Effects of Repurchases on Earnings per Share

Share repurchase may increase, decrease, or have no effect on EPS depending on how the repurchase is financed.

$$\text{EPS}=\frac{\text{Net income (NI)}}{\text{Shares outstanding}}$$

If the net income is constant, a smaller number of shares after the buyback leads to a higher EPS. If the buyback is financed with borrowed funds, both net income and outstanding shares will be decreased. This results in a lower EPS.

Internal Financing

The post-repurchase EPS will be higher than the pre-repurchase EPS if the rate of return on retained earnings is less than the cost of capital.

External Financing (Borrowed funds)

If repurchase is made with borrowed funds, the EPS will:

• increase if the After-tax cost of debt < Earnings yield of the shares before the repurchase.
• decrease if the After-tax cost of debt > Earnings yield of the shares before the repurchase.
• remain unchanged if the After-tax cost of debt = Earnings yield of the shares before the repurchase.

Example 1: Share Repurchases using Idle Cash

Grino Ltd. has the following information:

• Outstanding shares worth $12 million.
• Net income of $150 million.
• Grino’s share price is $40
• Cash worth $200 million is invested in government treasury bills at a zero percent interest.
• Grino’s analysts estimate that the shares could be bought in the open market at $50.

Calculate the impact on EPS if Grino buys back the shares at $50 using idle cash.

Solution

$$\text{Current EPS}=\frac{$150\ \text{million}}{$12\ \text{million}}=$12.5$$

After a share repurchase at $50, the number of shares outstanding reduces by 4 million \(\frac{$200,000,000}{$50}\), and the new shares outstanding is \(12,000,000-4,000,000=8\ \text{million}\).

EPS after repurchasing shares is \(\frac{$150,000,000}{8,000,000 \text{ shares}}=$18.75/ \text{share}\).

EPS has increased by 50% because Grino used idle cash to repurchase the shares.

Example 2: Share Repurchases using Borrowed Funds

Jefferson Systems will borrow $16 million to finance a share repurchase. The following information is given:

• Earnings after-tax is $9 million.
• EPS before share repurchase is $3.
• Shares outstanding is 3 million.
• Planned share repurchase is 300,000 shares.

Calculate the EPS after the share buyback and after-tax cost of borrowing as 6%.

Solution

$$\begin{align*}\text{EPS after repurchasing}&=\frac{(\text{Earnings}-\text{After-tax cost of funds})}{\text{Shares outstanding after buyback}}\\ \\ &=\frac{[$9,000,000-($16,000,000\times0.06)]}{2,700,000 \text{ shares}}\\&=$2.98/ \text{share}\end{align*}$$

We can see that with an after-tax cost of debt of 6%, the EPS decreased from $3 to $2.98.

Question

A firm has 3 million outstanding shares and earnings of €6 million. It has €12 million in idle cash that it plans to use to repurchase shares in the open market. The firm’s current share price is €60. The firm is planning to use the entire €12 million to finance the purchase.

The firm’s EPS after the repurchase will be closest to:

1. €2.00.
2. €2.14.
3. €3.00.

Solution

The correct answer is B.

The company can repurchase 200,000 shares \(\bigg(\frac{€12,000,000}{€60}\bigg)\). After the repurchase, the number of outstanding shares would be 2.8 million shares (3,000,000 – 200,000 shares).

$$\text{EPS after repurchasing the shares}=\frac{€6,000,000}{2,800,000 \text{ shares}}=€2.14/ \text{share}$$

A is incorrect. This is the earnings before the share buyback.

$$\text{EPS before repurchasing the shares}=\frac{€6,000,000}{3,000,000 \text{ shares}}=€2/ \text{share}$$

Reading 18: Analysis of Dividends and Share Repurchases 

LOS 18 (i) Calculate and compare the effect of a share repurchase on earnings per share when 1) the repurchase is financed by the company’s surplus cash and 2) the company uses debt to finance the repurchase.