Question

Consider Pacific Energy Company and Atlantic Energy, Inc., both of which reported earnings of $962,000. Without new projects, both firms will continue to generate earnings of $962,000 in perpetuity. Assume that all earnings are paid as dividends and that both firms require a return of 12 percent.

  

a.	What is the current PE ratio for each company? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.	Pacific Energy Company has a new project that will generate additional earnings of $112,000 each year in perpetuity. Calculate the new PE ratio of the company. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

c.	Atlantic Energy has a new project that will increase earnings by $212,000 in perpetuity. Calculate the new PE ratio of the firm. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Please provide details as much as possible with formulas and calculations (excel is preferred). Thank you.

Answer 1

Ans #a:

Given Data

D = Dividend = Earnings = $962,000

i = Required rate of return = 12% i.e 0.12

As per the given data we can compute the total value of firm by Dividend Discount Model.

Since Dividend earning is perpetual, the value of firm = D ÷ i

                                                                                                = 962000 ÷ 0.12

                                                                                                = $8,016,667 (Rounded off)

The value of the firm can also be calculated by = Total no of shares × Price per share

The formula for PE ratio = Price per share ÷ Earnings per share

If we will multiply “Total no of shares” in both “Price of a share” & ”Earnings per share”, the ratio value will not be changed.

PE Ratio = (Total no of shares × Price of a share) ÷ (Total no of shares × Earnings per share)

               = Value of Firm ÷ Total Earnings

                = 8,016,667 ÷ 962,000

                = 8.33 (Rounded off)

Hence current PE ratio of each company is 8.33

Ans #b:

Given data

Additional earning = $112,000

Hence

D = Dividend = Earnings = $962000 + $112000 = $1,074,000

i = Required rate of return = 12% i.e 0.12

Hence as per dividend discount model = value of firm = D ÷ i

                                                                                                = 1074000 ÷ 0.12

                                                                                                = $8,950,000

It was assumed that the value of the firm has been changed as variance in Earnings.

By applying the formula explained in Ans #a

PE ratio = 8950000 ÷ 1074000

              = 8.33

Hence the PE ratio of Pacific Energy Company after considering new project is unchanged i.e 8.33

Ans #C:

Given data

Additional earning = $212,000

Hence

D = Dividend = Earnings = $962000 + $212000 = $1,174,000

i = Required rate of return = 12% i.e 0.12

Hence as per dividend discount model = value of firm = D ÷ i

                                                                                                = 1174000 ÷ 0.12

                                                                                                = $9,783,333 (Rounded off)

It was assumed that the value of the firm has been changed as variance in Earnings.

By applying the formula explained in Ans #a

PE ratio = 9783333 ÷ 1174000

              = 8.33

Hence the PE ratio of Atlantic Energy Company after considering new project will be unchanged i.e 8.33

SUMMERY

In Excell the above 3 cases will be computed as follows: