Question

• AWC does not grow; it generates a constant annual cash flow of $100m per year forever

• AWC holds $250m in cash and has no debt (it is an all-equity financed firm)

• AWC has 100 million of shares outstanding and its shareholders expect a return of 10% on their investment

• The value of AMC non-cash assets is thus the present value of a no-growth perpetuity of $100m at 10%1:

V(non-cash assets) = $100/10% = $1,000

• The value of all AWC assets = Cash holding + V(non-cash assets) = $250m + $1,000m = $1,250m

• The value of AWC equity = The value of all its assets (because AMC has no debt) = $1,250m

• AWC share price (P) is thus:

P = Value of equity/Number of shares = $1, 250m/ 100m = $12.50  

Recommendation No.1: AWC uses its cash to pay an immediate dividend of $250 million

• Immediate dividend per share = DPS0 = Total dividend payment /Number of shares = $250m/100m = $2.50  

• AWC does not grow and pays out all its future annual perpetual cash flow of $100m in dividend

• AWC perpetual annual dividend per share starting at the end of the first year: DPS = $100m/$100m = $1

• AWC ex-dividend share price after the immediate dividend payment is thus:1

100m Pex = PV(perpetual dPS of $1 at 10%) = $1/10% = $10

• Shareholder wealth per share (WS) after the immediate dividend payment is thus: WS = dPS0 + Pex = $2.50 + $10 = $12.50

Recommendation No.2: AWC repurchases $250 million of its shares in the open market at $12.50

• Number of shares repurchased = $250m/$12.50 = 20m  

• Number of shares outstanding after the repurchase = 100m – 20m = 80m

• Dividend per share after the repurchase (starting at the end of the first year): DPS = 100m/80m = $1.25

• AWC share price after the repurchase is thus:

Prep = PV(perpetual dPS of $1.25 at 10%) = $1.25/10% = $12.50

Recommendation No.3: AWC issues 100 million in equity and pays an immediate dividend of 350 million

• Number of new shares issued = $100m/ $12.50 =8m

• Total number of shares after the share issuance = 100m + 8m = 108m

• Immediate dividend per share after the share issuance: DPS0 = $350m /108m= $3.24

• Perpetual future dividend per share after the share issuance: DPS = $100m/108 m = $0.926

• AWC ex-dividend share price after the repurchase is thus:

Pex = PV(perpetual dPS of $0.926 at 10%) = $0.926/10% = $9.26

• Shareholder wealth per share (WS) after the immediate dividend payment is thus: WS = dPSo + Pex = $3.24 + $9.26 = $12.50?

Suppose the board of AWC decides to invest the $250 million of cash in 1-year government bills yielding 4 percent and use the proceeds from the sale of the bills to pay a higher dividend next year.

a. What would be AWC share price in this case?

b. Compare the share price with the deferred dividend to the share price when the $250 million is immediately paid out in dividends. What can you conclude?

Answer 1

Soln : a) Here, the AWC invest 250 million of cash in 1 year government bills yield 4%

So, net gain after 1 year = 250*1.04 = $260 mn

Now, that is paid as dividend next year, So, the share price = (260/100)/1.1 + 1/10% = $12.36

Dividend paid per share in the next year = 260m/100m = 2.6

(b) So, as we see here, if the dividend paid next year the price is reduced to $12.36 compare to the price of 12.50, when dividend paid immediately. We can conclude that it is better to provde dividend immediately rather than investing in treasury bills for better valuation of share price. As the yield of treasury bills are low, due to which the price has come down in case of deferred.