Question

Case 8.1 The Boise Boyz Company

The Boise Boyz Company (BBC) currently has a single line of business, buoys. The company is considering the purchase of one of two companies, each in a different line of business: The Treasure Search Company (TSC) and the Old Lady Knitting Company (OLKC). BBC is four times as large as TSC and OLKC, each considered alone. The financial analysts of BBC have worked up some numbers to present to the CFO, Bobby Boyz, regarding returns on BBC and the two other companies for the next year. The analysts project the following:

Economic Environment Returns Probability BBC TSC OLKC

Economic recovery 20% 15% 20% 11% Stagnant economy 50% 8% 10% 10% Recession 30% 1% –10% 9%

Answer the following questions regarding the evaluation of the acquisition of TSC and OLKC, using a spreadsheet to perform the calculations:

A. What is the expected return and standard deviation of these returns for each company?

B. What is the expected return if BBC acquires TSC? OLKC?

C. What is the standard deviation of the portfolio consisting of BBC and TSC? BBC and OLKC?

D. Based on the expected return and the portfolio standard deviation, which acquisition is preferred: TSC or OLKC? Explain your reasoning.

Answer 1

Economic Environment		Returns	Returns	Returns
	Probability	BBC	TSC	OLKC
Economic Recovery	20%	15%	20%	11%
Stagnant Economy	50%	8%	10%	10%
Recession	30%	1%	-10%	9%

(a). What is the expected return and standard deviation of these returns for each company?
Expected return = $\sum xP$

Standard deviation = $\sqrt{(\sum x^{2}P) - \mu ^2}$

The expected return can be calculated by factoring in the probability of each economic environment.
For BBC
Expected return = (0.2)(15) + (0.5)(8) + (0.3)(1) = 7.3%
Standard deviation = sqrt{(0.2)(15²) + (0.5)(64) + (0.3)(1) - (7.3²)} = 4.9%

For TSC
Expected return = (0.2)(20) + (0.5)(10) + (0.3)(-10) = 6%
Standard deviation = 11.13%

For OLKC
Expected return = (0.2)(11) + (0.5)(10) + (0.3)(9) = 9.9%
Standard deviation = 0.7%

(b). What is the expected rate of return if BBC acquires

TSC: Expected rate of return = average of both rates of return
Expected return = (4.9 + 6)/2 = 5.45%

OLKC:
Expected return = (4.9 + 9.9)/2 = 7.4%

(c). What is the standard deviation when BBC acquires

TSC:
d1 = return of TSC - total return (BBC + TSC) = 0.55
d2 = return of BBC - total return (BBC + TSC) = -0.55
Combined standard deviation = (4.9 + 11.13 + (2)(0.55²))/2 = 8.3175%

OLKC:
d1 = return of OLKC - total return (BBC + OLKC) = -2.5
d2 = return of BBC - total return (BBC + OLKC) = 2.5
Combined standard deviation = (4.9 + 0.7 + (2)(2.5²))/2 = 9.05%

(d). When OLKC is acquired, the expected returns are greater. A lower standard deviation is also preferred, so that actual values match expected returns. In this case, acquiring OLKC will be better for BBC, even though the standard deviation is greater (but only by 0.7%), since the returns are greater.

Hope this helped!