Value of a Firm Firm F has the following features:

• EBITDA is 200 in year 1, 300 in year 2, 400 in year 3, and then grows at a 10% rate until infinity.

• Depreciation is 100 in the first 3 years and then decreases at a 10% rate until infinity.

• Amortization is 20 each year until infinity.

• Firm F has issued a perpetual bond with face value 1000 and coupon rate 5%.

• The cost of debt is rB =5%.

• Firm F operates in Texas the first 3 years and then moves to California.

• Corporate tax rate is 30% in Texas and 40% in California.

• Covariance between return on equity of a comparable (same features as firm F except the capital structure) unlevered firm and the market return is 0.008

• Volatility of the market return is 10%

• Expected market return is 15%

• Risk-free rate is 3%

  Remark: The notation t+ stands for time t right after cash-flows have been paid.

(a) (2 points) Compute the value at time 3+ of a security that pays the EBITDA (VEBITDA). Hint: 3+Discount the cash-flows at the unlevered cost of equity.

(b) (2 points) Compute the value at time 3+ of a security that pays the depreciation amounts (V Depr). 3+

Hint: Discount the cash-flows at the unlevered cost of equity.

(c) (2 points) Compute the value at time 3+ of a security that pays the amortization amounts (V Amor). 3+

Hint: Discount the cash-flows at the unlevered cost of equity.

(d) (2 points) Compute the value at time 3+ of firm Fs tax shields (TS3+).

(e) (2 points) Compute the value at time 3+ of the comparable unlevered firm (S0,3+).

(f) (2 points) Compute the value at time 3+ of firm F (A3+).

(g) (2 points) Compute the value at time 3+ of firm Fs debt (B3+).

(h) (2 points) Compute the value at time 3+ of firm Fs equity (S3+).

(i) (2 points) Compute the value at time 0 of a security that pays time 1, time 2, and time 3 unlevered cash-flows (V UCF1,2,3 ).

(j) (2 points) Compute the value at time 0 of the comparable unlevered firm (S0).

(k) (2 points) Compute the value at time 0 of a security that pays time 1, time 2, and time 3 tax-savings of firm F (V T S1,2,3 ).

(l) (2 points) Compute the value at time 0 of firm F (A).

(m) (2 points) Compute the value at time 0 of firm Fs debt (B).

(n) (2 points) Compute the value at time 0 of firm Fs equity (S).