Question

Click here to read the eBook: Business and Financial Risk 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 $15 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: $4.2 million with a 0.2 probability, $3.5 million with a 0.5 probability, and $0.5 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. RÔE = % σ = % CV = Debt/Capital ratio is 10%, interest rate is 9%. RÔE = % σ = % CV = Debt/Capital ratio is 50%, interest rate is 11%. RÔE = % σ = % CV = Debt/Capital ratio is 60%, interest rate is 14%. RÔE = % σ = % CV =

		Grade it Now Save & Continue
		Continue without saving

Answer 1

Calculation of Return of Equity, Standard deviation and coefficient of variation under 4 different capital structures:

Total Capital = $15 millions

Return on Equity = Earnings after tax/Average Equity

Standard deviation = (ΣP(X_i - μ)²)^(1/2) , where X_i = return on each probability, μ = Average return

Coefficient of variation = Standard deviation/Average return*100

(i) Debt/Capital ratio is 0:

Equity = $15 millions, Debt = 0

Calculation of Earnings after tax:

EBIT($ in millions)	Earnings after interest & tax (EAT) ($ in millions)	Probability (P)	EAT*P	Xi - μ	(Xi - μ)2	P*(Xi - μ)2
4.2	=(4.2-0)*(1-0.4) = 2.52	0.2	0.504	0.876	0.767376	0.15348
3.5	=(3.5-0)*(1-0.4) = 2.10	0.5	1.05	0.456	0.207936	0.10397
0.5	=(0.5-0)*(1-0.4) = 0.30	0.3	0.09	-1.344	1.806336	0.5419
			1.644			0.79934

Earnings after tax= $1.644 million

(a) Return on Equity = ($1.644/$15) millions

= 10.96%

(b) Standard deviation = (0.79934)^1/2

= 0.89

(c) Coefficient of variation = 0.89/1.644*100

= 54.38%

(ii) Debt/Capital ratio is 10%:

Equity = $15 millions*90% = $13.5 millions, Debt = $15 millions*10% = $1.5 millions

Interest cost = $1.5 million * 9% = $0.135 million

Calculation of Earnings after tax:

EBIT ($ in millions)	Earnings after interest & tax (EAT) ($ in millions)	Probability (P)	EAT*P	Xi - μ	(Xi - μ)2	P*(Xi - μ)2
4.2	2.44	0.2	0.4878	0.876	0.767376	0.15348
3.5	2.02	0.5	1.0095	0.456	0.207936	0.10397
0.5	0.22	0.3	0.0657	-1.344	1.806336	0.5419
			1.563			0.79934

Earnings after tax= $1.563 million

(a) Return on Equity = ($1.563/$13.5) millions

= 11.58%

(b) Standard deviation = (0.79934)^1/2

= 0.89

(c) Coefficient of variation = 0.89/1.563*100

= 57.20%

(iii) Debt/Capital ratio is 50%:

Equity = $15 millions*50% = $7.5 millions, Debt = $15 millions*50% = $7.5 millions

Interest cost = $7.5 million * 11% = $0.825 million

Calculation of Earnings after tax:

EBIT ($ in millions)	Earnings after interest & tax (EAT) ($ in millions)	Probability (P)	EAT*P	Xi - μ	(Xi - μ)2	P*(Xi - μ)2
4.2	2.03	0.2	0.405	0.876	0.767376	0.15348
3.5	1.61	0.5	0.8025	0.456	0.207936	0.10397
0.5	-0.20	0.3	-0.0585	-1.344	1.806336	0.5419
			1.149			0.79934

(a) Return on Equity = ($1.149/$7.5) millions

= 15.32%

(b) Standard deviation = (0.79934)^1/2

= 0.89

(c) Coefficient of variation = 0.89/1.563*100

= 77.81%

(iv)Debt/Capital ratio is 60%:

Equity = $15 millions*40% = $6 millions, Debt = $15 millions*60% = $9 millions

Interest cost = $9 million * 14% = $1.26 million

Calculation of Earnings after tax:

EBIT ($ in millions)	Earnings after interest & tax (EAT) ($ in millions)	Probability (P)	EAT*P	Xi - μ	(Xi - μ)2	P*(Xi - μ)2
4.2	1.76	0.2	0.3528	0.876	0.767376	0.15348
3.5	1.34	0.5	0.672	0.456	0.207936	0.10397
0.5	-0.46	0.3	-0.1368	-1.344	1.806336	0.5419
			0.888			0.79934

(a) Return on Equity = ($0.888/$6) millions

= 14.8%

(b) Standard deviation = (0.79934)^1/2

= 0.89

(c) Coefficient of variation = 0.89/0.888*100

= 100.68%

Therefore, final answers are as follows:

Debt/Capital ratio is 0.

ROE= 10.96

σ = 0.89

CV = 54.38%

Debt/Capital ratio is 10%, interest rate is 9%.

ROE = 11.58%

σ = 0.89

CV = 57.20%

Debt/Capital ratio is 50%, interest rate is 11%.

ROE = 15.32%

σ = 0.89

CV = 77.81%

Debt/Capital ratio is 60%, interest rate is 14%.

ROE = 14.8%

σ = 0.89

CV = 100.68%