Question

1. A stock is expected to pay the following dividends per share over the next three years, respectively: $1.50, $1.95 and $2.20. If you expect to be able to sell the stock for $54.26 in three years and your required rate of return is 8%, what is the most that you should be willing to pay for a share of this stock today?

Answer 1

Answer:

The answer is $47.88

Explanation:

In this question, to identify the stock's price is to calculate the present value of all expected future cash flow gained from holding and disposal the stock which are discounted at the required rate of return, that is 8% in this case.

In detailed:

- Present value of the dividend expected to receive in Year 1 (PV Y1): 1.5/1.08 = $1.389

- Present value of the dividend expected to receive in Year 2 (PV Y2): 1.95/1.08^2 = $1.672

- Present value of the dividend and sale proceed from stock disposal expected to receive in Year 3 (PV Y3): (2.2+54.26)/1.08^3 = $44.820

-Stock's price = PV Y1 + PV Y2 + PV Y3 = $47.88

Answer 2

Answer:The answer is $47.88

Explanation:

Using the formula

Present worth = X/( 1 + R/ 100)∧n

Where X = dividend , R = Rate of return, n = number of years

1.50/(1 + 8/100)∧N

= 1.50/ ( 1.08)∧1

= 1.50/ 1.08

= 1.39

1.95/(1 + 8/100)∧2

= 1.95/(1 + 0.08)∧2

= 1.95/(1.08)∧2

= 1.95/1.1664

= 1.67

Since the stock is expected to be sold in year 3 at $54.26, Therefore the third year will be

X + Selling price of the stock/(1+ R/100)∧n

= 2.20 + 54.26/ (1 + 8/100)∧3

= 56.46/(1.08)∧3

= 56.46/1.259712

= 44.82

To determine the price to pay for the share today, we add the present worth of the years together

= 1.39 + 1.67 + 44.82

= 47.88

Therefore the price to pay today for the share = $47.88