Question

In: Finance

Consider the following historical information for Sonny’s Body Shop over the past five years. Year 2014...

Consider the following historical information for Sonny’s Body Shop over the past five years.

	Year 2014	Year 2015	Year 2016	Year 2017	Year 2018
Stock price($)	100	120	147	192	180
EPS	10	12	14	16	20

Earnings are expected to grow at 10% for the next four years. Using the company’s historical average PE ratio as a bench mark, (a) what is the target stock price next year? (b) What about four years from now?

Expert Solution

Part a:

Historical PE calculation:

PE ratio=Stock price/Earnings per share

Year 2014: Stock price in the year 2014/Earnings per share in the year 2014=$100/$10=10

Year 2015: Stock price in the year 2015/Earnings per share in the year 2015=$120/$12=10

Year 2016: Stock price in the year 2016/Earnings per share in the year 2016=$147/$14=10.5

Year 2017: Stock price in the year 2017/Earnings per share in the year 2017=$192/$16=12

Year 2018: Stock price in the year 2018/Earnings per share in the year 2018=$180/$20=9

Average PE from year 2014 to 2018=Total value of the observations/Number of observations
=(10+10+10.5+12+9)/5=10.3
For our calculations, we will use this average PE ratio as a bench mark (as given in the question).

Given that the earnings are expected to grow at 10% for the next four years, earnings per share should also increase by 10% (assuming there will be no change in the number of shares outstanding in the coming years)

Year 2018: EPS=20

Year 2019: EPS=20*(1+10%)=20*(1.1)=22

Year 2020: EPS=20*(1+10%)*(1+10%)=20*(1.1)*(1.1)=24.2

Year 2021: EPS=20*(1+10%)*(1+10%)*(1+10%)=20*(1.1)*(1.1)*(1.1)=26.62

Year 2022: EPS=20*(1+10%)*(1+10%)*(1+10%)*(1+10%)=20*(1.1)*(1.1)*(1.1)*(1.1)=29.282

Target price in year 2019 =(EPS in year 2019)*(Average PE)
Average PE as we have calculated is 10.3
EPS in year 2019=$22
Target price in year 2019=$22*10.3=$226.6

Part b:

Four years from now means year 2022
Given that, we need to use company’s historical average PE ratio as a bench mark.
So, PE=10.3
EPS in the year 2022=29.282
Stock price in the year 2022=PE*EPS=10.3*29.282=301.6046
Therefore, the stock price four years from year 2018 (that is year 2022) is $301.6046 or $301.60 (Rounded up to 2 decimal places)

jeff jeffy answered 1 year ago

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