Question

CHOCO is a new firm that has raised £150,000 (book value) by selling ordinary shares. Management plans to earn 20% rate of return on equity (ROE), which is more than the 15% rate of return in comparable risk investments. 50% of all the earnings will be re- invested in the firm.

a) What will be the value of dividends and the growth rate for CHOCO?

b) What will be CHOCO ratio of market value to book value?

c) How would the MV/BV ratio change if CHOCO can earn only 10% rate of return on its investments. Explain your results.

Answer 1

	Book value of equity		150000
	ROE		20%
	ROE = net income/book value of equity	20% = net income/150000	net income = 150000*20% = 30000
1-	dividend payment = 50% of net income	30000*50%	15000
1-	growth rate = retention ratio*ROE	50%*20%	10.0%
	expected dividend = current dividend*(1+growth rate)	15000*(1.10)	16500
	Market value = expected dividend/(required rate of return on equity-growth rate)	16500/(15%-10%)	330000
2-	market value to book value ratio = market value/book value	330000/150000	2.2
	Book value of equity		150000
	ROE		10%
	ROE = net income/book value of equity	10% = net income/150000	net income = 150000*10% = 15000
	dividend payment = 50% of net income	15000*50%	7500
	growth rate = retention ratio*ROE	50%*10%	5.00%
	expected dividend = current dividend*(1+growth rate)	7500*(1.05)	7875
	Market value = expected dividend/(required rate of return on equity-growth rate)	7875/(15%-5%)	78750
3-	market value to book value ratio = market value/book value	78750/150000	0.525
	Market value to book value ratio will decrease as due to lower growth rate and ROE less than required rate of return market value of the firm will decline as ROE < required rate of return (10%<15%) so investors will withdraw their funds from the company as a result value of value of firm will decrease