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# 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 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 16: Analysis of Dividends and Share Repurchases

LOS 16 (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

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