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 $12 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: $5.6 million with a 0.2 probability, $2 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 =

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

в D E F G H I 1 1 Total Capital Debt to capital ratio Equity Debt Interest rate $12,000,000 0% $12,000,000 $0.00 0% State Probability EBIT Interest EBT $0.00 $5,600,000.00 $0.00 $2,000,000.00 $0.00 $500,000.00 0.5 $2,000,000.00 Tax(40%) $2,240,000.00 $800,000.00 $200,000.00 Net Income $3,360,000.00 $1,200,000.00 $300,000.00 ROE 0.2800 0.1000 0.0250 2 E(ROE) 11.35% 8.94% CV 0.79 2 Total Capital Debt to capital ratio Equity Debt Interest rate $12,000,000 10% $10,800,000 $1,200,000 9% 1 ability EBIT 0.2 $5,600,000.00 .50 $2,000,000.00 0.3 $500,000.00 interest EBT $108,000.00 $5,492,000.00 $108,000.00 $1,892,000.00 $108,000.00 $392,000.00 Tax(40%) $2,196,800.00 $756,800.00 $156,800.00 Net Income $3,295,200.00 $1,135,200.00 $235,200.00 ROE 0.3051 0.1051 0.0218 2 0 3 E(ROE) 12.01% 9.93% 0.83 3 Total Capital Debt to capital ratio Equity Debt Interest rate $12,000,000 50% $6,000,000 $6,000,000 11% State 1 Net Income $2,964,000.00 Probability EBIT | 0.2 $5,600,000.00 0.5 $2,000,000.00 0.3 $500,000.00 Interest EBT $660,000.00 $4,940,000.00 $660,000.00 $1,340,000.00 $660,000.00 $160,000.00 Tax(40%) $1,976,000.00 $536,000.00 $64,000.00 ROE 0.4940 0.1340 -0.0160 -$96,000.00 E(ROE) 16 16.10% 17.87% 1.11 CV 4 Total Capital Debt to capital ratio Equity Debt Interest rate $12,000,000 60% $4,800,000 $7,200,000 14% State 1 2 3 Probability EBIT interest EBT 0.2 $5,600,000.00 $1,008,000.00 $4,592,000.00 0.5 $2,000,000.00 $1,008,000.00 $992,000.00 0.31 $500,000.00 $1,008,000.00 - $508,000.00 Tax(40%) $1,836,800.00 $396,800.00 $203,200.00 Net Income $2,755,200.00 $595,200.00 $304,800.00 0 ROE 0.5740 .1240 -0.0635 E(ROE) 15.78% 22.34% 1.42

Cell reference -

LA B G H 2 1 Total Capital 12000000 3 Debt to capital ratio o 4 Equity =C2-C5 5 Debt =C2C3 Interest rate 10 8 Probability 2 State 0 0 1 2 11 5 10 . .5 10.3 EBIT Interest 600000 =C5*C6 2000000 =E9 500000 =E10 EBT Tax(40%) Net Income ROE =D9-E9 =F9*0.4 =F9-G9 =H9/04 =D10-E10 =F10*0.4 =F10-G10 =H10/04 -011-E11 =F11*0.4 =F11-611 =H11/04 13 13 E(ROE) lo CV =SUMPRODUCT(C9:C11,19:111) =SQRT(SUMPRODUCT(C13-19:111)^2,09:C11)) =C14/013 15 17 2 Total Capital 12000000 18 Debt to capital ratio 0.1 Equity =C17-C20 Debt =C17*C18 Interest rate 0.09 State 7 Probability 0.2 EBIT Interest EBT Tax(40%) Net Income ROE 5600000 -C20*021-D24-E24 -F24*0.4 |=F24-G24 -H24/C19 2000000 =E24 =D25-E25 =F25*0.4 =F25-G25 =H25/C19 500000 =E25 =D26-E26 =F26*0.4 =F26-G26 =H26/C19 2 0.5 0.3 E(ROI =SUMPRODUCT(C24:C26,124:126) =SQRT(SUMPRODUCT((C28-124:126)^2,c24:C26)) =C29/C28 Icy 33 32 3 Total Capital 12000000 Debt to capital ratio 0.5 34 Equity =C32-C35 35 Debt =C32°C33 Interest rate 0.11 State Probability 39 40 2 0.2 0.5 0.3 EBIT Interest EBT Tax(40%) Net Income ROE 5600000 =C35*C36 =D39-E39 =F39*0.4 |=F39-G39 =H39/C34 2000000 =E39 =D40-E40 =F40*0.4 =F40-G40 =H40/C34 500000 =E40 =D41-E41 =F41*0.4 =F41-G41 =H41/C34 E(ROE =SUMPRODUCT(C39:C41,139:141) =SQRT(SUMPRODUCT((C43-139:141)^2,C39:041)) =C44/C43 |cv 47 4 Total Capital 12000000 48 Debt to capital ratio 0.6 49 Equity =C47-C50 Debt =C47°C48 Interest rate 10.14 State U Probability 54 55 0.2 0.5 10.3 EBIT Interest EBT Tax(40%) Net Income ROE 5600000 =C50*051 =D54-E54 =F54*0.4 =F54-G54 =H54/C49 2000000 =E54 =D55-555 =F55*0.4 =F55-G55 =H55/C49 500000 =E55 =D56-E56 =F56*0.4 =F56-656 =H56/C49 56 S7 58 59 E(ROE) =SUMPRODUCT(C54:C56,154:156) =SQRT(SUMPRODUCT(C58-154:156)^2,C54:C56)) =C59/c58 609 CV

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