# Week 8 Weekly Case

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• Published : May 8, 2011

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1. What do you expect to drive a company’s price-to-book equity and price-to-earnings multiples?

PE ratio is expected to be affected by various factors include company earnings, payout ratio, growth rate and cost of equity. From the dividend discount model we know that P0=EPS0×Payout ratio×(1+gn)r-gn , thus P0EPS0=PE ratio=Payout ratio×(1+gn)r-gn. Thus we see that the PE ratio is an increasing function of the payout ratio and the growth rate and a decreasing function of the riskiness of the firm.

The determinants of PBV ratio can also be explored by using the dividend discount model. We know thatP0=DPS1ke-gn, substituting for DPS1 =EPS1(payout ratio), the value of the equity can be written as: P0=EPS1×Payout ratioke-gn, Defining the return on equity (ROE)= EPS1/Book value of equity0,the value of equity can be written as P0=BV0×ROE×Payout ratioke-gn. This formulation can be simplified to the follow: P0BV=PBV ratio=(ROE-gn)ke-gn. Thus, the price-book value ratio of a stable is determined by differential between the return on equity and its cost of equity. It the return on equity exceeds the cost of equity, the price will exceed the book value of equity; if the return on equity is lower than the cost of equity, the price will be lower than the book value of equity.

2. Match the price to earnings valuation multiples below with each of the four restaurant businesses discussed above. What is your reasoning for the matches you selected?

Company A: PE ratio of 9.6 is most suitable for company A. Question 1 shows how the reinvestment rate of the company and its dividend payout rate affect the PE ratio of the company. It can be seen from the question that company A is the largest company among the others 3 in term of the size and history. The company has over a thousand of store including franchisees and thus, the reinvestment need is less than the other 3 companies and hence the growth rate is consequently to be low comparatively.

Company B: High PE...