Question

In: Finance

In Bermuda there are no corporate income taxes. Consider two Bermuda firms with perfectly correlated earnings....

In Bermuda there are no corporate income taxes. Consider two Bermuda firms with perfectly correlated earnings. The first is Debt Galore and the second is Debt Zero. Each company is expected to earn $35 million (before interest) in perpetuity. All these earnings are distributed as interest or dividend. Debt Galore has $150 million of perpetual risk free debt. The interest on this debt is 7%. It has 1.5 million shares priced at $115 per share. Debt Zero has no debt. It has 3.6 million share at $86 per share. Capital markets are perfect and there are no transaction costs.

a) Is there an arbitrage opportunity?

b) Construct a zero-risk, zero-investment portfolio with $1 million invested in the equity of Debt Zero that generates a positive income in perpetuity.

Solutions

Expert Solution

Earning analysis of with Debt and Debt free (Debt Zero) firm :

Given Data :

Consider two Bermuda firms with perfectly correlated earnings.

Debt Galore Debt Zero
no corporate income taxes no corporate income taxes
company is expected to earn $35 million (before interest) in perpetuity. All these earnings are distributed as interest or dividend. company is expected to earn $35 million (before interest) in perpetuity. All these earnings are distributed as interest or dividend.
Debt Galore has $150 million of perpetual risk free debt. The interest on this debt is 7%. It has 1.5 million shares priced at $115 per share. Debt Zero has no debt. It has 3.6 million share at $86 per share. Capital markets are perfect and there are no transaction costs.

Analysis of Earning:

Capital Structure Debt Galore Debt Zero
Equity capital

=1.5 million shares x $115 per share

=172.50

=3.6 million share x $86 per share

=309.60

Debt =150.00 =0
Total ($ in Million) =322.50 =309.60

Earnings per share:

Particulars Debt Galore ($ in million) Debt Zero ($ in million)
Earnings before Interest 35.00 35.00
Less: Interest on Debt

10.50

($ 150 million x 7%)

0
Earnings after debt =24.50 = 35.00
Number of shares in millions 1.5 3.6
Earning per share

= $24.50 / 1.5 million

= 16.33

= $ 35.00 / 3.6 million

= 9.722

Earnings on equity holder in hand

= 16.33 / 115 x 100

= 14.20%

= 9.722 /86 x 100

= 11.30%

a) Is there an arbitrage opportunity? :

There is an arbitrage opportunity.

As in the debt galore firm the equity share price per share be $ 115 . It means if we invest $ 100 in the share of Debt galore then we get return of 12.35% ( 100/115 x 14.20%)

The market price per share of Debt galore firm be $ 809.72 ( $ 115/14.20% or $ 100/12.35%)

In Debt zero firm the equity share price per share be $ 86. It means if we invest $ 100 in the share of Debt zero firm then we get return of 13.14% ( 100/86 x 11.30% )

The market price of the Debt zero firm be $ 761.06 ($ 86 / 11.30% or $100/13.14%)

Hence, there is an arbitrage opportunity in Debt Zero firm as the investor get more return in investing the Debt zero firm.

To maximize the value of share one can invest returns from debt galore firm in debt zero firm.

b) Construct a zero-risk, zero-investment portfolio with $1 million invested in the equity of Debt Zero that generates a positive income in perpetuity.

Investment = $1 million

Number of shares allotted against $ 1 million investment = $ 1 million / $ 86 = 11627.91 say 11628 shares

Earnings on Investment = $ 9.722 x 11628 shares = $ 113047 /-

Here, we get the return of $ 113047 for perpetuity.

Investor can hedge this opportunity by investing it in:

1. Either in Debt zero firm for same returns

2. Either in Debt galore firm in Debentures to earn 7 % return

3. Or in Debt Galore to equity to earn 12.35% return


Related Solutions

Consider two perfectly positively correlated risky securities, A and B
Consider two perfectly positively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. Solve for the minimum variance portfolio (i.e., what are the weights in A and B of the minimum variance portfolio). What is the variance of this portfolio?
4. Diversification can eliminate risk if two events are perfectly negatively correlated. Suppose that two firms...
4. Diversification can eliminate risk if two events are perfectly negatively correlated. Suppose that two firms are competing for a government contract and have an equal chance of winning. Because only one firm can win, the other must lose, so the two events are perfectly negatively correlated. You can buy a share of stock in either firm for $20. The stock of the firm that wins the contract will worth $40, while the stock of the loser will worth $10....
Consider a world of corporate taxes along with personal taxes on income from shares and on...
Consider a world of corporate taxes along with personal taxes on income from shares and on income from bonds. (i) Prove that the gain from leverage is less than the gain without personal taxes. (ii) With appropriate tax rates, is it possible that the gain could be negative? If so, provide a numerical example.
Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate...
Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 22%. B has an expected rate of return of 10% and a standard deviation of return of 24%. The weight of security B in the minimum-variance portfolio is _________. a 62.01% b 47.83% c 45.75% d 43.84%
Suppose that the annual returns on two shares are perfectly negatively correlated and that r_m= 0.07,...
Suppose that the annual returns on two shares are perfectly negatively correlated and that r_m= 0.07, r_n= 0.20,σ_m=0.12 , and σ_n=0.5. Assuming that there are no arbitrage opportunities, by using the Goal Seek function (excel) calculate the weight (proportion) of the two assets that produce the lowest portfolio variance? (Use the Goal Seek function)
Question 2 Suppose that the annual returns on two shares are perfectly negatively correlated and that...
Question 2 Suppose that the annual returns on two shares are perfectly negatively correlated and that ?=0.07, ? ?= 0.20,?= 0.12 , and ?= 0.5. Assuming that there are no arbitrage opportunities, by using ??? the Goal Seek function (excel) calculate the weight (proportion) of the two assets that produce the lowest portfolio variance? (Use the Goal Seek function) MAYBANK Years Share price Dividends 2010 MYR 8.500 0.4400 2011 MYR 8.700 0.3600 2012 MYR 8.200 0.3300 2013 MYR 8.880 0.3100...
A study of 248 advertising firms revealed their income after taxes: Income after Taxes Number of...
A study of 248 advertising firms revealed their income after taxes: Income after Taxes Number of Firms Under $1 million 132 $1 million to $20 million 63 $20 million or more 53 What is the probability an advertising firm selected at random has under $1 million in income after taxes? (Round your answer to 2 decimal places.) b-1. What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an...
III. Income Taxes If Congress voted to eliminate corporate taxes, what would be the effect on...
III. Income Taxes If Congress voted to eliminate corporate taxes, what would be the effect on Target Corporation's income statement and balance sheet? Defend your response. Calculate the income tax rate for Target Corporation. What effect will an increase in income of $2,000,000 have on Target Corporation? What are the effects on the balance sheet and income statement? Justify your response. How much did Target Corporation pay in foreign taxes last year? What percentage of its income is United States...
Income Taxes If Congress voted to eliminate corporate taxes, what would be the effect on Target...
Income Taxes If Congress voted to eliminate corporate taxes, what would be the effect on Target Corporation's income statement and balance sheet? Defend your response. Calculate the income tax rate for Target Corporation. What effect will an increase in income of $2,000,000 have on Target Corporation? What are the effects on the balance sheet and income statement? Justify your response. How much did Target Corporation pay in foreign taxes last year? What percentage of its income is United States vs....
Consider a perfectly competitive market in which all firms areidentical. The market is in the...
Consider a perfectly competitive market in which all firms are identical. The market is in the long-run equilibrium, the market equilibrium price is P , and each firm produces   q units of good.The government decides to impose a tax of size T per unit of good.a)     After the tax is imposed, how would the market equilibrium price and quantity change in the short-run? How does the quantity produced by each firm change in the short-run? Illustrate your answers using a diagram....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT