Depreciation with a 20% debt ratio to go with the Net Income of $90 million so,
FCFE = $90 million - (1 – 0.20) ($0-$10 million) = $98 million available for dividends
Problem # 14
Find the Required Rate of Return for each project:
Risk-free rate is 6%
Risk Premium is 5.5%
D/E ratio is 20%
Corporate Tax Rate is 40%
Project A, Beta of 2.0, Re for equity is: 6% + 2.0 (5.5%) = 17%
IRR = 21% > Equity Hurdle Rate, accept
Initial Cost is $500 (million)
Project B, Beta of 1.5, Re for equity is: 6% + 1.5 (5.5%) = 14.25%
IRR = 20% > Equity Hurdle Rate, accept
Initial Cost is $600 (million)
Project C, Beta of 1.0, Re for equity is: 6% + 1.0 (5.5%) = 11.5%
IRR = 12% > Equity Hurdle Rate, accept
Initial Cost is $500 (million)
All projects are a go with total required funding of $1,600 million
FCFE = Net Income$1,000 million
-(Cap Exp – Dep) x (1 -0.2)
($1,600 - $500) x (0.8) - $880 million
- (Δ Work. Capital) (0.25) x (1 - 0.2)
- ($5,000 x 0.08) x (0.25) x (0.8) - $80 million
Available for Dividends $40 million
Problem #16
Again we look at the cost of equity and debt to find the equity hurdle for each project and then determine the acceptable projects. First question though…what risk-free rate should we use, 3% T-Bill or 6.25% Treasury Bond? These are long term projects so we will select the Treasury Bond.
Project A: Equity required = 6.25% + 1.0 (5.5%) = 11.75%
Project A: ROE, CF to Equity, $12,500 / $100,000 = 12.5%
Accept project, initial cost of $100,000 from equity
Project B: Equity required = 6.25% + 1.5 (5.5%) = 14.5%
Project B: ROE, CF to Equity, $14,000 / $100,000 = 14.0%
Reject project
Project C: Equity required = 6.25% + 1.8 (5.5%) = 16.15%
Project C: ROE, CF to Equity, $8,000 / $50,000 = 16.0%
Reject project
Project D: Equity required = 6.25% + 2.0 (5.5%) = 17.25%
Project D: ROE, CF to Equity, $12,000 / $50,000 = 24.0%
Accept project, initial cost of $50,000 from equity
Total cash outlay for equity holders on these projects is $150,000
Now find the cash flow available for financing
Find Net Income:
Revenues $1,000,000 x 1.10 $1,100,000
Expenses (40% of Revenue) 440,000
Depreciation (No Change) 100,000
EBIT $ 560,000
Interest Expense (No Change) 100,000
Taxable Income$ 460,000
Taxes (40%) 184,000
NET INCOME$ 276,000
Free Cash Flow to Equity
FCFE = Net Income$ 276,000
-(Cap Exp – Dep) x (1 -0.4)
($150 - $100) x (0.6) - 30,000
- (Δ Work. Capital) (0.50) x (1 - 0.4)
- ($1,000 x 0.10) x (0.50) x (0.6) - 30,000
Available for Dividends $216,000
b. If the company pays out $1 per share and has 100,000 shares outstanding, it will pay out $100,000 leaving $116,000 in the company…with a current balance of $150,000 the year end balance will grow to $266,000 if all goes exactly as planned, but of course, cash flow is not smooth and plans do not always work out as we intend so this is just a projected balance.