16.1 Arbitrage in a World of Taxation

Question 1

How can miss equilibrium create arbitrage opportunities in a world of tax

Answer 1

• Need to consider how to find the market equilibrium in the world of tax deductibility of debt interest
• Allows the identification of shares that are not in equilibrium and then profit by arbitraging
• Arbitrage is worthwhile when two identical assets are trading at different prices

Question 2

How does Modigliani and Miller identify arbitrage in a world of tax

Answer 2

• Here the value of a geared company should be greater than the value of an ungeared company
  VG = Vu + Dt
• This is the equilibrium position the two companies do not have the same value If this does not hold, then arbitrage is worthwhile *MM illustrate this for both cases
  VG > Vu + Dt
  VG < Vu + Dt
  *Want to move from a relatively over-priced company to the relatively under-priced company

Question 3

What are the considerations for risk when arbitraging

Answer 3

• If you are looking to switch between an ungeared company and a geared company you must consider both business and financial risk
• The business risk is maintained by buying the same proportion of the company
• The finance risk is maintained by either borrowing or lending depending if you are moving from geared to ungeared or the other way around
• Take the starting position as the investors risk preference and make sure they end up on the same risk level

Question 4

What happens to risk as you move from a geared company to an ungeared company

Answer 4

• The initial investment has both financial and business risk
• The subsequent only has business risk
• There is no financial risk in the company as it doesn’t have debt
• Therefore, need to take on financial risk personally by borrowing

Question 5

What must be followed in arbitrage

Answer 5

• We are always and only interested in moving from an overvalued to an undervalued company
• We may want to move from an ungeared company to a geared company.
• To maintain total riskiness, we need to eliminate the financial risk in the geared company
  o This we do either by buying both equity and debt in the geared company or by buying the equity of the geared company and lending elsewhere
• Either way, the first part of the equation above is the amount of the geared company’s equity to buy the remainder is the amount to borrow or lend
  o Negative borrowing is lending

Question 6

What are some of the assumptions of MM in a world of tax when arbitraging

Answer 6

• Another point to note is that this formula is derived from MM They deal in perpetuities and so we have to deal in perpetuities
• When we are dealing with a company which is not generating a stream of constant annual earnings, then we have to find the constant annual equivalent of that stream

Question 7

Arbitraging between differently geared companies of unequal size

Answer 7

Formula is too complex to put here but need to be able to explain is creation