###### The Equity Risk Premium

The equity risk premium (ERP) is the additional return (premium) required by investors... **Read More**

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.

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.

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.

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.

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

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.

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%.

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

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:

- €2.00.
- €2.14.
- €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.*