If a firm's required rate of return equals the firm's return on equity,there is no advantage to increasing the firm's growth.Suppose a no-growth firm had a required rate of return and a ROE of 12% and a stock price of $40.However,if the firm is able to increase the ROE to 15% with a plowback ratio of 50%,what is the present value of growth opportunities now? (Last year's dividends were $2.00/share).

Question

Quizplus · Accepted Answer

The present value of growth opportunities (PVGO) can be calculated using the formula: PVGO = P - (D1 / r), where P is the price with growth, D1 is the dividend next year, and r is the required rate of return. With a new ROE of 15% and a plowback ratio of 50%, the growth rate (g) is 7.5%. The new dividend (D1) is $2.00 * (1 - 0.5) = $1.00. The price with growth is calculated as D1 / (r - g) = $1.00 / (0.12 - 0.075) = $28.57. The PVGO is $40 - $28.57 = $11.43. However, the closest option is $7.78, indicating a possible error in the options or assumptions.

If a Firm's Required Rate of Return Equals the Firm's