Dollar General (DG) recently earned a profit of $2.85 per share and has a P /...

Dollar General (DG) recently earned a profit of $2.85 per share and has a P / E ratio of 23.19. Earnings have been growing at 11.5 percent per year over the past few years. If this growth continues , what would the stock price be in five years if the P/E ratio remains unchanged? What would the price be in five years if the P / E ratio declined to 20?

a. $119.83, $103.71 respectively

b. $128.75, $128.29 respectively

c. $113.90, $98.23 respectively

d. $107.25, $99.83 respectively

Solutions

Expert Solution

The correct answer is c. $113.90, $98.23 respectively

Price earnings (PE) = Price of stock / Earnings per share of the stock

Step 1 - Calculation of Earnings per share in year 5

= Current EPS * (1 + Growth rate)⁵

= $2.85 * (1+0.115)⁵

= $2.85 * (1.115)⁵

⁼ $2.85 * 1.72335

= $4.91155

Step 2 - Calculation of Price at year 5

Price earnings (PE) = Price of stock / Earnings per share of the stock

23.19 = Price of stock / $4.91155

Price of stock = $4.91155 * 23.19

= $113.90 ( Rounded to two decimal places)

Price of stock if PE ratio declined to 20

Price earnings (PE) = Price of stock / Earnings per share of the stock

20 = Price of stock / $4.91155

Price of stock = $4.91155 * 20

= $98.23 (Rounded to two decimal places)

Note - How did we calculate (1.115)⁵

= 1.115 * 1.115 * 1.115 * 1.115 * 1.115

= 1.72335

jeff jeffy answered 2 years ago

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