Question

Pfizer paid its stockholders a dividend of $5 per share yesterday. Today, the company announced that they plan to increase that dividend by $1.00 per share for each of the next three years. After that, they plan to keep their dividend at $8 per share forever. The variance of Pfizer’s stock is .09, the variance of the market is .04, and the correlation between Pfizer’s stock and the market is .05. The risk-free rate is 3% and the market-risk premium is 5.7%. Pfizer has $100 million shares of stock outstanding and $50 million of debt. The YTM for its is 8%. Use the dividend discount model to find the price per share of Pfizer’s stock.

Answer 1

First we need to calculate beta of the Pfizer's stock using below formula:

Beta of a stock = correlation between stock and market*(stock's standard deviation/market's standard deviation)

Standard deviation of stock = Variance^1/2 = 0.09^1/2 = 0.3

Standard deviation of market = 0.04^1/2 = 0.2

Beta = 0.05*(0.3/0.2) = 0.05*1.5 = 0.075

Cost of equity = Risk-free rate + beta*market risk premium = 3% + 0.075*5.7%= 3% + 0.4275 = 3.43%

Cost of debt is its YTM which is 8%.

Now we calculate weighted average cost of capital (WACC) which will be used to calculate value of stock.

WACC = weight of debt*after-tax cost of debt + weight of common stock*cost of common stock

Tax rate is not given. so we assume YTM is after-tax.

Total market value of firm = market value of debt + market value of common stock

Total market value of firm = $50 million + $100 million = $150 million

weight of debt = market value of debt/Total market value of firm = $50/150 = 0.33

weight of equity = $100/$150 = 0.67

WACC = 0.33*8% + 0.67*3.43% = 2.64% + 2.29 = 4.93%

Dividend year 1 = $5 + $1 = $6; Dividend year 2 = $6 + $1 = $7; Dividend year 3 = $7 + $1 = $8; Dividend year 4 = $8

price per share of Pfizer’s stock = Dividend year 1/(1+WACC)¹ + Dividend year 2/(1+WACC)² ...Dividend year 4/(WACC - dividend growth rate)

Dividend will be $8 forever from year 4 and beyond. So, dividend growth rate after year 3 is ($8/$8) - 1 = 1 - 1 = 0%.

price per share of Pfizer’s stock = $6/1.0493¹ + $7/1.0493² + $8/1.0493³ + [$8/(0.0493 - 0)]/1.0493³

price per share of Pfizer’s stock = $6/1.0493 + $7/1.1010 + $8/1.1553 + $162.27/1.1553

price per share of Pfizer’s stock = $5.72 + $6.36 + $6.92 + $140.46 = $159.46