Question

FINANCIAL LEVERAGE EFFECTS The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $10 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $5.1 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $0.7 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations. Debt/Capital ratio is 0. ROE = CV = Debt/Capital ratio is 10%, interest rate is 9%. RÔE = CV = Debt/Capital ratio is 50%, interest rate is 11%. ROE = CV = Debt/Capital ratio is 60%, interest rate is 14%. RÔE =

Answer 1

a) ROE under Debt/capital ratio = 0 ie. 0 debt can be calculated as

	State 1	State 2	State 3
	prob =0.2	prob =0.5	prob =0.3
EBIT	5.1	2.8	0.7
less Interest	0	0	0
EBT	5.1	2.8	0.7
Less Tax	2.04	1.12	0.28
PAT	3.06	1.68	0.42
ROE	0.306	0.168	0.042

So, Expected ROE can be calculated as

Expected ROE=Pi * ROE

So, Expected ROE = 0.2*0.306+0.5*0.168+0.3*0.042

=.1578 = 15.78%

The Standard Deviation can be calculated as

  

ROE = Pi * (ROE; – ROE)2

= sqrt {0.2* (0.306-0.1578)² + 0.5* (0.168-0.1578)² + 0.3*(0.042-0.1578)² }

=0.092019 = 9.20%

CV = Standard Deviation / Mean = 0.092019/0.1578 = 0.58

b)   ROE under Debt/capital ratio = 10% ie. $1 million debt (@9%) and $9 million equity can be calculated as

	State 1	State 2	State 3
	prob =0.2	prob =0.5	prob =0.3
EBIT	5.1	2.8	0.7
less Interest	0.09	0.09	0.09
EBT	5.01	2.71	0.61
Less Tax	2.004	1.084	0.244
PAT	3.006	1.626	0.366
ROE	0.334	0.180667	0.040667

So, Expected ROE can be calculated as

Expected ROE=Pi * ROE

So, Expected ROE = 0.2*0.334+0.5*0.180667+0.3*0.040667

=0.16933 = 16.93%

The Standard Deviation can be calculated as

  

ROE = Pi * (ROE; – ROE)2

= sqrt {0.2* (0.334-0.1693)² + 0.5* (0.18067-0.1693)² + 0.3*(0.40667-0.1693)² }

=0.102244 = 10.22%

CV = Standard Deviation / Mean = 0.102244/0.1693 = 0.60

c)    ROE under Debt/capital ratio = 50% ie. $5 million debt (@11%) and $5 million equity can be calculated as

	State 1	State 2	State 3
	prob =0.2	prob =0.5	prob =0.3
EBIT	5.1	2.8	0.7
less Interest	0.55	0.55	0.55
EBT	4.55	2.25	0.15
Less Tax	1.82	0.9	0.06
PAT	2.73	1.35	0.09
ROE	0.546	0.27	0.018

So, Expected ROE can be calculated as

Expected ROE=Pi * ROE

So, Expected ROE = 0.2*0.546+0.5*0.27+0.3* 0.018

=0.2496 = 24.96%

The Standard Deviation can be calculated as

  

ROE = Pi * (ROE; – ROE)2

= sqrt {0.2* (0.546-0.2496)² + 0.5* (0.27-0.2496)² + 0.3*(0.018-0.2496)² }

=0.1840 = 18.40%

CV = Standard Deviation / Mean = 0.1840/0.2496 = 0.74

d) ROE under Debt/capital ratio = 60% ie. $6 million debt (@14%) and $4 million equity can be calculated as

	State 1	State 2	State 3
	prob =0.2	prob =0.5	prob =0.3
EBIT	5.1	2.8	0.7
less Interest	0.84	0.84	0.84
EBT	4.26	1.96	-0.14
Less Tax	1.704	0.784	-0.056
PAT	2.556	1.176	-0.084
ROE	0.639	0.294	-0.021

So, Expected ROE can be calculated as

Expected ROE=Pi * ROE

So, Expected ROE = 0.2*0.639+0.5*0.294+0.3* (-0.021)

=0.2685 = 26.85%

The Standard Deviation can be calculated as

  

ROE = Pi * (ROE; – ROE)2

= sqrt {0.2* (0.639-0.2685)² + 0.5* (0.294-0.2685)² + 0.3*(-0.021-0.2685)² }

=0.2300 = 23.00%

CV = Standard Deviation / Mean = 0.2300/0.2685 = 0.86