Question

A company has equity with market value $100 million and debt with market value at $70 million. The debt pays perpetual expected coupons of $3.5 million annually.

The numbers above are prior to a stock buyback being announced.

The company uses some of its cash buyback stock on of $20 million. As a result of the fall in its cash, the expected coupon payment to debt reduce to $3.4 million (expected payments is the probability-weighted future coupons and the probability that in some future states of the world the firm would default has increased due to the stock buyback). Also the rate of discount Rd for expected coupons paid to debt rises to 5.25%.

Assume Modigliani Miller is true (which also means there are no taxes).

What will be the value of equity after the stock buyback? (Do not include the $20 million that is paid to the equity holder.)

Write the answer in millions rounded to the nearest whole number.

Answer 1

According to Modigliani Miller, the total value of the firm remains the same before and after the stock buyback, and is equal to the sum of the market value of equity and debt. Therefore:

Total value of the firm = Market value of equity + Market value of debt

Before the stock buyback:
Total value of the firm = $100 million + $70 million = $170 million

After the stock buyback:
Total value of the firm = Market value of equity after the buyback + Market value of debt

Let's denote the market value of equity after the buyback as E. We know that $20 million was used to buyback stock, so:

Market value of equity after the buyback = Market value of equity before the buyback - $20 million

We also know that the expected coupon payment to debt has reduced to $3.4 million and the rate of discount has increased to 5.25%. Using the perpetuity formula, we can calculate the market value of debt after the stock buyback:

Market value of debt = Expected coupon payment to debt / Rd = $3.4 million / 0.0525 = $64.76 million

Plugging this into the equation for total value of the firm:

$170 million = E - $20 million + $64.76 million

Solving for E:

E = $125.24 million

Rounding to the nearest whole number, the value of equity after the stock buyback is $125 million.