What is the current value of a share of McDonalds if its current dividend is $1.50 and dividends are expected to grow at an annual rate of 20 percent for the next 5 years? Assume the investor has a required rate of return of 15 percent and expects to sell the security in 5 years for $72.
A) $44.31
B) $35.78
C) $39.63
D) $72.00

Question

Quizplus · Accepted Answer

The value of a share of McDonald's can be calculated using the Dividend Discount Model (DDM) for a growing dividend, which is adjusted to account for the sale of the security in 5 years. The formula to calculate the present value of the expected dividends and the sale price is:$$ P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \frac{D_3}{(1+r)^3} + \frac{D_4}{(1+r)^4} + \frac{D_5 + P_5}{(1+r)^5} $$Given:- $D_0 = $1.50$, the current dividend.- Growth rate $g = 20\% = 0.20$.- Required rate of return $r = 15\% = 0.15$.- Sale price in 5 years $P_5 = $72$.First, calculate the dividends for the next 5 years:- $D_1 = D_0 \times (1 + g) = $1.50 \times (1 + 0.20) = $1.80$- $D_2 = D_1 \times (1 + g) = $1.80 \times (1 + 0.20) = $2.16$- $D_3 = D_2 \times (1 + g) = $2.16 \times (1 + 0.20) = $2.592$- $D_4 = D_3 \times (1 + g) = $2.592 \times (1 + 0.20) = $3.1104$- $D_5 = D_4 \times (1 + g) = $3.1104 \times (1 + 0.20) = $3.73248$Now, calculate the present value of these dividends and the sale price:$$ P_0 = \frac{$1.80}{(1+0.15)^1} + \frac{$2.16}{(1+0.15)^2} + \frac{$2.592}{(1+0.15)^3} + \frac{$3.1104}{(1+0.15)^4} + \frac{$3.73248 + $72}{(1+0.15)^5} $$$$ P_0 = $1.5652 + $1.6327 + $1.6985 + $1.7625 + $38.6711 = $44.3299 $$Rounded to two decimal places, the current value of a share of McDonald's is approximately $44.31.

What Is the Current Value of a Share of McDonalds