Reference no: EM132932659

1 Payout Policy/Capital Structure

Consider a firm F that generates a single cash-flow in one year which depends on the state of the economy:
-Boom (probability 1/2) 5m
-Recession (probability 1/2) 1m
-F has 2,000 bonds outstanding with face value $1,000 and a 6% coupon, one year matu rity.
-There are no taxes, and the risk free rate is 3%
-F has 1m cash at the beginning of year 1.
-F's cost of debt is 4% regardless of the payout policy they choose.
F can distribute at the beginning of year 1 either 70% of its cash or 30% of its cash. The cash retained by the firm is invested at the risk free rate. Stockholders invest the dividend they receive at the beginning of year 1 at the risk free rate as well.

1.1 Which of the two payout policies maximize stockholder payoffs at the end of year 1?

1.2 Anticipating that the firm will choose to payout 70% of its cash at the start of year 1, the market value of the firm's bonds is 1.5m, calculate the expected bankruptcy costs on the firm's assets.
1.3 * Suppose instead that the market value of the bonds are 2m regardless of the payout policy chosen. The required return on the firm's assets is 10%, and the required return on equity if the firm had zero cash is 12%. Which of the two payout policies will the firm's shareholders optimally undertake and why?

2 Agency Costs
F generates a single cash-flow in one year. This cash-flow depends on the strategy chosen by the management:
- The safe strategy yields a certain cash-flow of $3,500,
- The risky strategy yields a high cash-flow of $15,000 with probability 0.2, and a low cash-flow of $625 with probability 0.8.
F has 3 stocks outstanding and one bond with a $2,000 face value, a 5% annual coupon and a one-year maturity. All agents are risk neutral and the risk free rate is 5%.

2.1 If the bond is non-convertible, which strategy does the management choose and why?

2.2 If the bond is convertible with a conversion ratio of 4, which strategy does the management choose and why? In what cases do the bondholders convert in what cases do they not convert (they can see the cashflow before converting)?

2.3 suppose the bond has not been issued yet and that both projects cost 2,000. The firm wants to issue the same convertible bond as in 2.2 but must include one of the following covenants to the bond:
-Covenant A: restricts the firm to only invest in the safe asset.
-Covenant B: restricts the firm to only invest in the risky asset.
Assuming the creditors pay market value for the bonds, which covenant will the firm include and why?

3 Agency Costs/Bank Regulation
Suppose that you are a bank regulator who knows that there are two types of bank's under your jurisdiction, high quality (H) and low quality (L), who differ in their ability to screen loan applications for credit worthy borrowers. Using past data you estimate that roughly 70% of banks are high quality and 30% are low quality. High quality banks generate a cashflow per loan of 100k with probability .8 and 0 with probability .2. A low quality bank on the other hand generates a cashflow per loan of 100k with probability .5 and 0 with probability .5 These banks primarily make small loans to local businesses which creates a social benefit of 4% per dollar lent (i.e. if the bank lends $10 then the social benefit is 4%*$10). When a bank fails though, it generates a social cost of 15% per dollar of losses to the banks creditors (i.e. if creditors lose $10 then the social costs is 15%*$10). As a regulator you must choose a "capital requirement", dictating how much the banks can borrow to make loans, in order to maximize the expected social value. Each loan costs$50k and generates the returns described above. Additionally, the bank's start with $50k of their own money to invest. You, as the regulator, are debating whether to let the banks borrow money to issue 0, 1, or 2 additional loans. We assume the bank's find it optimal to issue as many loans as possible but can only raise additional funds by borrowing. This means banks will always make at least 1 loan with their initial $50k and will make an additional 0, 1, or 2 loans with borrowed money depending on how much the regulator allows them to borrow. All loans generate the same cash flow (e.g. if the H-type makes 3 loans then with prob .8 each loan generates a cashflow of 100k and with .2 each loan generates a cash flow of 0. Similarly, if the L-type makes 3 loans then each loan generates a cash flow of 100k with prob .5 and each loan generates a cashflow of 0 with probability .5).

3.1 Assume the regulator knows which banks are H-type and which are L-type. What is the expected social value (i.e. social benefit minus expected social cost) if the regulator allows the H-type bank to borrow 0, $50k, or $100k to make additional loans? What bout the L-type bank? How much will the regulator optimally allow the H-type and L-type bank's to borrow? (remember all bank always makes at least 1 loan, so they will either make 1, 2, or 3 loans depending on whether the regulator allows them to borrow 0, $50k, or $100k. Also note that the social cost only applies to borrowed money lost in default, not the bank's initial $50k, and the social benefit applies to money lent, not the realized cashflow).
3.2 Suppose instead that the regulator cannot tell which bank is H-type and which is L-type. How much will the regulator optimally allow the bank's to borrow? What is the expected social value of this optimal policy?

3.3 The regulator is deciding whether to invest in a "stress testing" technology that will allow them to distinguish H-type banks from L-type banks. How much would the regulator be willing to pay for this technology?