Question

Start-Up Industries is a new firm that has raised $310 million by selling shares of stock. Management plans to earn a rate of return on equity of 20%, which is more than the 15% rate of return available on comparable-risk investments. Half of all earnings will be reinvested in the firm.

a. What will be Start-Up’s ratio of market value to book value?

b. What will be Start-Up’s ratio of market value to book value if the firm can earn only a rate of return of 10% on its investments?

Answer 1

In this case ,

As half the earnings will be reinvested in the firm

Dividend payout ratio = retention ratio = 0.5

growth rate of the firm = Plowback ratio * Return on Equity

a) In the first case,

Total Income = 20% of Equity

= 20% of $310 million

= $62 million

Dividend = 0.5 * $62 million = $31 million

growth rate = 0.5* 20% = 10% = 0.1

required rate = 15% = 0.15

So, by constant growth model

Market value = Total Dividend / (required rate - growth rate)

=$31 million / (0.15- 0.10)

=$620 million

Therefore, Market value to book value = $ 620 million/ #310 million = 2

b) In this case,

Total Income = 10% of Equity (Investment)

= 10% of $310 million

= $31 million

Dividend = 0.5 * $31 million = $15.5 million

growth rate = 0.5* 10% = 5% = 0.05

required rate = 15% = 0.15

So, by constant growth model

Market value = Total Dividend / (required rate - growth rate)

=$15.5 million / (0.15- 0.05)

=$155 million

Therefore, Market value to book value = $ 155 million/ #310 million = 0.5