Question

Project financing Suppose an unlevered firm has a perpetual cash flow and market value of

EBIT = 100

E = 1000

The number of outstanding shares is,

N0 = 500

The firm considers investing in a project that costs $300 and returns a perpetual cash flow of $40.

Cost, C0 = 300

Cash flow, X = 40

Should the company invest in this project?

Now suppose the company will invest in this project. If the company issues equity to fund the project, what would be the project's impact on:

- Earning per share?

- Number of shares?

- Share price?

- P/E ratio?

If the company issues debt to fund the project, what would be the project's impact on:

- Earning per share?

- Number of shares?

- Share price?

- P/E ratio?

- Cost of equity capital?

Assume the debt is risk-free,

Rf = 5%

Answer 1

Current Scenario at the company:

EBIT = $ 100 million and Company Value = $ 1000 million

As the company is entirely equity financed, it would have zero Interest Expense and zero Principal Repayment.Additionally, the problem statement does not mention any tax rate, working capital changes, depreciation and capital expenditure whatsoever.

Let the unlevered cost of equity be denoted by r(e)

Also, EBIT x (1 - Tax Rate) - Changes in Net Working Capital - Capital Expenditure + Depreciation = FCFF (Free Cash Flow to Firm)

As already mentioned all other terms other than the EBIT are missing from the problem statement and are hence assumed to be zero.

Therefore, E = (EBIT/FCFF) / r(e) = 100 / r(e)

1000 = 100 / r(e)

r(e) = 0.1 or 10%

The company decides to undertake a project with initial cost of $ 300 million and an annual perpetual cash flow of $ 40 million. Also, the company plans to issue common stock (equity) to finance this project and hence the project should have risk level equal to that of the entire firm(therefore the company's overall unlevered cost of equity should be used as the discounting factor).

Hence, Net Value Generate by the Project = PV of Perpetual Project Cash Flow - Project Cost

= (40 / r(e)) - 300

= (40/0.1) - 300

= 400 - 300

= $ 100 million

As the net value generated by this project is positive (to the tune of $ 100 million) , the company should take up this project.

Before, undertaking the project the company had 500 million outstanding shares and a total value of $1000 million.

Therefore, Price per Share = 1000 / 500 = $ 2 per share

Earnings per share = EBIT / N0 = 100 / 500 = $ 0.2 per share

PE Ratio = Price per share / Earnings per share = 2 / 0.2 = 10

Post issuance of fresh shares for financing the project, the corresponding numbers would change somewhat like given below:

Project Financing Required = $ 300 million

Price per Share = $ 2

Number of New Shares Issued = N(n) = 300 / 2 = 150 million

Number of Shares Outstanding after share issue = N0 + N(n) = 500 + 150 = 650 million

The Project generates a net value of $ 100 million for the company. New Company Value = E(n) = E+NPV(Project)

= 1000 + 100

= $ 1100 million

Therefore, New Price Per Share = 1100 / 650 = $ 1.6923 per share

Earnings Per Share = (100+40) / 650 = $0.21538 or approximately $ 0.2154 per share

New PE Ratio = 1.6923 / 0.2154 = 7.8565

As is visible the price per share drops , the EPS increases and the PE ratio goes down, upon new share issue to finance the project.

If the project is financed through raising a debt of $ 300 million, instead of raising fresh equity, then:

Number of Shares = 500 million

Earnings = 100 + 40 = $ 140 million

Earnings Per Share = 140 / 500 = $0.28 per share

New Capital Structure: Equity Value = E = $ 1000 million and Debt Value = D = $ 300 million

Cost of Debt =5% and Cost of Equity = 10%

Therefore, Cost of Capital = 10 x [E/(E+D)] + 5 x [D/(E+D)] = 10 x (1000/1300) + 5 x (300/1300) = 8.846%

New Share Price = Earnings Per Share / Cost of Capital = 0.28 / 0.08846 = $ 3.1652 per share

PE Ratio = 3.1652 / 0.28 = 11.3043

When the debt is raised the cost of equity capital would increase as the unlevered cost of equity (all equity financed cost) would now get levered owing to the debt component in the company's capital structure.