Question

Drakes Inc wishes to maintain a growth rate of 11 percent per year and a debt-equity ratio of .2. Profit margin is 5.9 percent and the ratio of total assets to sales is constant at 1.56.

  

What dividend payout ratio is necessary to achieve this growth rate under these constraints? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

What is the maximum growth rate possible? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Solution:
a.	Dividend payout ratio	-118.35%
Working Notes:
	To get payout ratio , we have first get ROE
	Using the DuPont identity to calculate ROE
	ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
	Then retention ratio using sustainable growth rate formula using above ROE and at last we get our Dividend payout ratio
	Using the DuPont identity to calculate ROE
	ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
	Profit margin = 5.9%
	Total asset turnover = Sales / Total assets
	Given
	total assets /sales =1.56
	So
	Sales/ total assets = 1/1.56
	Equity multiplier = 1+ debt-equity ratio = 1.20
Hence	ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
	ROE = (5.9%)(1/1.56)(1+.20)
	ROE = 0.045384615
Now	Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
	11% = (0.045384615 x b)/(1- (0.045384615 x b))
	0.11 -0.004992308 b = 0.045384615 b
	b = 0.11 /(0.045384615 + 0.004992308)
	b = 2.183539475
	b= retention ratio which can be maximum 1 , as per computation we get 2.183539 , means the growth rate is not sustainable.
At last	Dividend Payout ratio = 1 – b
	Dividend Payout ratio = 1 – 2.183539475
	Dividend Payout ratio = -1.183539475
	Dividend Payout ratio = -1.183539475 x 100	multiplying by 100 to get it in percentage terms
	Dividend Payout ratio =-118.35%
b.	Maximum growth rate possible	4.75%
Working Notes:
	As per our computation is a. Dividend payout ratio is negative 1.18 which is the possible, lowest dividend payout ratio can be ZERO, means 100% retention ratio or 1 . And maximum growth rate possible at 1 retention ratio
	so we will take 1 as retention ratio not 2.183539475 as it could not be possible
	Maximum sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
	Maximum sustainable growth rate = (ROE × b) / (1 – (ROE × b))
	Maximum sustainable growth rate = (0.045384615 x 1) / (1- (0.045384615 x 1))
	Maximum sustainable growth rate = 0.0475423
	Maximum sustainable growth rate = 4.75423%
	Maximum sustainable growth rate = 4.75%
Please feel free to ask if anything about above solution in comment section of the question.