Question

RBC stock pays a quarterly dividend and is expected to pay $1 per share in 3 months from today. Assume investors wish a return of ?^(4)=10%, and they expect the dividends to grow at a rate of ?^(4)=5%. Assume they expect the dividends to grow at this rate forever. Show all of your work!

a.) What is the current value of one RBC share?

b.) Suppose investors are mistaken and the growth rate for the dividends is really ?^(4)=3%. How much has the market overvalued RBC stock?

Answer 1

a). Expected Quarterly Dividend(D1) = $ 1 per share

Required rate of return = 10% compounded quarterly

Quarterly Required rate(ke) = 10%/4 = 2.5%

Growth rate = 5% compounded Quarterly

Quarterly Growth rate (g) = 5%/4 = 1.25%

Calculating the Current value of share:-

Price = 1/(0.025-0.0125)

Price = $80 per share

b). As investors were mistaken and growth rate was = 3% compounded Quarterly

Quarterly Growth rate (g) = 3%/4 = 0.75%

Calculating the Current value of share:-

Price = 1/(0.025-0.0075)

Price = $57.14 per share

As per growth rate of 3% , Price of Stock should be $ 57.14 while investors were mistaken and the Price is $ 80.

Thus, the market has overvalued RBC Stock by $ 80 - $ 57.14 = $ 22.86 per share