Question

AMC Corporation currently has an enterprise value of $400 million and $100 million in excess cash. The firm has 10 million shares outstanding and no debt. Suppose AMC uses its excess cash to repurchase shares. After the share repurchase, news will come out that will change AMC’s enterprise value to either $600 million or $200 million.

1. What is AMC’s share price prior to the share repurchase?

2. What is AMC’s share price after the repurchase if its enterprise value goes up? What is AMC’s share price after the repurchase if its enterprise value declines?

3. Suppose AMC waits until after the news comes out to do the share repurchase. What is AMC’s share price after the repurchase if its enterprise value goes up? What is AMC’s share price after the repurchase if its enterprise value declines?

4. Suppose AMC management expects good news to come out. Based on your answers to parts b and c, if management desires to maximize AMC’s ultimate share price, will they undertake the repurchase before or after the news comes out? When would management undertake the repurchase if they expect bad news to come out?

5. Given your answer to part d, what effect would you expect an announcement of a share repurchase to have on the stock price? Why?

Answer 1

Equity value = Enterprise value - Debt + Cash

Part (1)

All financials are in $ mn, nos. of shares in mn and share price in $ / share.

Equity value before repurchase, E₀ = 400 - 0 + 100 = 500

Number of shares outstanding before repurchase, N₀ = 10

Hence, price per share before repurchase, P₀ = E₀ / N₀ = 500 / 10 = $ 50 per share

Part (2)

Numbers of shares repurchased, n = Surplus cash / P₀ = 100 / 50 = 2 mn

Numbers of shares outstanding after repurchase, N₁ = N₀ - n = 10 - 2 = 8

if its enterprise value goes up

Equity value after repurchase, E_1up = Enterprise value_1up - Debt + Cash_1up = 600 - 0 + 0 = 600

Hence, share price, P_1up = E_1up / N₁ = 600 / 8 = $ 75 / share

if its enterprise value goes down

Equity value after repurchase, E_1down = Enterprise value_1down - Debt + Cash_1down = 200 - 0 + 0 = 200

Hence, share price, P_1down = E_1down / N₁ = 200 / 8 = $ 25 / share

Part (3)

if its enterprise value goes up

E_1up = Enterprise value_1up - Debt + Cash = 600 - 0 + 100 = 700

Hence, share price, P_1up = E_1up / N₀ = 700 / 10 = $ 70 / share

Since, repurchase will take place at this price, the share price after repurchase will remain same as this level i.e. $ 70 / share

if its enterprise value goes down

E_1down = Enterprise value_1down - Debt + Cash = 200 - 0 + 100 = 300

Hence, share price, P_1down = E_1down / N₀ = 300 / 10 = $ 30 / share

Since, repurchase will take place at this price, the share price after repurchase will remain same as this level i.e. $ 30 / share

Part (4)

if its enterprise value goes up

P_1up = 75 if share repurchase takes place prior to good news

P_1up = 70 if share repurchase takes place prior to good news

Since, the objective is to maximize share price, the management should undertake repurchase prior to good news come out.

if its enterprise value goes down

P_1down = 25 if share repurchase takes place prior to good news

P_1down = 30 if share repurchase takes place prior to good news

Since, the objective is to maximize share price, the management should undertake repurchase after to good news come out.

Part (5)

Announcement of share repurchase should not mathematically impact the share price. Share price declines due to reduction in cash balance but the same is offset by increase in price due to the reduction in number of shares. Hence, mathematically share repurchase or its announcement should not impact the share price.

However, practically an announcement of share repurchase can alter the stock price in either way. There had been instances where announcement of share buybacks have improved the prices and there had been instances where such announcement has led to decline. Based on this question, we can see that a share repurchase announcement can impact the share prices either way.