In this appendix we are going to see three more examples of a LBO with di¤erent characteristics which end up with debt holders expropriation. The …rst example deals with the use of the …rm’s assets as collateral, the second example deals with the issuance of senior debt and, …nally, the last example deals with the issuance of junior debt.
7.1
Example 1: Use of the …rm’s assets as collateral
Assume a three date economy (t = 0; 1; 2) with risk free interest rate normalized to zero (r = 0) and risk neutral agents where there exist a ”penniless” entrepreneur, a LBO specialist and one …rm represented by an investment project at t = 0 with the following characteristics: Division t = 0 t = 1 t = 2 Investment -100 Cash Flow A 100 p = 1 2 B 20 A 90 1 p = 12 B 10 NPV 10
The …rm consists of an investment project of 100 at t = 0 and is divided in two divisions (A and B). If the entrepreneur manages to raise the funds to start the company (100) it will produce a cash ‡ow at t = 2 of either 120 or 100 depending on the state of the economy (expansion or recession) with a probability of a half for each state. If the economy is favorable, division A will produce 100 and division B will produce 20. If the economy is not favorable division A will produce 90 and division B will produce 10.
There also exists an unanticipated possibility of the …rm being acquired at t = 1 by means of a LBO.
Assume that at t = 0 the entrepreneur raises 100 issuing an unsecured bond to start the company with a promised repayment of 100 at t = 2. Again, under the assumption that the possibility of a LBO occurring at t = 1 is not anticipated the debt is riskless. At t = 1.
First I price the di¤erent claims issued by the …rm if a LBO does not occur: Debt = 100
Equity = 20 1 2 + 0
1 2 = 10
In this case, the entrepreneur earns all the net present value of the project while the debt holders earn the opportunity cost of the funds lent, which is the risk free interest rate equal to zero.
Second, I analyze what happens at t = 1 if a LBO occurs. Assume that at t = 1 the LBO specialist realizes that there is an opportunity of making a pro…t by means of a LBO. She could make it by raising 10 to buy the …rm’s equity collateralizing the debt with division B of the …rm. In this case, the promised repayment will be 10 at t = 2 because the new debt is riskless.
At t = 2, if the economy is favorable the unsecured debt holders will receive 100 and the collateralized debt holders will receive 10. But, if the economy is not favorable the unsecured debt holders will only receive 90 because division B have been used to collateralize the debt issued to buy the …rm.
I price the di¤erent claims issued by the …rm: CollateralizedDebt = 10 U nsecuredDebt = 100 1 2+ 90 1 2 = 95 Equity = 10 1 2+ 0 1 2 = 5
The LBO specialist could then sell the equity for 5 and make an immediate gain. Again, debt holders have been expropriated.
7.2
Example 2: Issuance of Senior Debt
Assume again a three date economy (t = 0; 1; 2) with risk free interest rate normalized to zero (r = 0) and risk neutral agents where there exist a ”penniless”entrepreneur, a LBO specialist and one …rm represented by an investment project at t = 0 with the following characteristics:
t = 0 t = 1 t = 2 Investment -100 Cash Flow 150 p = 1 2 100 1 p = 12 NPV 25
If the entrepreneur manages to raise the funds to start the …rm (100) it will produce a cash ‡ow at t = 2 of either 150 if the business cycle is favorable or 100 if the business cycle is unfavorable with a probability of a half for each possible world.
Finally, there also exists an unanticipated possibility of the …rm being acquired at t = 1 by means of a LBO.
Assume that at t = 0 the entrepreneur issues a bond to start the company with promised repayment of 100 at t = 2. By doing this, she will raise 100 because under the assumption that the possibility of a LBO occurring at t = 1 is not anticipated the debt is riskless. At t = 1.
First I price the di¤erent claims issued by the …rm if a LBO does not occur: Debt = 100 1 2 + 100 1 2 = 100 Equity = 50 1 2 + 0 1 2 = 25
In this case, the entrepreneur earns all the net present value of the project while the debt holders earn the opportunity cost of the funds lent, which is the risk free interest rate equal to zero.
Second, I analyze what happens at t = 1 if a LBO occurs. Assume that at t = 1 the LBO specialist realizes that there is an opportunity of making a pro…t by means of a LBO. She could make it by raising 30 in order to buy the equity of the …rm. She can do it by issuing a bond maturing at t = 2 with face value of 30 and higher seniority than the outstanding debt. Then, she could buy the equity …rm for 25 and then automatically pay herself a dividend equal to the di¤erence between the new funds borrowed (30) and the equity price. By doing this, the LBO specialist will earn 5. Finally, she could sell the equity she has and make a pro…t.
Pricing the di¤erent claims issued by the …rm we obtain: OutstandingDebt = 100 1 2+ 70 1 2 = 85 N ewDebt = 30 Equity = 20 1 2 + 0 1 2 = 10
If the LBO specialist sells at t = 1 the equity for 10 she will make an overall pro…t of 15 which she clearly expropriated from the original debt holders.
7.3
Example 3: Issuance of Junior Debt
Consider the example of a …rm which has no cash ‡ow in the current period but will have a cash ‡ow of 150 or 50 in the next period depending on the economy being favorable or not. With the same assumptions as before the going concern value of the …rm is 100. Furthermore, assume a liquidation value of 110. This …rm’s capital structure consists of equity and debt. Suppose the debt includes an obligation to pay 100 next years and 10 the current year to senior lenders. In this situation the …rm is currently bankrupt and should be liquidated to pay the senior lenders what it is owed to them.
First I price the di¤erent claims issued by the …rm if a LBO does not occur: Debt B = 10 + 100 = 110
Equity E = 0
In this case, the equity holders have a value of zero because the …rm is bankrupt. Second, I analyze what happens at t = 1 if a LBO occurs. Assume that at t = 1 the LBO specialist realizes that there is an opportunity of making a pro…t by means of a LBO. She could make it by buying the …rm for 0 to equity holders, raising 10 by means of junior debt with a promise repayment of 30 next year and use it to pay the coupon which is owed the current year, preventing the …rm from going bankrupt and keeping it working until next year.
In this situation, the price of the di¤erent claims issued by the …rm is: SeniorDebt = 100 1 2 + 50 1 2 = 75 J uniorDebt = 30 1 2 = 15 Equity = 20 1 2 = 10
The LBO specialist could then sell the equity for 10 and make an immediate gain. Again, debt holders have been expropriated.
As we have seen, LBO consequences can go against debt holders interest because they lose value by means of a decrease in the market price of the debt they hold.