Final answer:
The present value of growth opportunities (PVGO) for Parcel Corporation is calculated by subtracting the earnings capitalization value from the actual value of the company's stock using the Gordon Growth Model. After expected earnings and dividends are considered, the PVGO comes out to $46.67 per share.
Step-by-step explanation:
To calculate the present value of growth opportunities (PVGO) for Parcel Corporation, we must first compute the value of the company with no growth and then compare it to the actual value of the company given its growth prospects. The value of the company if it were to pay a constant dividend forever (with no growth) can be computed using the dividend payout and the required rate of return.
The expected dividend next year is $5 per share, and the dividend payout ratio is 50%, meaning the expected earnings are $5 / 0.50 = $10 per share. The value of the company with no growth, often called the earnings capitalization value, will be the earnings divided by the required rate of return, so $10 / 0.12 = $83.33 per share.
Given that dividends are expected to grow at a constant rate (g) of 8% forever, we can use the Gordon Growth Model (also known as the dividend discount model) to calculate the actual value of the company's stock (P), which is given by: P = D0 x (1+g) / (r - g), where D0 is the dividend just paid (here it's $5), g is the growth rate (0.08), and r is the required rate of return (0.12). Therefore, the actual price using the Gordon Growth Model would be $5 x (1+0.08) / (0.12 - 0.08) = $130 per share.
The PVGO is the actual price minus the earnings capitalization value, so PVGO = $130 - $83.33 = $46.67 per share. This amount represents the value of the company's growth opportunities.