6. Suppose NPI’s reinvestment rate on all future retained earnings were 12% instead of the 16% assumed in the previous problem. (Continue to assume initial earnings of $16 million.) If the dividend payout ratio were increased to 0.75, what happens to the growth rate and the value of NPI? Suppose the dividend payout ratios were decreased to 0.50, how would growth and value change? What would happen to growth and value if the firm stopped reinvesting any earnings and paid out all earnings as dividends?
To calculate the growth rate and value of NPI under different scenarios, we need to use the dividend growth model formula.
The dividend growth rate (g) is calculated as the product of the retention ratio (1 - payout ratio) and return on equity (ROE):
g = (1 - payout ratio) * ROE
The value of the firm (V) using the dividend growth model is calculated as follows:
V = D / (r - g)
where D is the dividend, r is the required rate of return, and g is the growth rate.
Let's go through each scenario step by step.
1. If NPI's reinvestment rate on all future retained earnings were 12% instead of the assumed 16%, while the dividend payout ratio increased to 0.75:
- The retention ratio would be 1 - payout ratio = 1 - 0.75 = 0.25
- Let's assume the return on equity (ROE) remains constant.
- The new growth rate (g) would be 0.25 * ROE.
- To calculate the value (V), we need more information like the required rate of return (r) and the initial dividend (D). Without these values, we cannot determine the exact change in growth rate and value.
2. If the dividend payout ratio decreased to 0.50:
- The new payout ratio would be 0.50.
- The new retention ratio would be 1 - payout ratio = 1 - 0.50 = 0.50
- The new growth rate (g) would be 0.50 * ROE.
- Again, without the required rate of return (r) and the initial dividend (D), we cannot calculate the exact change in growth rate and value.
3. If the firm stopped reinvesting any earnings and paid out all earnings as dividends:
- The retention ratio would be 0.
- Consequently, the growth rate (g) would be 0.
- In this scenario, since there is no growth, the value of NPI would solely depend on the dividends it pays out and the required rate of return (r).
Please provide the required rate of return (r) and the initial dividend (D) to calculate the growth rate and value accurately for each scenario.