PROBLEM 3.2. Consider a company which is due to generate a single cash-flow, equal either to SEK 2500 or to SEK 1 500, in one year. The claims on the company’s cash-flows consist of both debt and equity, and the company’s shareholders have limited liability. The market value of the company is equal to SEK 1 750, and the assumptions of Modigliani-Miller irrelevance theorem are satisfied. The risk-free rate of interest is equal to 2%.
1. Suppose that the company’s debt consists of a single “bond.” This bond entitles the investor(s) to a payment of SEK 1300 due in one year. Provide the current market value of the bond and the company’s equity.
2. Suppose that the company’s debt consists of a senior bond and a subordinate bond. The bonds entitle the investors to a payment of SEK 1 300 and a payment of SEK 500, respectively; both payments are due in one year. Provide the current market value of each bond and the company’s equity.
Hint. In this Problem, we are given the market value of the company. Hence, to use the “replication” strategy to find the price of any given security, we must find a combination of an ideal security that includes both the firm’s equity and the firm’s debt, on one hand, and risk-free debt, on the other hand, whose value in each state is identical to that of the security to be priced. For example, using m and f to indicate the positions in the ideal security and risk-free debt, respectively, we can write the system determining the replicating portfolio for the firm’s equity in 3.2.1 as:
2500- 1300 = 2500x m + 1.02x( 1500- 1300= 1500x m + 1.02x f