Question

I am working on these study questions and am having trouble understanding how it all works together. Any help would be greatly appreciated!!

An all equity firm is expected to generate perpetual EBIT of $50 million per year forever. The corporate tax rate is 0% in a fantasy no tax world. The firm has an unlevered (asset or EV) Beta of 1.0. The risk-free rate is 5% and the market risk premium is 6%. The number of outstanding shares is 10 million.

1. Calculate the existing WACC of this all equity or unlevered firm. Calculate the total value of

this all equity firm and the existing share price.

2. The firm decides to replace part of the equity financing with perpetual debt. The firm issues

$100 million of permanent debt at the riskless interest rate of 5%, and repurchases $100 million of equity.

A. Find the new value of the levered firm.
B. Find the new number of shares outstanding, and the new share price.

3. Calculate the new equity Beta, new cost of equity, and new WACC following this capital

structure change. Assume a debt beta of zero.

Answer 1

(1) As the firm is all equity financed or unlevered, the firm's WACC will equal its unlevered cost of capital which in turn will equal its unlevered cost of equity (as the only component of the capital structure is equity)

Asset Beta = 1, Risk-Free Rate = 5%, Market Risk Premium = 6%

Therefore, Unlevered Cost of Equity = Rf + Unlevered beta x Market Risk Premium = 5 + 1 x 6 = 11%

Perpetual EBIT = $ 50 million and Number of Shares Outstanding = N = 10 million

Total Value of All Equity Firm = Perpetual EBIT / Unlevered Cost of Equity = 50 / 0.1 = $ 500 million

Price per Share = 500 / 10 = $ 50

(2) The firm decides to issue debt worth $ 100 million and repurchase common stock worth $ 100 million with the debt proceeds. The debt is raised at the risk-free rate of 5%

As the firm exists in a world of 0% taxes, the levering of the firm lead to no addition to firm value owing to the benefits of interest tax shields. In a 0% ideal world, by Modigliani-Miller theorem 1, the firm's value will entirely be determined by its earnings power. Now, as the firm's earnings power remains constant irrespective of its capital structure, the values of the levered and unlevered firm will be equal.

Therefore, Value of levered firm = $ 500 million

Common Stock Repurchased = $ 100 million and Price per Share = $ 50

Therefore, Number of Shares Repurchased = 100 / 50 = 2 million

Number of Shares Outstanding = 10 - 2 = 8 million

(3) Asset Beta = 1, New Debt to Equity Ratio = DE = (100/400) = 0.25 (assuming firm value is constant at $ 500 million), Risk_Free Rate = Rf = 5 % and market risk premium = 6%

Therefore, New Equity Beta = Asset beta x [1+(1-Tax Rate) x DE] = 1 x [1+(1-0) x (0.25)] = 1.25

New Cost of Equity = 5 + 1.25 x 6 = 12.5 %

New WACC = 12.5 x (400/500) + (1-0) x 5 x (100/500) = 11%