Treadless Tires Inc.is currently all equity financed.It used to be leveraged,but it recently issued 20,000 new shares at $25 per share.The proceeds from the new issue were used to repay all of its debt.Financial details for the current and old capital structures are presented in the table below.
Assume that Treadless generates perpetual annual EBIT at a constant level.Assume that all cash flows occur at the end of the year and we are currently at the beginning of a year.Assume that taxes are zero.Assume that all of net income is paid out as a dividend.Assume that the debt is perpetual with annual coupons at 4%.Assume that individual investors can borrow and lend at the same interest rate (and with the same terms)as corporations.
Ron Platt is a shareholder in Treadless who owns 5,000 shares.After the new issue,Ron is unhappy with his dividends.How many shares does Ron have to buy (or sell)in order to return his annual cash flows to the level he enjoyed when the company was leveraged?

Question

Quizplus · Accepted Answer

Under the levered capital structure the investor will receive annual cash flows of 5,000 × $3.5 = $17,500. To achieve this cash flow under the all-equity capital structure he will have to buy more shares through borrowing. Denote the number of shares owned originally as O. Denote the number owned after this trade as N. Denote the stock price at which the shares are purchased as P. The interest paid on the loan to buy more shares is: Interest paid = (N - O) × P × k_d If we subtract the interest paid from the dividends received after the trade, then we can solve for N. The annual cash flows from the investment are: Cash Flows = N × DPS - Interest Paid The first term is the value of dividends received at his new ownership level of N under the all equity capital structure ($2.50). We set this expression equal to $17,500 (the annual cash flows desired by the investor) and we solve for N. $17,500 = N × DPS - Interest Paid $17,500 = N × DPS - ((N - O) × P × k_d $17,500 = N × DPS + ((O× P × k_d) - (N × P × k_d)) N × DPS - (N × P × k_d) = $17,500 - (O × P × k_d) N × (DPS - P × k_d) = $17,500 - (O × P × k_d) N = 11ea7fdb_fc5f_9824_a768_bdc676ae8d13_TB2902_11 N = 11ea7fdb_fc5f_9825_a768_9df15ffe2fee_TB2902_11 = 8,333.33 Since N > O, this means that the investor buys 3,333.33 more shares.