Question

You are managing an all-equity firm that has 1 million shares outstanding in year 0. The firm has fixed assets with value A, which is constant over time. As the manager, you know the value of A but investors only learn it in year 3; as a result, the market price of shares in year 3 will reflect the value of A.In addition to the fixed assets firm has 1million pound of excess cash at year 0 deposited in a non interest bearing bank account and opportunity to invest 11.5 million pounds in year-2 in a project that

subsequently yields £11.9 million in year 3. Therefore, in order to invest in the project, the firm needs to raise additional funds of £10.5 million.

Your objective is to maximize the firm’s share price in year 3.

a. Assume that you can raise £10.5 million by issuing new shares at a price of £8.11 per share before making the potential investment in year 2. If the value of the firm’s fixed assets is A = £12 million, would you issue shares and invest in the project or not? What if A = £6 million?

b. Now assume that an investment banker informs you that you could use the £1 million of excess cash to repurchase shares at a price of £11.55 per share in year 1, and then raise the full £11.5 million needed to invest in the project by issuing new shares at a price of £8 per share in year 2. If the value of the firm’s existing assets A = £12 million, which of the following alternatives would you choose: (i) repurchase shares in year 1 and then do nothing in year 2, (ii) repurchase shares in year 1 and then issue new shares and invest in the project in year 2, (iii) do nothing in both years. How would your answers change if A = £6 million? What if A = £9 million?

Answer 1

a) If the value of assets is 12 million pounds, the 1 million shares must have a value of 12 pounds each. Hence , raising new capital by issuing shares at 8.11 pounds will not be beneficial as it will lower the value of the company at the end of year 3 when the asset value is known to investors

No. of shares issued = 10.5 milliom/8.11 =1294698 shares.

Value of firm after 3 years = 12 million + 11.9 million =23.9 million pounds with 2,294,698 shares

Value per share = 23,900,000/2294698 = 10.42 pounds per share

If shares are not issued, value of company after 3 years = 12 million + 1 million cash = 13 million and no of shares =1 million

Value per share = 13 million /1 million = 13 pounds per share

However, if the Asset value is 6 million pounds, each share is worth 6 pounds. Hence, raising new capital by issuing shares at  8.11 pounds per share is good

In this case ,

Value of firm after 3 years = 6 million + 11.9 million =17.9 million pounds with 2,294,698 shares

Value per share = 17,900,000/2294698 = 7.80 pounds per share

If shares are not issued, value of company after 3 years = 6 million + 1 million cash = 7 million and no of shares =1 million

Value per share = 7 million /1 million = 7 pounds per share

So, one should not issue shares if A =12 million pounds but should issue shares if A = 6 million pounds

b) If A= 12 million

i) If shares are repurchased at 11.55 pounds per share,

No. of shares repurchased = 1000000/11.55= 86580

If nothing is done in year 2 then

Value of one share at end of year 3 = 12 million/(1 million - 86580) = 13.14 pounds per share

ii) Now if New Shares are issued, No of new shares issued = 11,500,000/8 = 1437500

Total no of shares = 1000000-86580+1437500 = 2350920

So, value of one share at the end of year 3= (12million+11.9 million)/2350920 = 10.17 pounds per share

iii)

If nothing is done in both years, value of share at end of 3 years= (12 million+1 million)/1 million = 13 pounds per share

So, one should choose option (i) repurchase shares in year 1 and then do nothing in year 2

If A= 6 million

i) If shares are repurchased at 11.55 pounds per share,

No. of shares repurchased = 1000000/11.55= 86580

If nothing is done in year 2 then

Value of one share at end of year 3 = 6 million/(1 million - 86580) = 6.57 pounds per share

ii) Now if New Shares are issued, No of new shares issued = 11,500,000/8 = 1437500

Total no of shares = 1000000-86580+1437500 = 2350920

So, value of one share at the end of year 3= (6million+11.9 million)/2350920 = 7.61 pounds per share

iii)

If nothing is done in both years, value of share at end of 3 years= (6 million+1 million)/1 million = 7 pounds per share

So, one should choose option (ii) repurchase shares in year 1 and then issue new shares and invest in the project in year 2

If A= 9 million

i) If shares are repurchased at 11.55 pounds per share,

No. of shares repurchased = 1000000/11.55= 86580

If nothing is done in year 2 then

Value of one share at end of year 3 = 9 million/(1 million - 86580) = 9.85 pounds per share

ii) Now if New Shares are issued, No of new shares issued = 11,500,000/8 = 1437500

Total no of shares = 1000000-86580+1437500 = 2350920

So, value of one share at the end of year 3= (9million+11.9 million)/2350920 = 8.89 pounds per share

iii)

If nothing is done in both years, value of share at end of 3 years= (9 million+1 million)/1 million = 10 pounds per share

So, one should choose option (iii) do nothing in both years