Question

UltraMX Corp., an all equity exchange traded company, is planning to invest in a project as follows:

• Initial investment = $100 million.
• The project is financed with debt and equity in same proportion (i.e., one part of debt to one part of equity).
• Expected cash flows after tax = $10 million in perpetuity.
• Tax rate = 25%
• Cost of debt after tax of project (4%)
• Equity beta of project = 1.5
• UltraMX beta = 0.8
• Market risk premium (MRP) =6%.
• Risk-free rate = 3%.

Based on above information, answer the following questions:

1. Calculate the appropriate discount rate (cost of capital) for UltraMX project.

2. Determine whether UltraMX should accept or reject the project using NPV and IRR, respectively.

3. Assume the current market value of the firm is $500 million and markets are efficient in the semi-strong form:

1) what would happen to the value of the firm after announcing the project?

2) what would be the percent change in the share price of UltraMX after announcing the project?

3) what would be the fair value of UltraMX after announcing the project?

Answer 1

(a) Post-Tax Cost of Debt = 4%, Equity Beta = 1.5, MRP = 6% and Risk_Free Rate = 3 %

Therefore, Cost of Equity = 3+1.5 x 6 = 12 %

Capital Structure: one part debt and one part equity

Debt Proportion = Equity Proportion = 0.5

Discount Rate of Project = 4 x 0.5 + 12 x 0.5 = 8 %

(b) Expected Project Cash Flows = $ 10 million in perpetuity, Initial Investment = $ 100 million, Discount Rate = 8 %

Therefore, NPV = (10/0.08) - 100 = $ 25 million

Let the project IRR be r

Therefore, 100 = 10/r

r = 10/100 = 0.1 or 10 %

As the project NPV is positive and discount rate lower than project IRR, the project is value accretive in nature and should be accepted.

(c) (i) Project Announcement will push up the value of the firm by an amount equal to the present value of the interest tax shield generated by the 50% debt financing the rpoject.

Post-Tax Cost of Debt = 4 % and Tax Rate = 34 %

Interest Rate = 4/(1-0.34) = 6.061 %

Debt = $ 50 million

Therefore, Present Value of Interest Tax Shield = (50 x 0.06061 x 0.34) / 0.06061 = $ 17 million

(ii) Original Firm Value = $ 500 million and Change in Value = $ 17 million

% Change in Share Price = 17/500 = 0.034 or 3.4 %

(iii) Fair Value of the Firm = Original Firm Value + NPV generated by project announced = 500 + 25 = $ 525 million