Two firms, Kit plc and Kat plc, are identical except for their capital structure. Both will earn £300 million in a boom and £100 million in a slump. Kit plc is entirely equity-financed, and therefore shareholders receive the entire income. Its shares are valued at £1 billion. Kat plc has issued £800 million of risk-free debt at an interest rate of 10%, and therefore £80 million of Kat plc income is paid out in interest. There is no taxation and investors can borrow and lend at the risk-free rate of interest. Moreover, you are told that £10 invested in the market portfolio today grows as follows: Today In 1 year £10 £15 (good state) £5 (bad state) a) What is the risk-neutral probability of the good state realisation? What is the value of Kat plc stock? Show all your calculations and comment on your results. b) Suppose that you invest £40 million in Kit plc stock. Is there an alternative investment in Kat plc that would give identical payoffs in both good and bad state realisations? What is the expected payoff from such a strategy? Show all your calculations and comment on your results. c) Suppose now that you hold £40 million in Kat plc stock. Design an alternative strategy involving Kit plc that would have identical payoffs. Show all your calculations and comment on your results.
Two firms, Kit plc and Kat plc, are identical except for their capital structure. Both will earn £300 million in a boom and £100 million in a slump. Kit plc is entirely equity-financed, and therefore shareholders receive the entire income. Its shares are valued at £1 billion. Kat plc has issued £800 million of risk-free debt at an interest rate of 10%, and therefore £80 million of Kat plc income is paid out in interest. There is no
Moreover, you are told that £10 invested in the market portfolio today grows as follows:
Today
In 1 year
£10
£15 (good state)
£5 (bad state)
a) What is the risk-neutral probability of the good state realisation? What is the value of Kat plc stock? Show all your calculations and comment on your results.
b) Suppose that you invest £40 million in Kit plc stock. Is there an alternative investment in Kat plc that would give identical payoffs in both good and bad state realisations? What is the expected payoff from such a strategy? Show all your calculations and comment on your results.
c) Suppose now that you hold £40 million in Kat plc stock. Design an alternative strategy involving Kit plc that would have identical payoffs. Show all your calculations and comment on your results.
Step by step
Solved in 4 steps with 1 images
