Question

c) A firm has the following capital structure: 100 million shares outstanding, trading at £1.5 per share, and £100 million of debt. The beta of the firm’s stock is 1.5. The firm’s cost of equity is 10 percent, and the yield on riskless bonds is 2.5 percent. There is no tax. Assuming that the firm can borrow at the risk free rate and that both CAPM (Capital Asset Pricing Model) and the Modigliani-Miller theorem hold, answer the following questions.

iv) Suppose the firm changes its capital structure so that its debt increases to £150 million, and the equity decreases by £50 million. What should be the firm’s cost of equity after the change?

*Different question*

c) A firm has the following capital structure: £100 million of equity (market value) with 100 million shares outstanding, and £100 million of debt. The beta of the firm’s stock is 1.6. The firm’s cost of equity is 10 percent, and the yield on riskless bonds is 2 percent. There is no tax. Assuming that the firm can borrow at the risk free rate and that both CAPM (Capital Asset Pricing Model) and the Modigliani-Miller theorem hold, answer the following questions

iv) Suppose the firm changes its capital structure so that its debt increases to £140 million, and the equity decreases to £60 million. What should be the firm’s cost of equity after the change?

Answer 1

Part 1:

Given,

Number of shares= 100 Million.   Current price per share= £ 1.5.

Therefore, market value of equity (E) = £ 1.5*100 Million= £ 150 Million

Amount of debt (D) = £ 100 Million.

Therefore, value of the firm (V) = E + D= £ 150 Million + £ 100 Million = £ 250 Million

Cost of equity (R_e) = 10%, cost of borrowing (R_d) (stated as risk free rate)= 2.5%. Tax rate= Nil

Weighted Average Cost of Capital (WACC) = (E/V)*R_e + (D/V)*R_d

=(150/250)*10% + (100/250)*2.5%   = 0.6*10% + 0.4*2.5% = 7%

Upon increase in debt to £150 Million and decrease in equity by £50 Million,

Revised equity (E)= £ 150 Million- £ 50 Million= £ 100 Million

Revised Debt (D) = £150 Million. Retaining WACC at 7%, Let revised cost of equity be Re%

7%= (100/250)*R_e1% + (150/100)*2.5% .   0.07= 0.4*R_e1 + 0.6*0.025

Revised Cost of equity R_e1 = 0.07-(0.6*0.025)/0.4 = 13.75%

Part 2:

Given,

Market value of equity (E) = £ 100 Million

Amount of debt (D) = £ 100 Million.

Therefore, value of the firm (V) = E + D= £ 100 Million + £ 100 Million = £ 200 Million

Cost of equity (R_e) = 10%, cost of borrowing (R_d) (stated as risk free rate)= 2%. Tax rate= Nil

Weighted Average Cost of Capital (WACC) = (E/V)*R_e + (D/V)*R_d

=(100/200)*10% + (100/200)*2.5%   = 0.5*10% + 0.5*2% = 6%

Upon increase in debt to £140 Million and decrease in equity to £60 Million,

Retaining WACC at 6%, Let revised cost of equity be R_e2%

6%= (60/200)*R_e2% + (140/200)*2% .   0.06= 0.3*R_e2 + 0.7*0.02

Cost of equity after change R_e2 = 0.06-(0.7*0.02)/0.3 = 15.3333%