Lesson 6 Homework 100 Points Chapter 11 Q1: What is the essential difference bet

Lesson 6 Homework
100 Points
Chapter 11
Q1: What is the essential difference between sensitivity analysis and scenario analysis?
Solution:
Example for Question 2: Calculating Break-Even: In each of the following cases, calculate the accounting
break-even and the cash break-even points. Ignore any tax effects in calculating the cash break-even.
Unit
Price Unit Variable Cost Fixed Costs Depreciation
$2,980
46
9
$2,135
41
3
$8,100,000
185,000
2,770
$3,100,000
183,000
1,050
Solution:
The cash break-even equation is:
QC = FC/(P – v)
And the accounting break-even equation is:
QA = (FC + D)/(P – v)
Using these equations, we find the following cash and accounting break-even points:
a. QC = $8,100,000/($2,980 – 2,135) QA = ($8,100,000 + 3,100,000)/($2,980 – 2,135)
QC = 9,585.80 QA = 13,254.44
b. QC = $185,000/($46 – 41) QA = ($185,000 + 183,000)/($46 – 41)
QC = 37,000 QA = 73,600
c. QC = $2,770/($9 – 3) QA = ($2,770 + 1,050)/($9 – 3)
QC = 461.67 QA = 636.67
(Please also see Homework 6 Excel Examples for computation on Excel)
Q2: Calculating Break-Even: In each of the following cases, calculate the accounting break-even and the
cash break-even points. Ignore any tax effects in calculating the cash break-even.
Unit
Price Unit Variable Cost Fixed Costs Depreciation
$2,080
40
9
$2,150
35
3
$6,100,000
185,000
2,770
$3,100,000
183,000
1,050
(Please follow above example to solve this question)
Example for Question 3: Using Break-Even Analysis: Consider a project with the following data:
Accounting break-even quantity = 13,700 units; cash break-even quantity = 9,600 units; life = five years;
fixed costs = $185,000; variable costs = $23 per unit; required return = 12 percent. Ignoring the effect of
taxes, find the financial break-even quantity.
Solution:
In order to calculate the financial break-even, we need the OCF of the project. We can use the cash and
accounting break-even points to find the OCF. First, we will use the cash break-even to find the price
of the product as follows:
QC = FC/(P – v)
9,600 = $185,000/(P – $23)
P = $42.27
Now that we know the product price, we can use the accounting break-even equation to find the
depreciation. Doing so, we find the annual depreciation must be:
QA = (FC + D)/(P – v)
13,700 = ($185,000 + D)/($42.27 – 23)
Depreciation = $79,010
We now know the annual depreciation amount. Assuming straight-line depreciation is used, the
initial investment in equipment must be five times the annual depreciation, or:
Initial investment = 5($79,010)
Initial investment = $395,052
The PV of the OCF must be equal to this value at the financial break-even since the NPV is zero, so:
$395,052 = OCF(PVIFA12%,5)
OCF = $109,591.29
We can now use this OCF in the financial break-even equation to find the financial break-even sales
quantity:
QF = ($185,000 + 109,591.29)/($42.27 – 23)
QF = 15,286.90
(Please also see Homework 6 Excel Examples for computation on Excel)
Q3: Using Break-Even Analysis: Consider a project with the following data: Accounting break-even
quantity = 13,700 units; cash break-even quantity = 9,000 units; life = five years; fixed costs = $180,000;
variable costs = $20 per unit; required return = 12 percent. Ignoring the effect of taxes, find the financial
break-even quantity.
(Please follow above example to solve this question)
Chapter 13
Q4: In broad terms, why are some risks diversifiable? Why are some risks nondiversifiable? Does it
follow that an investor can control the level of unsystematic risk in a portfolio, but not the level of
systematic risk?
Solution:
Example for Question 5: Portfolio Expected Return: You own a portfolio that is invested 35 percent in
Stock X, 20 percent in Stock Y, and 45 percent in Stock Z. The expected returns on these three stocks are
9 percent, 15 percent, and 12 percent, respectively. What is the expected return on the portfolio?
Solution:
The expected return of a portfolio is the sum of the weight of each asset times the expected return of each
asset. So, the expected return of the portfolio is:
E(RP) = .35(.09) + .20(.15) + .45(.12)
E(RP) = .1155, or 11.55%
(Please also see Homework 6 Excel Examples for computation on Excel)
Q5: Portfolio Expected Return: You own a portfolio that is invested 30 percent in Stock X, 18 percent in
Stock Y, and 52 percent in Stock Z. The expected returns on these three stocks are 10 percent, 15
percent, and 12 percent, respectively. What is the expected return on the portfolio?
(Please follow above example to solve this question)
Example for Question 6: Returns and Standard Deviations: Consider the following information:
State of
Economy
Probability of
State of
Economy
Rate of Return If State Occurs
Stock A Stock B Stock C
Boom
Good
Poor
Bust
.10
.60
.25
.05
.35
.16
−.01
−.12
.40
.17
−.03
−.18
.27
.08
−.04
−.09
a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected
return of the portfolio?
b. What is the variance of this portfolio? The standard deviation?
Solution:
a. This portfolio does not have an equal weight in each asset. We first need to find the return of the
portfolio in each state of the economy. To do this, we will multiply the return of each asset by
its portfolio weight and then sum the products to get the portfolio return in each state of the
economy. Doing so, we get:
Boom: RP = .30(.35) + .40(.40) + .30(.27) = .3460, or 34.60%
Good: RP = .30(.16) + .40(.17) + .30(.08) = .1400, or 14.00%
Poor: RP = .30(–.01) + .40(–.03) + .30(–.04) = –.0270, or –2.70%
Bust: RP = .30(–.12) + .40(–.18) + .30(–.09) = –.1350, or –13.50%
And the expected return of the portfolio is:
E(RP) = .10(.3460) + .60(.1400) + .25(–.0270) + .05(–.1350)
E(RP) = .1051, or 10.51%
b. To calculate the standard deviation, we first need to calculate the variance. To find the variance,
we find the squared deviations from the expected return. We then multiply each possible
squared deviation by its probability, then add all of these up. The result is the variance. So, the
variance and standard deviation of the portfolio are:
P2 = .10(.3460 – .1051)2 + .60(.1400 – .1051)2 + .25(–.0270 – .1051)2 + .05(–.1350 – .1051)2
P2 = .01378
P = .013781/2
P = .1174, or 11.74%
(Please also see Homework 6 Excel Examples for computation on Excel)
Q6: Returns and Standard Deviations: Consider the following information:
State of
Economy
Probability of
State of
Economy
Rate of Return If State Occurs
Stock A Stock B Stock C
Boom
Good
Poor
Bust
.10
.50
.25
.15
.35
.16
−.02
−.12
.40
.15
−.03
−.18
.27
.08
−.04
−.10
c. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected
return of the portfolio?
d. What is the variance of this portfolio? The standard deviation?
(Please follow above example to solve this question)
Example for Question 7: Using CAPM: A stock has a beta of 1.15, the expected return on the market is
10.3 percent, and the risk-free rate is 3.1 percent. What must the expected return on this stock be?
Solution:
CAPM states the relationship between the risk of an asset and its expected return. CAPM is:
E(Ri) = Rf + [E(RM) – Rf] × i
Substituting the values we are given, we find:
E(Ri) = .031 + (.103 – .031)(1.15)
E(Ri) = .1138, or 11.38%
(Please also see Homework 6 Excel Examples for computation on Excel)
Q7: Using CAPM: A stock has a beta of 1.50, the expected return on the market is 10.5 percent, and the
risk-free rate is 3.5 percent. What must the expected return on this stock be?
(Please follow above example to solve this question)
Example for Question 8: Using CAPM: A stock has an expected return of 10.2 percent, the risk-free rate
is 3.9 percent, and the market risk premium is 7.2 percent. What must the beta of this stock be?
Solution:
We are given the values for the CAPM except for the beta of the stock. We need to substitute these values
into the CAPM, and solve for the beta of the stock. One important thing we need to realize is that we are
given the market risk premium. The market risk premium is the expected return of the market minus the
risk-free rate. We must be careful not to use this value as the expected return of the market. Using the
CAPM, we find:
E(Ri) = .102 = .039 + .072i
i = .88
(Please also see Homework 6 Excel Examples for computation on Excel)
Q8: Using CAPM: A stock has an expected return of 10.8 percent, the risk-free rate is 3.6 percent, and
the market risk premium is 7.5 percent. What must the beta of this stock be?
(Please follow above example to solve this question)

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