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1) Ladders, Inc
1) Ladders, Inc. has a net profit margin of 5.7% on sales of $48.1 million. It has book value of equity of $41.9 million and total book liabilities of $29.6 million. What is Ladders' ROE? ROA? Note: Assume the value of Interest Expense is equal to zero. What is Ladders' ROE? Ladders' ROE is %. (Round to two decimal places.)
2) In December 2015, General Electric (GE) had a book value of equity of $98.2 billion, 9.4 billion shares outstanding, and a market price of $28.55 per share. GE also had cash of $100.6 billion, and total debt of $201.1 billion. a. What was GE's market capitalization? What was GE's market-to-book ratio? b. What was GE's book debt-equity ratio? What was GE's market debt-equity ratio? c. What was GE's enterprise value? a. What was GE's market capitalization? GE's market capitalization was $ billion. (Round to one decimal place.)
3)
Given two random variables x and y
State of Nature Probability variable x variable y
I 0.2 18 0
II 0. 2 5 -3
III 0.2 12 15
IV 0.2 4 12
V 0.2 6 1
(i) Calculate the mean and variance of each of these variables and the covariance between them
(ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following part folios.
% in x 125 100 75 50 25 0 -25
% in y -25 0 25 50 75 100 125
(iii)Find the portfolio that has the minimum variance.
(iv)Let portfolio A have 75% in x and portfolio B has 25% in x. Calculate the covariance between the two portfolios.
(v) Calculate the covariance between the minimum variance portfolio and portfolio A.
Expert Solution
1)
Computation of Return of Equity (ROE):
Net income = Sales x Net profit margin
Net income = $48.1 million x 5.7%
Net income = $2.7417 million
Shareholder's equity $41.9 million
Return on Equity = Net income/Shareholder's equity X 100
Return on Equity = $2.7417 million/$41.9 million X100
Return on Equity = 6.54% P.a.
Computation of Return on Assets (ROA):
Return on Assets = Net income/Total Average assets X 100
Total Average assets = Current assets + Long term asset
or
Total Average assets = Shareholder's equity + total outside liabilities
Therefore, total average assets = $41.9 million + $29.6 million = $ 71.5 million.
Return on Assets = $2.7417 million/$71.5 million X100
Return on Assets = 3.83% P.a.
2)
Question summary : Given data of GE is :
Book value of Equity =$98.2billion ( 9.4 billion shares with market price $28.55)
Cash = 100.6 billion
Total debt = $ 201.1 billion
Answer :
A1 a
GE's market capitalization = Outstanding number of share * market price
= 9.4 billion shares * $28.55
= 268.37 billion $
Ge's market to book ratio = Market value of Equity / book value of Equity
= 268.37 billion $ / $98.2 billion
= 2.73 times
A2 b . GE's book debt -equity ratio = Book value of debt / book value of Equity
= $ 201.1 billion / $98.2 billion = 2.05
GE's market debt -equity ratio = market value of debt / market value of Equity
= $ 201.1 billion / $268.37 billion = 0.75
A3 . c
GE's Enterprise Value = Market capitalization + Total Debt - Cash
= $268.37 billion + $ 201.1 billion - 100.6 billion
EV = 368.87 billion $
A a)
GE's market capitalization = Outstanding number of share * market price
= 9.4 billion shares * $28.55
= 268.37 billion $
3)
1. Mean of x(x')= sum of values of x/ number of values of x=(18+5+12+4+6)/5=9
Variance of x= 
=(81+16+9+25+9)/4=35
Mean of y(y')= sum of values of y/ number of values of y=(0-3+15+12+1)/5=5
Variance of y= sum of 
=(25+64+100+49+9+16)/4=65.75
Covariance of x and y= 
=[(9*-5)+(-4*-8)+(3*10)+(-5*7)+(-3*-4)]/4= -1.5
2. Mean and Variance of each portfolio
a. mean= 1.25*9+(-.25*5)=10
Variance=
*35+(
)*65.75+2*1.25*-0.25*-1.5=59.744
b. mean=1*9+0*5=9
Variance=
*35+0*65.75+2*1*0*-1.5=35
c.mean= 0.75*9+(0.25*5)=8
Variance=
*35+(
)*65.75+2*0.75*0.25*-1.5=23.23
d.mean= 0.5*9+(0.5*5)=7
Variance=
*35+()*65.75+2*0.5*0.5*-1.5=24.44
e.mean= 0.75*5+(0.25*9)=6
Variance=*65.75+()*35+2*0.75*0.25*-1.5=38.6
f. mean=1*5+0*9=5
Variance=*65.75+0*35+2*1*0*-1.5=65.75
g. mean= 1.25*5+(-.25*9)=4
Variance=*65.75+()*35+2*1.25*-0.25*-1.5=105.86
3. Minimum variance portfolio is the one with 75% allocated to x and 25% allocated to y
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