Question

The firm Lando expects cash flows in one year’s time of $90 million if the economy is in a good state or $40 million if it is in a bad state. Both states are equally likely.
The firm also has debt with face value $65 million due in one year.

Lando is considering a new project that would require an investment of $30 million today and would result in a cash flow in one year’s time of $47 million in the good state of the economy or $32 million in the bad state.

Investors are all risk neutral and the risk free rate is zero.
(a) What are the expected values of the firm's equity and debt without the new project?

Lando can finance the project by issuing new debt of $30 million. If the firm goes bankrupt the new debt will have a lower priority for repayment than the firm’s existing debt.

(b) If the new project is accepted, what will be the value of the firm’s cash flow in each state after paying the original debtholders? What payment must Lando promise to the new debtholders in the good state of the economy?

(c) What will be the expected value of Lando’s equity? Will Lando’s managers choose to accept the project? Why/why not?

Alternatively, Lando can issue new equity of $30 million to finance the project.

(d) What proportion of its equity must Lando give to the new equityholders? Will Lando’s managers choose to accept the project now? Why/why not?

Answer 1

a)

await amount flow in 1 year = 90x0.5 + 40x0.5 = 65 million

mortage price after 1 year = 65 million

the danger free rate is 0 hence ,the present worth of cash flows stay same as the worth of cash flows after 1 year

total firm worth after 1 year = 65 million

debt value is worth after 1 year = 65 million

equity value is fv - dv = 65 -65 = 0

b)

Since the hazard -free rate is zero therefore we can disregard the discounting impact on the cashflows.

Good state economy

Cash flows ot be acquire = real cash flows + cash flows through new work is = 90 + 47 = 137

cash flow after giving the original mortgage holder = 137 - 65 = 72 million

Lando can promise to give the full cash of 30 million to the new debtholders

Bad state economy

cash flows to be acquire = 40 +32 = 72

cash flows later repaying original debt holders = 72 - 65 = 7 million

c)

equity worth in case of fine economy = fv - dv = 137 - 65 - 30 = 42 million

equity worth in case of bad economy = 72 - 65 - 30 = limited to zero

so await equity worth = 42 x0.5 + 0x0.5 = 21 million

so As the worth is greater than  0 so we should allow the new project .