5. Next year, NPI expects net income of $16 million. Its plans to reinvest 0.5 of its earnings and pay out the 0.5 as dividends. Its cost of equity capital of 12%. If NPI earns a 16% rate of return on the funds reinvested, what is the growth rate and value of NPI? Hypothetically, had the firm not reinvested any of its earnings and paid out 100% of earnings as dividends, what would have been the value? How much does reinvesting contribute to firm value?

To find the growth rate and value of NPI when it reinvests a portion of its earnings, you can use the Gordon Growth Model. The formula for the Gordon Growth Model is as follows:

Value = Dividends / (Cost of Equity - Growth Rate)

In this case, NPI plans to reinvest 0.5 of its earnings and pay out 0.5 as dividends. Next year's net income is expected to be $16 million. Therefore, the dividends will be $16 million * 0.5 = $8 million.

To calculate the growth rate, you can use the following formula:

Growth Rate = Return on Invested Capital * Retained Earnings Ratio

In this case, the return on invested capital is 16% and the retained earnings ratio is 0.5. Therefore, the growth rate is 16% * 0.5 = 8%.

Now, let's calculate the value of NPI:

Value = Dividends / (Cost of Equity - Growth Rate)
Value = $8 million / (0.12 - 0.08)
Value = $8 million / 0.04
Value = $200 million

Therefore, the value of NPI, when it reinvests a portion of its earnings, would be $200 million.

Now, let's calculate the value of NPI if it had not reinvested any of its earnings and paid out 100% of its earnings as dividends:

Value = Dividends / Cost of Equity
Value = $16 million * 0.5 / 0.12
Value = $8 million / 0.12
Value = $66.67 million

So, hypothetically, if NPI had not reinvested any of its earnings and paid out 100% of earnings as dividends, the value of the firm would have been $66.67 million.

To determine how much reinvesting contributes to firm value, we can calculate the difference between the two values:

Reinvestment Contribution = Value with Reinvestment - Value without Reinvestment
Reinvestment Contribution = $200 million - $66.67 million
Reinvestment Contribution = $133.33 million

Therefore, reinvesting contributes $133.33 million to the firm's value.