Question

The beta of the equity of CDE Company is 1.67 and CDE has a debt-to-equity ratio of 0.67 calculated at market values. The debt is risk-free and perpetual. CDE generates annual EBIT of $100 and has 100 shares of common stock outstanding. The expected return on the market portfolio is 15% and the risk-free interest rate is 5%. The corporate tax rate is 30%. Assume that personal taxes and bankruptcy costs are not relevant.

1. Compute the current market value of CDE Company.

2. CDE is considering an expansion project that will require an initial investment of 133.33. This expansion project is estimated to increase the firm’s annual EBIT by 20%. Determine the new value of CDE if it undertakes the investment and finances it 100% with debt, permanently altering its leverage. Also find the new value of the equity and the new share price.

3. If the investment in part 2 is financed entirely with new equity, how many shares must be issued? What is the new equilibrium price of the shares?

4. Should CDE undertake the project? Hint: Is the new value of the firm greater then the old value of the firm plus the investment?

Answer 1

(1) Cost of Debt = Risk-Free Rate = kd = 5 %, Market Portfolio Return = 15 % and Beta = 1.67

Using CAPM, Cost of Equity = ke = Risk-Free Rate + Beta x (Market Portfolio Return - Risk-Free Rate) = 5 + 1.67 x (15-5) = 21.7 %

EBIT = $ 100 and Tax Rate = t = 30 %

NOPAT = EBIT x (1-t) = 100 x (1-0.3) = $ 70

D/E = 2/3.

Therefore, D/V = 2/5 and E/V = 3/5

Therefore, WACC = D/V x (1-t) x kd + (E/V) x ke = 2/5 x (1-0.3) x 5 + (3/5) x 21.7 = 14.42 %

Firm Value = NOPAT / WACC = 70 / 0.1442 = $ 485.44 approximately

Equity Value = 60% of Firm Value = 0.6 x 485.44 = $ 291.264 and Debt Value = 40 % of Firm Value = 0.4 x 485.44 = $ 194.176

Number of Common Shares Outstanding = N = 100

Therefore, Stock Value = 291.264 / 100 = $ 2.91264 per share

(2) Initial Investment = $ 133.33

New EBIT = 100 x 1.2 = $ 120 and NOPAT = 120 x (1-0.3) = $ 84

Incremental EBIT = (84 - 70) = $ 14

Incremental Value = 14 / 0.1442 = $ 97.087

New Firm Value = Old Firm Value + Project NPV = 485.44 + 97.087 = $ 582.527

As this project is entirely debt financed, New Debt Value = Old Debt Value + Initial Investment = 194.176 + 133.33 = $ 327.506

New Equity Value = 582.527 - 327.506 = $ 255.021

N = 100

Price per Share = 255.021 / 100 = $ 2.55021

(3) Original Firm Value = $ 485.44 with Equity = $ 291.264 and Debt = $ 194.176

Project is entirely equity financed and assuming that market is perfectly efficient, the net impact of undertaking the project would be reflected on the company's stock price almost immediately. The net impact of undertaking the project is actually the project's NPV.

Therefore, Project NPV = 97.087 - 133.33 = - $ 36.243

New Firm Value (post equity issue announcement and before actual equity issue) = 485.44 - 36.243 = $ 449.197

Debt Value = $ 194.176 (remains constant as the new project is completely equity financed)

New Equity Value = 449.197 - 194.176 = $ 255.021

N = 100

Stock Price = $ 2.55021

As the share price changes from $ 2.91624 (calculated in part 1) to $ 2.55021 upon equity issuance announcement(and before actual equity issue) , the new shares to be issued will be raised at the reduced price.

Therefore, Number of Shares Issued = Initial Investment / 2.55021 = 133.33 / 2.55021 = 52.28 approximately.

The new equilibrium share price is the price at which new equity is issued which is $ 2.55021

(4) Old Firm Value + Initial Investment = 485.44 + 133.33 = V1 = $ 618.77

and New Firm Value = Old Firm Value + PV of Project = 485.44 + 97.087 = V2 = $ 582.527

As V2 < V1, CDE should not undertake the project as doing the same reduces firm value. The same can be determined by calculating the project's NPV as (97.087 - 133.33) = - $ 36.243 which shows that the project is value diluting owing to its negative NPV. Hence, the project should not be undertaken.