Question

The following are the P/E ratios, growth rates, beta and payout ratios of some firms in the same industry
Company	P/E Ratio	Growth rate	Beta	Payout
BOE	17.3	3.50%	1.1	28%
GD	15.5	11.50%	1.25	40%
GMH	16.5	13.00%	0.85	41%
GRU	11.4	10.50%	0.8	37%
LK	10.2	9.50%	0.85	37%
LG	12.4	14.00%	0.85	11%
LR	13.3	16.50%	0.75	23%
MM	11	8.00%	0.85	22%
MD	22.6	13.00%	1.15	37%
NR	9.5	9.00%	1.05	47%
RY	12.1	9.50%	0.75	28%
RW	13.9	11.50%	1	38%
TH	8.7	5.50%	0.95	15%
UI	10.4	4.50%	0.7	50%
A. Estimate the average and median P/E ratios. What, if anything, would these averages tell you?
B. An analyst concludes that firm TH is undervalued, because its P/E ratio is lower than the industry average. Under what conditions is this statement true? Would you agree with it here?
C. Now use a regression methodology to estimate the P/E ratio of company TH.

Answer 1

Q(a)	Average & Median P/E Ratios

Average P/E

Formula

Average P/E = Sum of total P/E values / No. of companies

S.No.	Company	P/E Ratio
1	TH	8.7
2	NR	9.5
3	LK	10.2
4	UI	10.4
5	MM	11
6	GRU	11.4
7	RY	12.1
8	LG	12.4
9	LR	13.3
10	RW	13.9
11	GD	15.5
12	GH	16.5
13	BOE	17.3
14	MD	22.6
	Total	184.8

Here,
1	Total of P/E values	184.8
2	No. of companies in the cohort	14
Answer	Average (1/2)	13.2

Median P/E Ratio

Step 1 : Arrange P/E values in ascending order as follows:

S.No.	Company	P/E Ratio
1	TH	8.7
2	NR	9.5
3	LK	10.2
4	UI	10.4
5	MM	11
6	GRU	11.4
7	RY	12.1
8	LG	12.4
9	LR	13.3
10	RW	13.9
11	GD	15.5
12	GMH	16.5
13	BOE	17.3
14	MD	22.6
	Total P/E	184.8

	Median P/E value
Step 1	Arrange P/E Values in ascending order	See table above
Step 2	Ascertain total No. of companies in the cohort	14
Step 3	Median value = Step 2 /2+1 = 14/2 +1 => 7+1=8
=>	The median value =( P/E of 7 th company + P/E of 8 th company in the ascending order)
	(LR with value = 12.1 + MM with value 12.4)/2	12.25
Answer	Median =	12.25

Therefore, Average P/E = 13.2 and Median P/ E = 12.25

Implication of Average and Median P/E Ratio

The first assumption to make is that all companies in this cohort / table belong to the same industry. Assuming that they do belong to the same industry, an Average P/E value provides an indicator of how much the market values earnings in this industry, given the expected growth potential and risk for the industry.

The Median P/E value correct the skew in P/E ratio of companies in the industry. The average P/E ratio can be skewed by companies with very high P/E values like MD, BOE and GD. The median P/E identifies the firm with median P/E value.

Q (b)

The assertion can be validated if, and only if, the following two conditions are filfilled, viz.,

i) TH experiences similar growth potential and risk profile typical of a firm in the industry. Further, TH is able to generate and distribute dividends similar to a typical firm in the industry;

ii) TH has experiences a growth potential higher than the typical firm in the industry; and has a lower risk profle in comparison with a typical firm in the industry.

Q (c )

Regression of P/E ratios on fundamentals results in the following equation:

P/E = -2.33 + 35.74 Growth Rate+ 11.97 Beta + 2.90 Payour

=> R ₂ = 0.4068

( The above values have been determined using the Regression Equation :

PE = a (intercept) + B_{1 *} Pay Out Ratio + B₂ * Beta + B ₃ * Expected Growth Rate (EGR)

a (intercept)= Y - B₁X₁+B₂X₂+B₃X₃  

abd B1, B2 and B3 ( or Beta 1, Beta 2 and Beta 3) are determined by regression equation for the slope.