Question

A firm has Sh. 4 million of 7.5 % interest rate debt. Its expected EBIT is Sh. 0.9 million and its
cost of equity is 10 %. All assumptions of the Net Income theory apply.
Required:
a) Calculate the value of the firm using the Net Income approach
b) Calculate the cost of capital for the firm the Net Income approach
c) Estimate the value of the firm and the cost of capital if the amount of debt is changed to ;
(i) Sh. 5 million
(ii) Sh. 3 Million
(iii)Sh. 12 Million

Answer 1

Market value of debt = 4 million

Interest rate on debt = 7.5%

EBIT = 900,000

Cost of equity = 10%

We can calculate the value of the firm using the following approach,

EBIT = 900,000

Less interest on debt(7.5% of 4 million) = -300,000

Net income (EBIT - interest)   = 600,000

The market value of equity = net income/cost of equity

= 600,000 / 0.10

= 6,000,000

a)

The total value of the firm = Market value of equity + Market value of debt

  = 6,000,000 + 4,000,000

= Sh. 10,000,000

b)

Cost of capital of the firm = EBIT / Total value of the firm

= 900,000 / 10,000,000

= 9%

c)

i) if debt is now 5 million

EBIT = 900,000

Less interest on debt(7.5% of 5 million) = -375,000

Net income (EBIT - interest)   = 525,000

The market value of equity = net income/cost of equity

= 525,000 / 0.10

= 5,250,000

The total value of the firm = Market value of equity + Market value of debt

  = 5,250,,000 + 4,000,000

= Sh. 9,250,000

Cost of capital of the firm = EBIT / Total value of the firm

= 900,000 / 9,250,000

= 9.72%

ii) if debt is now 3 million

EBIT = 900,000

Less interest on debt(7.5% of 3 million) = -225,000

Net income (EBIT - interest)   = 675,000

The market value of equity = net income/cost of equity

= 675,000 / 0.10

= 6,750,000

The total value of the firm = Market value of equity + Market value of debt

  = 6,750,,000 + 4,000,000

= Sh. 10,750,000

Cost of capital of the firm = EBIT / Total value of the firm

= 900,000 / 10,750,000

= 8.37%

iii) if debt is now 5 million

EBIT = 900,000

Less interest on debt(7.5% of 12 million) = 900,000

Net income (EBIT - interest) = 0

The market value of equity = net income/cost of equity

= 0 / 0.10

= 0

The total value of the firm = Market value of equity + Market value of debt

  = 0+ 4,000,000

= Sh. 4,000,000

Cost of capital of the firm = EBIT / Total value of the firm

= 900,000 / 4,000,000

= 22.5%

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