The company’s stock is hundred percent owned by its several cofounders, and the
ID: 2712108 • Letter: T
Question
The company’s stock is hundred percent owned by its several cofounders, and the current market price of each of the 500,000 shares of stock is $20.
When you started your work, you were immediately assigned a big project. You were asked to evaluate a new investment project: opening a new “Coffee Cup” location in Pomona. Specifically, you were asked to analyze the projected sales revenues and costs and advise your boss on whether the project could be profitable. Below is the information regarding the project:
Project life
6 years
Initial investment raised solely from equity
$1,206,000
Number of “Coffee Cup” customers, per year
Out of this number, 75% are adults, and 25% are children.
100,000
Average price that an adult customer pays in year 1
This amount will be growing by $0.50 each following year
$6
Average price that a child customer pays each year
$3
Cost of preparing food and drinks and other variable costs, per each customer’s meal
$1
Equipment rental and other fixed costs, per year
$200,000
Systematic risk (i.e., Beta) of the project
1.17
Corporate tax rate is 34%. The project will fully depreciate on straight line over 6 years.
You also know that “Coffee Cup” has three main competitors in the coffee industry, also owned fully by their respective cofounders: Coffeebucks, Coffee Bean, and Pete’s Coffee. All but Coffeebucks are comparable in size to “Coffee Cup”, with Coffeebucks being roughly twice the size. Coffeebucks’ returns are not as prone to economy-wide up or downturns when compared to the returns on an average stock in the economy, and so its systematic risk, measured by Beta, is only 0.657. For Pete’s Coffee, though, the systematic risk is higher, with the Beta of 1.051, and it is even higher for Coffee Bean and equals 1.255. You did some research and figured out that the market risk of “Coffee Cup” reflects the average risk of the competitors.
Your boss also gave you some data – that might help you in your analysis – on annual returns of the US Treasury bills which are viewed as the riskless asset, as well as for the market portfolio proxied by Standard & Poor’s 500 index:
State of the economy
(all equally likely)
Annual returns (%)
Treasury bills
S&P 500
Boom
4
25
Normal
4
12
So-so
4
1
recession
4
-3
Based on the above information, answer the following questions:
Question 1. (4 points) After analyzing the “Coffee Cup” company’s performance over the past years, you have concluded that the company’s stock correctly reflects the amount of systematic risk that it has. Based on this, what expected annual rate of return on the company’s equity do investors require that would correctly compensate them for the amount of systematic risk? Calculate and explain.
Project life
6 years
Initial investment raised solely from equity
$1,206,000
Number of “Coffee Cup” customers, per year
Out of this number, 75% are adults, and 25% are children.
100,000
Average price that an adult customer pays in year 1
This amount will be growing by $0.50 each following year
$6
Average price that a child customer pays each year
$3
Cost of preparing food and drinks and other variable costs, per each customer’s meal
$1
Equipment rental and other fixed costs, per year
$200,000
Systematic risk (i.e., Beta) of the project
1.17
Explanation / Answer
Coffee Cup average beta=1.17
Expected Market return =Average Market return over 4 State of the economy=(25%+12%+1%-3%)/4=35/4 %= 8.75%
cost of Equity =re= risk-free rate+ beta*(market risk premium),Line or CAPM model is: Ri= Rf + Bi*(Rm-Rf) is the SML with slope (Rm-Rf) and intercept Rf with y axis as Ri and x axis as Bi.
where Ri= ith Security return
Rf =risk-free rate=4%=.04, Bi =Beta of ith security=1.17 and Rm= Expected Market return=8.75%=.0875
Ri= Rf + Bi*(Rm-Rf) =.04 + 1.17 *(.0875-.04) =0.095575 or 9.56%
Thus expected annual rate of return of 9.56% on the company’s equity do investors require that would correctly compensate them for the amount of systematic risk.