Stock \'b\": a stock that is constant growth whose last dividend (paid yesterday

Question

Stock 'b": a stock that is constant growth whose last dividend (paid yesterday) was $1.50 and whose dividend is expected to grow indefinitely at 4%:

a. Same stock as in “b” above, but the earnings and dividends are expected to decline by a constant 6% per year. Why might someone consider buying this stock, and at what price would it sell?

   b. Assume that the company in “b” above decides to embark on an aggressive expansion that requires additional capital. Management decides to finance the expansion by borrowing $40 million and by halting dividend payments to increase retained earnings. The projected free cash flows for the next 3 years are -$5 million (negative), $10 million and $20 million. After the third year, free cash flow is expected to grow at a constant 6%. The overall cost of capital is 10 percent. What would be the total value of the company? If it has 10 million shares of stock and $40 million in total debt, what is the price per share?

Explanation / Answer

1-

value of stock

expected dividend/(required rate of return-growth rate)

26

expected dividend

current dividend*(1+r)^n

1.5*(1.04)^1

1.56

growth rate

4%

required rate of return

10%

2-

value of stock

expected dividend/(required rate of return-growth rate)

8.8125

expected dividend

current dividend*(1+r)^n

1.5*(.96)^1

1.41

growth rate

-6%

required rate of return

10%

The company is earning something and paying some dividends, so it clearly has a value greater than zero.

3-

Year

cash flow

1

-5000000

2

10000000

3

20000000

4

20000000*(1.06)

21200000

value of firm

(21200000)/(10%-6%)

530000000

Year

cash flow

present value of cash flow = cash flow/(1+r)^n r= 10%

1

-5000000

-4545455

2

10000000

8264462.8

3

20000000

15026296

3

530000000

398196844

sum of present value of cash flow

416942149

value of debt

40000000

value of equity

376942149

no of shares outstanding

10000000

value of equity per share

37.694215

1-

value of stock

expected dividend/(required rate of return-growth rate)

26

expected dividend

current dividend*(1+r)^n

1.5*(1.04)^1

1.56

growth rate

4%

required rate of return

10%

2-

value of stock

expected dividend/(required rate of return-growth rate)

8.8125

expected dividend

current dividend*(1+r)^n

1.5*(.96)^1

1.41

growth rate

-6%

required rate of return

10%

The company is earning something and paying some dividends, so it clearly has a value greater than zero.

3-

Year

cash flow

1

-5000000

2

10000000

3

20000000

4

20000000*(1.06)

21200000

value of firm

(21200000)/(10%-6%)

530000000

Year

cash flow

present value of cash flow = cash flow/(1+r)^n r= 10%

1

-5000000

-4545455

2

10000000

8264462.8

3

20000000

15026296

3

530000000

398196844

sum of present value of cash flow

416942149

value of debt

40000000

value of equity

376942149

no of shares outstanding

10000000

value of equity per share

37.694215

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