Case Study 1_ Retirement Plan
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Case Study 1
Page 1
Case Study 1: Retirement Plan
Xuan Tu
Trine University
FIN 5823
Case Study 1
Page 2
This article discussed two approaches to compute the safe retirement income:
traditional approach and actuarial approach. The traditional approach takes 2 inputs:
-
expected return
-
median remaining lifespan
The actuarial approach takes 4 inputs:
-
expected return, -
portfolio volatility, -
median remaining lifespan,
-
confidence level
Both approaches compute the extraction rate.
The traditional approach is based on the assumption that:
-
the expected return is a constant value
-
the inflation is a constant value,
-
the lifespan is fixed
The disadvantage of this traditional approach is that it does not account for the
randomness in lifespan, inflation and market returns. It uses the average value
to represent the expected return which means there is a 50% possibility that
the return is below average and the retirement plan will fail. Similar case also
applies to the inflation rate and lifespan. In reality, many customers are
uncomfortable with the 50% chance of failure in their retirement plan.
However, the traditional plan cannot compute the extraction rate which gives a
higher success rate of retirement plan. The actuarial approach can better handle the randomness in lifespan, inflation
and market returns using Monte Carlo analysis. The portfolio volatility is taken
into consideration. This is achieved by finding a combination of stocks and
bonds which provide the same expected return as the traditional approach.
Given the volatility of the portfolio, the probability of a fully funded retirement
can be estimated.
In the case study, the arthur took an example of the following condition:
-
total return: 7%
-
inflation: 3%
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Related Questions
PLEASE ANSWER ALL THE QUESTIONS
Question 1
Fill the parts in the above table that are shaded in yellow. You will notice that there are nine line items.
Question 2
Using the data generated in the previous question (Question 1);a) Plot the Security Market Line (SML)
b) Superimpose the CAPM’s required return on the SML
c) Indicate which investments will plot on, above and below the SML?
d) If an investment’s expected return (mean return) does not plot on the SML, what does it show? Identify undervalued/overvalued investments from the graph
Question 3
From the information generated in the previous two questions;
a) Identify two investment alternatives that can be combined in a portfolio. Assume a 50-50 investment allocation in each investment alternative.
b) Compute the expected return of the portfolio thus formed.
c) Compute the portfolio’s beta. Is the portfolio aggressive or defensive?
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Arkansas Best Freightways is considering a purchase of three different potential trucks but is uncertain of the
cash inflows associated with the following investment scenarios.
Year
Year 0 (today)
Year 1
Year 2
Year 3
Year 4
Buy new truck
Increased profits
Increased profits
Increased profits
Increased profits
Investment 1
(85,000)
25,000
25,000
25,000
25,000
Investment 2
(105,000)
20,000
30,000
40,000
50,000
Investment 3
(125,000)
40,000
30,000
20,000
10,000
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The only kind of interest rate that can be used in the interest
Choose a match
formulas
engineering economy
Type of annuity where the series of payments continue
indefinitely
Choose a match
geometric gradient
Application of engineering or mathematical analysis and
synthesis to economic decisions
Choose a match
interest
A graphical representation of cashflows drawn on a time
Choose a match
principal
scale
perpetuity
Amount of money paid for the use of borrowed capital
Choose a match
cash flow diagram
Type of annuity where the payments are made at the end of
each period beginning on the first period
Choose a match
break even chart
A series of equal payments occurring at equal interval of
time.
Choose a match
ordinary annuity
a series of payments where annual payments increase or
decrease over time, by a constant percentage
Choose a match
compound interest
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Asset
A
B
C
E(Ri)
0.05
0.035
0.06
Variance
0.0015
0
0.008
You have not yet analyzed what your degree of risk aversion (A) is, but you know that your utility function behaves as follows: U[ E(Rp)] = E(Rp) - 0.5 * A * Variance. (See attached image for a better understanding)
You are asked to:(a) Find the optimal portfolio with these 3 assets {called wA, wB and wC}.b) Calculate the expected return and risk of the optimal portfolio for the following degrees of risk aversion (A):(i) A = 5(ii) A = 10(iii) A = 16
Please ASAP
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Select all of the time value of money factors that are known in a NPV assessment.
O Present value of single-sums
O Present value of annuities
O Interest rate
Number of periods
O Future value of single-sums
O Future value of annuities
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1. If you perform a NPV analysis on a perspective investment using a "d" = 15% and:
a. the NPV Is < 0, what can you tell me about the investment's IRR (time adjusted rate of return)?
b. the NPV is > 0, what can you tell me about the investment's IRR (time adjusted rate of return)?
c. the NPV is= 0, what can you tell me about the investment's IRR (time adjusted rate of return)?
2. We presume in Investment analysis that the payback method of evaluation is a better measure of.................than it is a measure of...................... We also think less of the payback method because it sometimes ignores the............., ..................of an investment since the................. the oftentimes occurs after the payback period has lapsed.
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Required:
Find the future value of the annuity, assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
Compare your findings in parts a(1) and a(2). All else being identical, which type of
annuity—ordinary or annuity due—is preferable? Explain why.
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The probability distributions of expected returns for the assets are shown in the following table:
Asset A
Prob
Return
0.2
-5%
0.4
10%
0.4
15%
a) Calculate the expected return for asset A.
b) Calculate the standard deviation for asset A.
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Use the following table to calculate the expected return from the asset.
Return
Probability
0.1
0.25
0.2
0.5
0.25
0.25
20.00%
18.75%
17.50%
15.00%
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Please answer fast I will rate for you sure....
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You are given the following data about Asset A and Asset B.
Asset A Asset B
Expected returns 8.6% 7.9%
Standard Deviation 3.8% 4.6%
Assuming that an investor is to choose between Asset A or Asset B, explain which asset
a rational investor will choose.
c) With the use of a diagram, explain why an investor will always choose a point on the
SML line.
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Question 1 Fill the parts in the above table that are shaded in yellow. You will notice that there are nineline items.
Question 2Using the data generated in the previous question (Question 1);a) Plot the Security Market Line (SML) b) Superimpose the CAPM’s required return on the SML c) Indicate which investments will plot on, above and below the SML? d) If an investment’s expected return (mean return) does not plot on the SML, what doesit show? Identify undervalued/overvalued investments from the graph
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Berdasarkan informasi tersebut a. Expected return Asset A b. Standard Deviation Asset A dan Asset B c. Portfolio AB Expected Return. d. Coefficient Correlation AB e. Portofolio AB Standard Deviation Please explain by Microsoft excel
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A decision maker has prepared the following payoff table.
States of Nature
High
95
Alternative
Low
Buy
10
Rent
65
35
Lease
45
50
Prior Probability
0.8
0.2
Using Baye's Decision Rule, what is the best decision and the expected payoff? (Round your answer to 1 decimal place.)
Best decision
Payoff
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Number of periods of time for a loan or investment.
Interest rate.
Future value of an investment based on a constant interest rate.
The constant periodic payment required to pay off a loan or investment.
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Time value of money question: Envision you are approached with an investment opportunity. You aregiven two alternatives to choose from. Investment A has a higher interest rate than Investment B.Investment A requires a greater number of periods until you receive the benefit than Investment B.
Applying concepts from the PV = FV/(1+r)^n (the NPV formula and discounting) describe the process ofhow you would decide which investment option would be better to invest in. Discussing how changes inboth the interest rate and the number of periods would affect this decision will help.
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Number of periods of time for a loan or investment.
The constant periodic payment required to pay off a loan or investment.
Periodic interest rate.
Present value of an investment.
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Beginning value
100
115.0
138.0
Year
1
2
3
End value
115.0
138.0
110.4
i.
compute the Arithmetic mean of the investment.
ii.
calculate the Geometric mean of the investment.
iii. With an appropriate illustration argue which one of the two measures issupe
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Vala
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The following investments and probabilities are presented:
INVESTMENT 1
Years
yield
probability
1
11
0.25
2
13
0.25
3
19
0.10
4
16
0.20
5
15
0.20
INVESTMENT 2
Years
yield
PROBABILITY
1
18
0.15
2
16
0.15
3
11
0.40
4
10
0.15
5
11
0.15
1
Calculate the expected return on each investment
2
Calculate the standard deviation of both investments and indicate which investment is riskier and why?
3
Calculate the coefficient of variation of both investments and indicate which investment is riskier and why?
In this case it is…
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Answers please
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When comparing investments with different horizons, the ____________ provides the more accurate comparison.
A. effective annual rate
B. average annual return
C. historical annual average
D. arithmetic average
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Present Value of an Annuity
Find the present value of the following ordinary annuities. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press PV, and find the PV of the annuity due.) Do not round intermediate calculations. Round your answers to the nearest cent.
$800 per year for 10 years at 8%.
$
$400 per year for 5 years at 4%.
$
$800 per year for 5 years at 0%.
$
Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities…
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