# L140 Econometrics Assignment-City, University of London

Instructions to students:  All questions are compulsory.

Materials:

Dictionaries are not permitted.

Question 1.

Company Dilemma Ltd. faces a choice between two mutually exclusive investment projects. The company has £100 million in outstanding debt, which need to be repaid one year from now. The interest rate on the debt is 5%, which is 1% more than the risk free rate. The market premium is expected to be 6%. Both possible projects require an initial investment of £10 million, which will be written o¤ entirely (i.e. full depreciation) after one year. Both projects generate cash  for one year only. Project A has a 50% chance of success, in which case it generates a cash ‡ow £40 million. If the project does not do well it generates £10 million. Project B has a success rate of 30% and generates £100 million in cash and £0 if it does not succeed. The project is A= 1 and B= 2 for projects A and B respectively. The corporate tax rate is 40%. Assume that the company has currently no other projects running, but it has assets worth £90 million that can be liquidated at that value at any time.

a)Which of the two projects, if any, should the company undertake? Support your answer with the necessary calculations.

b)Suppose now that the manager undertaking the project acts on behalf of the shareholders only, and the project is financed by a £10 million injection of new equity by existing shareholders. Which project, if any, will the manager choose? Comment on your findings.

Question 2.

Firm A is an all equity financed firm. Its current equity price is £1.06 cum dividend. Also, its current earnings per share (eps) and current dividend payment are 20p and 12p, respectively. The market expects the ratio of eps to dividend to stay the same in the future. Firm A’s rate of return on reinvested funds is equal to its equity cost of capital. Estimate firm A’s cost of capital.

a)Firm B has the same business risk as firm A and it is also all equity financed. Firm B’s current market capitalization is £25 million. It makes no profit currently, but is expected to make a constant profit of £1 million two and three years from now. All profits are paid out as dividends in the second and third years. After that profits grow at a constant rate forever, allowing the firm to pay out £1 million in dividends in year four and retaining 50% of profits. From then on firm B plans to retain the same fraction of profits each year and return the remainder to shareholders. Estimate firm B’s rate of return on reinvested funds.

b)Firm C also has the same business risk as firm A, however it is a levered company: C’s book value ratio of debt to equity is 1/4 and market value ratio of debt to equity is 1/3. The market risk premium is 6% and the risk free interest rate is 3%. Firm C’s debt beta is 0.2. Assuming that CAPM holds and corporate tax rate is 0%, estimate firm C’s equity cost of capital.

c) What is firm C’s cost of capital if corporate tax rate is 30%?

### Question 3: L140 Econometrics Assignment-City, University of London

a) Suppose risk-free borrowing and lending is available. If the Capital Pricing Model (CAPM) holds, how would you (theoretically) identify the investors who are more risk averse? Explain. You may use graphical displays to motivate your work.

b)In the CAPM, given risk-free borrowing and lending, effcient portfolios have no idiosyn-cratic (diversifiable) risk. True or false? Explain

Question 4.

a)The accepted theory of firm capital structure holds that businesses try to save as much money as possible by reducing their taxes by using debt to generate interest tax shields, while balancing this o¤ against the possible costs of financial distress that may arise if the firm finds itself without the money to meet its debt payments. Comment on this theory and, in particular, explain what the costs of financial distress are.

b)How does the theory mentioned in (a) compare to the Modigliani-Miller results regarding firm capital structure?