Royal Dutch Shell is a petroleum and petrochemicals company. It engages primarily in the exploration, production, and sale of crude oil and natural gas and the manufacture, transportation, and sale of petroleum and petrochemical products. The company operates in approximately 200 countries in North America, Europe, Asia-Pacific, Africa, South America, and the Middle East. Assume that during the past three years (Year 2, 1, and 0), Royal Dutch Shell generated the following total dividends to common equity shareholders (in USD millions):

                                                                        Year -2         Year -1           Year 0

Common dividend payments....................$ 8,142.........$ 9,001........$ 9,516

Stock repurchases...................................8,047............4,387..........3,573

Total dividends..................................$16,189.........$13,388........$13,089

Analysts project 5% growth in earnings over the next five years. Assuming concurrent 5% growth in dividends, the following table provides the amounts that analysts project for Royal Dutch Shell's total dividends for each of the next five years. In Year þ6, total dividends are projected for Royal Dutch Shell assuming that its income statement and balance sheet will grow at a long-term growth rate of 3%.

Year + 1 Year + 2 Year + 3 Year + 4 Year + 5 Year + 6

Projected growth 5% 5% 5% 5% 5% 3%

Projected total dividends

to common equity $13,743 $14,431 $15,152 $15,910 $16,705 $17,206

At the end of Year 0, Royal Dutch Shell had a market beta of 0.71. At that time, yields on intermediate-term U.S. Treasuries were 3.5%. Assume that the market required a 5.0% risk premium. Suppose Royal Dutch Shell had 6,241 million shares outstanding at the beginning of Year + 1 that traded at a share price of $24.87.

REQUIRED

a. Calculate the required rate of return on equity for Royal Dutch Shell as of the beginning of Year + 1.

b. Calculate the sum of the present value of total dividends for Years þ1 through þ5.

c. Calculate the continuing value of Royal Dutch Shell at the start of Year þ6 using the perpetuity-with-growth model with Year þ6 total dividends. Also compute the present value of continuing value as of the beginning of Year + 1.

d. Compute the total present value of dividends for Royal Dutch Shell as of the beginning of Year þ1. Remember to adjust the present value for midyear discounting.

e. Compute the value per share of Royal Dutch Shell as of the beginning of Year þ1.

f. Given the share price at the start of Year þ1, do Royal Dutch Shell shares appear underpriced, overpriced, or correctly priced?