Question

Suppose that you’re comparing two companies in the same industry that are the same in every way except their profitability.

Company A    Company B

Shareholder’s Equity              $100m                                  $100m

Invested Capital                       $100m                                  $100m

Return On Equity                           12%                                 4%

Cost of Equity                                  8%                                 8%

1. Begin with a simple comparison:

Value each of these companies assuming that the ROEs provided above are sustainable,
and that both companies have a sustainable growth rate = 0%.

1. What is the value of Company A using these assumptions?

2. What is the value of Company B using these assumptions?

3. Explain why one of these companies appears to be so much more valuable than the others.

2. Now explore how each of these companies would be affected by growth:

Value each of these companies assuming that the ROEs provided above are sustainable,
and that both companies have a sustainable growth rate = 5%.

1. What is the value of Company A using these assumptions?

2. What is the value of Company B using these assumptions?

3. What does this tell us about which of these companies should be reinvesting its
   cash flow in order to grow?
   

Answer 1

Value of business using Cost of equity and Return

Value = Return/ ( Cost of equity- growth rate)

1

a

Return = Invested Capital * Return%

i.e ($100m*12%)

i.e $12m

Cost of equity = 0.08 (8%)

Growth - 0

Value of Company A = ($12m )/(0.08-0) = $12m/0.08 = $150m

b

Return = $100m*4% = $4m

Cost of equity = 0.08 (8%)

Growth - 0

Value of Company A = ($4m )/(0.08-0) = $4m/0.08 = $50m

c

Value of Company A is more because Company A is taking funds @8% and giving return @12% which is a gain of 4%

Whereas company B is taking funds @8% but giving return of only 4$ which is a loss of 4% , so value is reduced

2

a

Return = Invested Capital * Return%

i.e ($100m*12%)

i.e $12m

Cost of equity = 0.08 (8%)

Growth - 0.05 (5%)

Value of Company A = ($12m )/(0.08-0.05) = $12m/0.03 = $400m

b

Return = $100m*4% = $4m

Cost of equity = 0.08 (8%)

Growth - 0.05 (5%)

Value of Company A = ($4m )/(0.08-0.05) = $4m/0.03 = $133.33m

c

Growth is increasing the value of company A , so Company A is reinvesting its cashflows. Company B has less return than cost, so it cannot reinvest its cashflow