Earnings available to repurchase shares = $20,000,000 x 50% = $10,000,000 — Anthony and Sarah both invested the common two very similar companies fact

Anthony and Sarah both invested in the common shares of two very similar companies. In fact, the only difference was that Sarah’s stock of Northern Petroleum paid a regular dividend while Anthony’s stock of Southern Petroleum repurchased shares instead. On seeing her first (of many) dividend cheques, Sarah promptly declared to Anthony that the dividend meant her stock had superior returns. Based on the data below, show one year out whether Sarah is correct.

SOLUTION

Southern Petroleum:

The current share price is equal to the present value of all stock repurchases made, divided by the current number of shares. The present value of all stock repurchases made is the discounted value of a constant growing perpetuity, so we can use the same formula as that used to find the present value of a constant growing dividend stream.

Earnings available to repurchase shares = $20,000,000 x 50% = $10,000,000

In year 1 Southern’s earnings will be $20,000,000 x 1.06 = $21,200,000.

Cash used to repurchase shares = $21,200,000 x 0.50 = $10,600,000.

Share price in one year = $10.60 x 1.06 = $11.236.

Shares repurchased = $10,600,000/$11.236 =943,396.

Shares remaining = 25,000,000 – 943,396 = 24,056,604