Question

I am considering investing in a new start-up firm, Herb’s Herbs (HH), that produces legal (at least for now) synthetic and herbal mood enhancers. The herbs are sold at convenience stores and HH expects growth to be strong. HH stock sells for $72/share and just paid a $4 per share dividend. HH expects revenues, earnings, and dividends to grow at 11% annually. Treasury bills offer a 2% annual rate of return and the market risk-premium is 9%. What is the beta (β) of HH stock? How much riskier is HH than the market?

Answer 1

Given the market price of the stock = 72

For a constant growing Dividend model

Price = Dividend of next year/(Cost of equity- Growth rate)

Dividend of next year = Dividend for current year *(1+ Growth rate)

=4*(1+11%)

=4.44

Price = Dividend of next year/(Cost of equity- Growth rate)

72= 4.44/(Cost fo equity- 11%)

Cost of equity - 11%= 4.44/72

Cost of equity -0.11= 0.061667

Cost of equity= 0.171667

or 17.1667%

We know that cost of equity is given as = Rf+ (Rm-RF)*Beta

Risk free rate= Rf= 2%

Market premium= Rm-RF= 9%

Cost of equity = 17.1667%

cost of equity is given as = Rf+ (Rm-RF)*Beta

17.1667% = 2%+9%* Beta

17.1667%-2%= 9%* beta

15.1667%=9%*Beta

Beta= 15.1667%/9%

Beta= 1.6852

Hence beta of stock = 1.6852

Since the beta of stock is 1.6852 and beta is a measure of risk hence stock is 1.6852 times riskier than the market

In other words If the market falls by 1% the stock will fall by 1.6852%