Question

Bingo, Bango, Bongo

Consider three firms, Bingo, Bango, and Bongo. All three firms just paid out a dividend

of $1. Bingo’s dividend growth rate is expected to be 6% forever, Bango’s growth is 0%

and is expected to stay that way, and Bongo’s dividends are expected to stay at $1 per

year for the next 5 years and then begin growing at a rate of 10% thereafter. The required

rate of return for each firm is 12%. There are no commission charges on any transactions

pertaining to these three firms.

1. At what price will each firms shares sell today (t=0), next year (t=1), and the year

after that (t=2)?

2. Which of the following investment strategies would maximize an investor’s

wealth 10 years from now if there are no personal or corporate income taxes?

Strategy A

Buy Bingo stock with all your wealth, reinvest your dividends in Bingo

stock and at the end of year 10 sell all shares

Strategy B

Buy Bango stock with all your wealth, reinvest your dividends in Bango

shares, and at the end of year 10 sell all your shares.

Strategy C

Buy Bingo stock with all your wealth; reinvest your dividends in Bingo

stock. However, after five years, sell all of your shares of Bingo stock,

and buy Bongo stock. Reinvest the dividends you receive from Bongo

stock in additional Bongo shares. At the end of year 10 sell all your

shares.

Answer 1

1)	BINGO:
	Price at t0 = 1*1.06/(0.12-0.06) =	$          17.67
	Price at t1 = 1*1.06^2/(0.12-0.06) =	$          18.73
	Price at t2 = 1*1.06^3/(0.12-0.06) =	$          19.85
	BANGO:
	Price at t0, t1 and t2 = 1/0.12 =	$             8.33
	BONGO:
	Price at t0 = 1*(1.12^5-1)/(0.12*1.12^5) + (1*1.10/(0.12-0.10))/1.12^5 =	$          34.81
	Price at t1= 1*(1.12^4-1)/(0.12*1.12^4) + (1*1.10/(0.12-0.10))/1.12^4 =	$          37.99
	Price at t2 = 1*(1.12^3-1)/(0.12*1.12^3) + (1*1.10/(0.12-0.10))/1.12^3 =	$          41.55
2)	Strategy C.
	As it seeks to invest in shares having higher growth rate during the period of
	investment which, is 10 years, thereby maximizing total wealth.
	Bing has 6% growth rate for 5 years, while the other two have 0 growth rate.
	From years 6 to 10, Bongo has maximum growth rate.