In: Finance
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.
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