Consider a project with free cash flows in one year of $133,582 in a weak market

Question

Consider a project with free cash flows in one year of $133,582 in a weak market or $160,703in a strong market, with each outcome being equally likely. The initial investment required for the project is $85,000,and the project's unlevered cost of capital is 14%. The risk-free interest rate is 5%. (Assume no taxes or distress costs.)

c. Suppose the initial $85,000 is instead raised by borrowing at the risk-free interest rate. What are the cash flows of the levered equity in a weak market and a strong market at the end of year 1, and what is its initial market value of the levered equity according to MM?Assume that the risk-free rate remains at its current level and ignore any arbitrage opportunity.

The cash flows of the levered equity in a weak market and a strong market at the end of year 1, and the initial market value of the levered equity according to MM is: (Round to the nearest dollar.) Date 0 Initial Value $85,000 44072 Date 1 Cash Flow Strong Economy Cash Flow Weak Economy Debt Levered Equity

Explanation / Answer

Solution:

E (FCFE) = P (strong) x FCFF (strong) + P (Weak) x FCFF (weak)

E (FCFE) = 0.5 x $160,703 + 0.5 x $133,582 = $147,142.5

Vu = E (FCFE)/(1 + RA) = $147,142.5/1.14 = $129,072.4

MV of debt at year 1 = MV of debt at year 0 (1 + Rf)

MV of debt at year 1 = $85,000 (1.05)

MV of debt at year 1 = $89,250 (under both economic states)

FCFE at year 1 and strong = FCFF at year 1 – Interest (1 – tax%) + Net Debt Issued

FCFE at year 1 and strong = $160,703 - $4,250 (1 – 0%) + (-$85,000)

FCFE at year 1 and strong = $71,453

FCFE at year 1 and weak = FCFF at year 1 – Interest (1 – tax%) + Net Debt Issued

FCFE at year 1 and weak = $133,582 - $4,250 (1 – 0%) + (-$85,000)

FCFE at year 1 and weak = $44,332

Under M &M (without taxes or bankruptcy costs)

VL = VU = MV of debt + MV of equity = $129,072.4

MV equity = VL – MV debt

MV equity = $129,072.4 - $85,000

MV equity = $44072.37

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