Sports-R-Us is a large sports retailer. Last month, Sports-R-Us announced that s

Question

Sports-R-Us is a large sports retailer. Last month, Sports-R-Us announced that shareholders of record on this coming Friday will receive a dividend of $3.50 per share. (Assume that the dividend will also be paid on Friday.) After this Friday, the next dividend is expected in one year's time. Dividends are expected to be paid annually in perpetuity and are expected to grow at a rate of 3.00%. Shareholders of Sports-R-Us require a 11.50% return on equity.

a. What is the stock price of Sports-R-Us on Tuesday? (Preceding the Friday Date of Record.)

b. What is the stock price of Sports-R-Us on Wednesday? (Preceding the Friday Date of Record.)

Explanation / Answer

Given : Current dividend per share on Friday =D0=3.5 Dividend growth rate =g=3% Return on Equity =k=11.5% After Dividend payout on Friday, the next dividend D1=3.5*1.03=             3.61 So Stock Price on Friday after dividend payout=3.61*1.03/(11.5%-3%)= $      43.74 So Stock Price Prior to dividend payout on Friday=3.5+43.74= $      47.24 So Cum dividend stock price on Thursday =47.24 Return on Equity =11.5% Discount factor for 1 day=1/(1+11.5%/365)=0.99968 So Discounted value of $3.5 dividend on Wednesday =0.99968*3.5=        3.4989 Discount factor for 1 day=1/(1+11.5%/365*2)=0.99937 So Discounted value of $3.5 dividend on Tuesday =0.99937*3.5=        3.4978 So Stock value on Wednesday=47.24+3.4989= $ 50.7436 So Stock value on Tuesday=47.24+3.4978= $ 50.7425

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