Sales growth Current assets/Sales Current liabilities/Sales Costs of goods sold/Sales Depreciation rate Interest rate on debt Interest paid on cash & marketable securities Tax rate Dividend payout ratio entered into the balance sheet and the interest is Year Income statement Sales Costs of goods sold Interest payments on debt Interest earned on cash & marketable securities Depreciation Profit before tax Taxes Profit after tax Dividends Retained earnings Balance sheet 1. PROJECT FINANCE In the project f 3.9 it is assumed that the firm pays off its initi installments of principal over five years. Change Debt repayment table (essentially a loan table from Cha the plug:
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Sales growth 15%Current assets/Sales 15%Current liabilities/Sales 8%Costs of goods sold/Sales 55%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 0%
entered into the balance sheet and the interest is put into the profit and loss statement.
Year12345
Year 0
Income statement
SalesCosts of goods soldInterest payments on debtInterest earned on cash & marketable securitiesDepreciationProfit before taxTaxesProfit after taxDividendsRetained earnings
Balance sheet
Cash and marketable securities - Current assets 200 Fixed assets At cost 2,000
1. PROJECT FINANCE In the project finance pro forma of section 3.9 it is assumed that the firm pays off its initial debt of 1,000 in equal installments of principal over five years. Change this assumption and assume instead that the firm pays off its debt in equal payments of interest and principal over five years.
Debt repayment table (essentially a loan table from Chapter 1): The principal amounts are
the plug: =C39-C28-C32
Depreciation - Net fixed assets 2,000 Total assets 2,200
Current liabilities 100 Debt Err:523Stock 1,100 Accumulated retained earnings - Total liabilities and equity Err:523
FREE CASH FLOW CALCULATION
Year 0
Profit after taxAdd back depreciationSubtract increase in current assetsAdd back increase in current liabilitiesSubtract increase in fixed assets at costAdd back after-tax interest on debt
Subtract after-tax interest on cash & mkt. securities
Free cash flow
RETURN ON EQUITY (ROE)
Year 0
Equity cash flow -1,100RETURN ON EQUITY (ROE) Err:523
Data table: ROE as a function of initial
equity investment 2,000
1,8001,6001,4001,2001,000
800
600400200
=B31-$B$7*(C30+B30)/2
Note that the cash flow generated by depreciation equals the increase in fixed assets at cost.
<-- No dividends until all the debt is paid off
Principal Debt Of which:
at begin. payment Repaidof year at end yr. Interest principal
2. MEGA Corporation is considering leasing an asset from BASIS A Corporation. Here are the relevant facts: Asset cost $250,000; Depreciation schedule:Year1: 30%; Year 2: 22%; Year 3: 19.20%; Year 4: 11.52%; Year 5: 11.52%; Year 6: 5.76%. Lease term 6 years. Lease payment $50,000 per year, at the beginning of years 0, 1, …, 5 Asset residual value =Zero; Tax rates MEGA:TC = 0% (MEGA has tax-loss carryforwards that prevent it from utilizing any additional tax shields) ;BASIS A: TC = 20%.Show that it will be advantageous both for MEGA to lease the asset and for BI to purchase the asset in order to lease it out to MEGA.
MEGA Corporation is considering leasing an asset from BASIS A Corporation. Here are the relevant facts:Asset cost $250,000; Depreciation schedule:Year1: 30%; Year 2: 22%; Year 3: 19.20%; Year 4: 11.52%; Year 5: 11.52%; Year 6: 5.76%. Lease
term 6 years. Lease payment $50,000 per year, at the beginning of years 0, 1, …, 5 Asset residual value =Zero; Tax rates MEGA:TC = 0% (MEGA has tax-loss carryforwards that prevent it from utilizing any additional tax shields) ;BASIS A: TC = 20%.Show that it will be advantageous both for MEGA to lease the asset and for BI to purchase the asset in order to lease it out to MEGA.
cost of asset 1,000,000lease term 15residual value 300,000equity 200,000debt 800,000 15-year term loan, equal payments of interest & principalinterest 10%annual debt payment 105,179 annual rent received 110,000 tax rate 40%
CALCULATING THE MULTIPLE-PHASES METHOD (MPM) RETURN--REQUIRES SOLVERinvestment at
year beginning of year cash flow
1 200,000 19,488
3. Your company is considering either purchasing or leasing an asset that costs $1,000,000. The asset, if purchased, will be depreciated on a straight-line basis over 15 years to a zero residual value. A leasing company is willing to lease the asset for $300,000 per year; the first payment on the lease is due at the time the lease is undertaken (i.e., year 0), and the remaining five payments are due at the beginning of years 1-15. Your company has a tax rate tc = 40 percent and can borrow at 10 percent from its bank. Reconsider the leveraged-leasing example. Show that if depreciation is straight line over 15 years, then the MPM rate of return is equal to the IRR. Explain.
CALCULATING THE MULTIPLE-PHASES METHOD (MPM) RETURN--REQUIRES SOLVERattribution of cash flow
income investment Explanation: When all of the cash flows8,357 11,131 from the lease are positive, the MPM return
Your company is considering either purchasing or leasing an asset that costs $1,000,000. The asset, if purchased, will be depreciated on a straight-line basis over 15 years to a zero residual value. A leasing company is willing to lease the asset for $300,000 per year; the first payment on the lease is due at the time the lease is undertaken (i.e., year 0), and the remaining five payments are due at the beginning of years 1-15. Your company has a tax rate tc = 40 percent and can borrow at 10 percent from its bank. Reconsider the leveraged-leasing example. Show that if depreciation is straight line
7,892 10,588 will be the same as the IRR. When the depreciation7,450 9,923 is straight-line over the life of the asset, this7,035 9,119 will be the case.6,654 8,1606,313 7,0266,019 5,6975,781 4,1515,608 2,3625,509 3025,497 -2,0605,583 -4,7595,781 -7,8316,109 -11,3196,582 -15,2697,220 172,780
will be the same as the IRR. When the depreciation
BASIC LEVERAGED LEASE EXAMPLE
To answer this question, you have to run the Solver macro found on the This program can also be run by [ctr]+a.
cost of asset 1,000,000lease term 15residual value 300,000equity 200,000debt 800,000 15-year term loan, equal payments of interest & principalinterest 10%annual debt payment 105,179 annual rent received 150,000 tax rate 40%
4.Your company is considering either purchasing or leasing an asset that costs $1,000,000. The asset, if purchased, will be depreciated on a straight-line basis over 15 years to a zero residual value. A leasing company is willing to lease the asset for $300,000 per year; the first payment on the lease is due at the time the lease is undertaken (i.e., year 0), and the remaining five payments are due at the beginning of years 1-15. Your company has a tax rate tc = 40 percent and can borrow at 10 percent from its bank. In the leveraged-lease example , find the lowest lease rental so that the MPM is equal to the IRR (assume the original depreciation schedule).
The VBA program on this workbook runs the Solver for a number of different values of the lease rent. The startingvalue is given in the cell "Start" (B40), and the increases are given by the cell "Increase" (B41).Thus, for the values given in this particular case, [ctr]+a will find the MPM for rents of 120000,122000, 124000 ...
Note that the MPM <= IRR.Here you can see that the smallest rent for which the MPM = IRR is 142,000 (this number is, of course, approximate).
Your score is:
15-year term loan, equal payments of interest & principal
principal repayment
at start loan of CASH
depreciation of year payment interest principal FLOW
Your company is considering either purchasing or leasing an asset that costs $1,000,000. The asset, if purchased, will be depreciated on a straight-line basis over 15 years to a zero residual value. A leasing company is willing to lease the asset for $300,000 per year; the first payment on the lease is due at the time the lease is undertaken (i.e., year 0), and the remaining five payments are due at the beginning of years 1-15. Your company has a tax rate tc = 40 percent and can borrow at 10 percent from its bank. In the leveraged-lease example , find the lowest lease rental so that the MPM is equal to the IRR (assume the original depreciation schedule).
Following are annual return statistics for two mutual funds from the Future Generation family: see rows 5-32 Use Excel to graph the combinations of standard deviation of return (x-axis) and expected return (y-axis) by varying the percentage of SP 500 in the portfolio from 0% to 100%.
Weekly statistics for optimal portfolioPortfolio mean -0.985% #VALUE!Portfolio variance 0.0011 #VALUE!Portfolio sigma 3.272%
Annual statistics for optimal portfolioPortfolio mean -51.25% #VALUE!Portfolio sigma 23.59% #VALUE!
Constant -0.4061 #VALUE!-0.2 -0.0019
-0.15 -0.0014-0.1 -0.0006
-0.05 0.00220 -0.6039
6. On the spreadsheet with this exam you will find the weekly stock prices and market capitalizations of equity for five American stocks. 6.1. For each stock, compute the mean returns, standard deviation of returns.6.2. Compute the variance-covariance matrix for the five stocks.6.3. Suppose that the annual interest rate is 5%. Find an optimal portfolio. Give the portfolio proportions and the portfolio’s annualized mean and annualized standard deviation.6.4. Is there an all positive portfolio on the efficient frontier?
Optimalportfolio
All positive portfolio? Below I do a data table for the constant.For all constants, the minimum portfolio position is negative
Weekly statistics for optimal portfolioPortfolio mean 77.110% #VALUE!Portfolio variance 0.0000 #VALUE!Portfolio sigma 0.028%
Annual statistics for optimal portfolioPortfolio mean 4009.71% #VALUE!Portfolio sigma 0.20% #VALUE!
7. Refer to the same data and variance-covariance matrix as in the previous problem.7.1. Compute the annualized expected returns for each stock under the following assumptions:• These five stocks constitute a benchmark portfolio. • The risk-free rate is 4% annually.• The expected annual benchmark return is 12%.7.2. Ms NNN is an eminent stock analyst. She thinks that the annualized return for Kroger will be 12% annually, but has no opinions about any of the other stock’s returns. What should be her optimal portfolio holdings of the five stocks?
Benchmark return
Benchmarkreturns
Annualreturns
Benchmark return
Constant 0.0017 #VALUE!-0.2 0.0017
-0.15 0.0017-0.1 0.0017
-0.05 0.00170 0.0017
0.05 0.00170.1 0.0017
0.15 0.00170.2 0.0017
0.25 0.00170.3 0.0017
0.35 0.00170.4 0.0017
0.45 0.00170.5 0.0017
0.55 0.00170.6 0.0017
0.65 0.00170.7 0.0017
0.75 0.00170.8 0.0017
0.85 0.00170.9 0.0017
0.95 0.00171 0.0017
1.05 0.00171.1 0.0017
1.15 0.00171.2 0.0017
1.25 0.00171.3 0.0017
1.35 0.00171.4 0.0017
1.45 0.00171.5 0.0017
1.55 0.00171.6 0.0017
All positive portfolio? Below I do a data table for the constant.For all constants, the minimum portfolio position is positive
Mean 0.08062 0.12146Variance 0.06714 0.22571Covariance 0.09672
Proportion of 1 -0.9Portfolio mean 15.82%Portfolio var. 53.84% 0.054385 0.814807 -0.33077775540131Portfolio st. dev. 73.38% 0.538414
Data table of portfolios
Proportion of 1 0.7338 15.82%-1.4 88.42% 17.86%
-1.15 80.86% 16.84%-0.9 73.38% 15.82%
-0.65 65.98% 14.80%-0.4 58.72% 13.78%
-0.15 51.64% 12.76%0.1 44.82% 11.74%
0.35 38.42% 10.72%0.6 32.67% 9.70%
0.85 27.97% 8.67%1.1 24.94% 7.65%
8. This problem returns to the four-asset problem Calculate the envelope set for these four assets and show that the individual assets all lie within this envelope set. You should get a graph.
20% 30% 40% 50% 60% 70% 80% 90% 100%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Efficient Frontier Showing the Individual Stocks
Standard deviation of portfolio
Ex
pe
cte
d p
ort
foli
o r
etu
rn
Stock B
Stock A
Stock C
Stock D
1.35 24.21% 6.63%1.6 25.97% 5.61%
1.85 29.78% 4.59%2.1 34.98% 3.57%
2.35 41.04% 2.55%2.6 47.64% 1.53%
2.85 54.58% 0.51%Stock A 24.49% 6.00%Stock B 67.08% 10.00%Stock C 87.75% 12.00%Stock D 94.34% 15.00%
20% 30% 40% 50% 60% 70% 80% 90% 100%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Efficient Frontier Showing the Individual Stocks
Standard deviation of portfolio
Ex
pe
cte
d p
ort
foli
o r
etu
rn
Stock B
Stock A
Stock C
Stock D
Mean minusconstant
1%5%7%
10%
Calculate the envelope set for these four assets and show that the individual assets all lie within this
20% 30% 40% 50% 60% 70% 80% 90% 100%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Efficient Frontier Showing the Individual Stocks
Standard deviation of portfolio
Ex
pe
cte
d p
ort
foli
o r
etu
rn
Stock B
Stock A
Stock C
Stock D
20% 30% 40% 50% 60% 70% 80% 90% 100%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Efficient Frontier Showing the Individual Stocks
Standard deviation of portfolio
Ex
pe
cte
d p
ort
foli
o r
etu
rn
Stock B
Stock A
Stock C
Stock D
DOW-JONES 30 INDUSTRIALS, RETURN DATA for Dec. 93 - April 99
9. Using the data base of the DJ Industrials—For American Airlines (AA), Procter & Gamble (PG), and GeneralElectric (GE)—compute:a. The average monthly returnsb. The covariances of the monthly returns: σAA,AA = Covariance(RAA, RAA), σPG,PG = Covariance(RPG, RPG), σGE,GE = Covariance (RGE,RGE)—these are equal to the variance of AA, PG, and GE respectively. σAA, GE = Covariance (RAA, RGE), σAA,PG = Covariance (RAA, RPG),σPG, GE = Covariance(RPG, RGE).c. What are the monthly expected return and monthly standard deviation of a portfolio which is invested in the three stocks respectively:0,2 and 0,4 and 0,4?
Mean return 19.63% 24.26% ### Mean returnReturn variance 0.036632975 0.08896225 ### Return varianceStandard deviati 19.14% 29.83% ### Standard deviationCovariance 0.0172 ### CovarianceCorrelation 0.3318 ### Correlation
11. KazZink and KazakhMys are two kazakh exploration firms. The following table (see rows 3-16) gives the end-of-year stock prices for each of the firms for the years 1995-2006 as well as the dividends paid in the years 1995-2006.a. For the decade 1995-2006 calculate the following:1.Annual returns from each of the shares. (Don't forget the dividends!)2.The mean, variance, and standard deviation of each stock's return.3.The covariance and the correlation coefficient of the returns.b. Graph the mean portfolio return (y-axis) against the standard deviation of the portfolio return (x-axis) for portfolios of the two shares in which the weight of KazZink goes from 0 to 1.4.
NOTE: you can also use
A B C D E F G
1
2
345
6
7
8
9
10
11
12
13
14
15
161718192021222324252627282930313233343536
UN-5H
Page 69
Proportion of KazZ 0.24Portfolio mean 23.15% ###Portfolio variance 5.98% ###Portfolio s. dev. 24.45% ###
S. dev. MeanProportion <-- Contains the data table header, which has been hidden
KazZink and KazakhMys are two kazakh exploration firms. The following table (see rows 3-16) gives the end-of-year stock prices for each of the firms for the years 1995-2006 as well as
1.Annual returns from each of the shares. (Don't forget the dividends!)
b. Graph the mean portfolio return (y-axis) against the standard deviation of the portfolio return (x-axis) for portfolios of the two shares in which the weight of KazZink goes from 0 to
NOTE: you can also use discrete returns
H I J
1
2
345
6
7
8
9
10
11
12
13
14
15
161718192021222324252627282930313233343536
UN-5H
Page 71
<-- Contains the data table header, which has been hidden
16% 18% 20% 22% 24% 26% 28% 30% 32%
17%
19%
21%
23%
25%
27%
Portfolio Returns--Pfizer and Merck
Standard deviation
Me
an
re
turn
16% 18% 20% 22% 24% 26% 28% 30% 32%
17%
19%
21%
23%
25%
27%
Portfolio Returns-KazZink and KazakhMys
Standard deviation
Me
an
re
turn
H I J37383940414243444546474849505152535455565758596061
Answer to Problem 1
Leggett Herman Shaw
La-Z-Boy Kimball Flexsteel & Platt Miller Industries
12.In the following table you will find annual return data for six furniture companies between the years 1982 and 1992. Use these data to calculate the variance-covariance matrix of the returns in the next sheet.
13. For the given variance- covariance matrix below : Supposing that the standard deviation of the market index is 18 percent,calculate the variance-covariance matrix using the single-index model.
mean 31.35% 37.07%variance 4.10% 6.15%covariance 0.0485016
sample portfolio calculation
proportion 0.3mean 35.35%variance 5.42%
14. DATA FOR 6 FURNITURE COMPANIES. In Chapter 8 you were asked to calculate the variance-covariance matrix of returns for six furniture companies. The calculated variance-covariance matrix and mean returns for these firms are as follows:(see rows 4-10) a. Given this matrix, and assuming that the risk-free rate is 0 percent, calculate the efficient portfolio of these six firms. b. Repeat, assuming that the risk-free rate is 10 percent. c. Use these two portfolios to generate an efficient frontier for the six furniture companies. Plot this frontier. d. Is there an efficient portfolio with only positive proportions of all the assets?[
A crude test to see if we can generate positive portfolio weights we vary r tosee what the portfolio proportions are (in a data table). No portfolioproportions seem to give a positive weight to the third asset.
Portfolio weightsLa-Z-Boy Kimball Flexsteel & Platt Miller
In Chapter 8 you were asked to calculate the variance-covariance matrix of returns for six furniture companies. The calculated variance-covariance matrix and mean returns for these firms are as follows:(see rows 4-10) a. Given this matrix, and assuming that the risk-free rate is 0 percent, calculate the efficient portfolio of these six firms. b. Repeat, assuming that the risk-free rate is 10 percent. c. Use these two portfolios to generate an efficient frontier for the six furniture companies. Plot this frontier. d. Is there an efficient portfolio with only positive proportions of all the assets?[
raw normalized When epsilon = 1, the variance-covariance matrix is the originalportfolio weights matrix (as in Exercise 1). For this case the optimized portfolio
3.1708 0.7203 contains at least one short-selling position (illustrated here).0.4861 0.1104 minimum
-2.4405 -0.5544 port. weight1.3533 0.3074 -0.5544 is zero. You can determine manually that when epsilon is larger0.0614 0.0140 than this, there are short-selling positions.1.7712 0.4023
diagonal. (Try setting epsilon = 0 to see what this means.)
15. A sufficient condition to produce positively weighted efficient portfolios is that the variance-covariance matrix be diagonal, that is, that σij = 0, for i≠j. By continuity, positively weighted portfolios will result if the offdiagonal elements of the variance-covariance matrix are sufficiently small compared to the diagonal. Consider a transformation of this matrix in which
We use Solver to determine epsilon so that the entry in cell E22
Epsilon "shrinks" the variance-covariance matrix towards the
When epsilon = 1, the variance-covariance matrix is the originalmatrix (as in Exercise 1). For this case the optimized portfoliocontains at least one short-selling position (illustrated here).
is zero. You can determine manually that when epsilon is largerthan this, there are short-selling positions.
diagonal. (Try setting epsilon = 0 to see what this means.)
to determine epsilon so that the entry in cell E22
"shrinks" the variance-covariance matrix towards the
Mean 0.09372 0.12707Variance 0.08624 0.20608Covariance 0.11692
Proportion of 1 -0.9Portfolio mean 15.71%Portfolio var. 41.39% 0.069854 0.743945 -0.39986641Portfolio st. dev. 64.34% 0.413933
Data table of portfolios
Proportion of 1 0.6434 15.71%-1.4 75.52% 17.37%
-1.15 69.89% 16.54%-0.9 64.34% 15.71%
-0.65 58.88% 14.87%-0.4 53.55% 14.04%
-0.15 48.39% 13.21%0.1 43.45% 12.37%
0.35 38.84% 11.54%0.6 34.66% 10.71%
0.85 31.11% 9.87%1.1 28.41% 9.04%
16. This problem returns to the four-asset problem considered in section 7.5:Calculate the envelope set for these four assets and show that the individual assets all lie within this envelope set. You should get a graph that looks something like the following:(see part in right of the calculations)
20% 30% 40% 50% 60% 70% 80%
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
20%
Efficient Frontier Showing the Individual Stocks
Standard deviation of portfolio
Ex
pe
cte
d p
ort
foli
o r
etu
rn
Stock B
Stock A
Stock C
Stock D
1.35 26.82% 8.21%1.6 26.55% 7.37%
1.85 27.63% 6.54%2.1 29.92% 5.70%
2.35 33.16% 4.87%2.6 37.12% 4.04%
2.85 41.58% 3.20%Stock A 31.62% 6.00%Stock B 54.77% 8.00%Stock C 63.25% 10.00%Stock D 70.71% 15.00%
Mean 2.33% #VALUE!Variance 0.56% #VALUE!Sigma 7.50% #VALUE!
17. The following table shows the var-covar matrix and the mean return for six stocks: a) compute the global minmum variance portfolio(GMVP), b) compute the efficient portfolio aasuming a monthly trisk-free rate of 0.45%, c) show the frontier as the expected return and standard deviation.
KrogerKR
FordF
TargetTGT
Juniper Networks
JNPRAholdAHO
KeyCorpKEY
Note that the book formula for the GMVP is for a row vector; here we want a column vector, hence Transpose.
Drawing the efficient frontier: By Proposition 2 of Chapter 9, the efficient frontier is the convex combination of any two frontier portfolios. Thus combining the GMVP and the efficient portfolio will give us the whole frontier. We do this below.
Covar -0.00233966 #VALUE!
Proportion of GMVP 0.3Proportion of efficient 0.7 #VALUE!
Drawing the efficient frontier: By Proposition 2 of Chapter 9, the efficient frontier is the convex combination of any two frontier portfolios. Thus combining the GMVP and the efficient portfolio will give us the whole frontier. We do this below.
Expected portfolioreturn
0% 5% 10% 15% 20% 25%
-3%
-2%
-1%
0%
1%
2%
3%
4%
5% Portfolio Returns & Sigma
Standard deviation
Exp
ecte
d r
etu
rn
0.24% 1-0.89% 10.48% 10.44% 1
-1.46% 11.04% 1
combination of GMVP and the eficient portfolio.
The following table shows the var-covar matrix and the mean return for six stocks: a) compute the global minmum variance portfolio(GMVP), b) compute the efficient portfolio aasuming a monthly trisk-free rate of 0.45%, c) show the
Mean returns
Note that the book formula for the GMVP is for a row vector; here we want a column vector, hence Transpose.
Drawing the efficient frontier: By Proposition 2 of Chapter 9, the efficient frontier is the convex combination of any two frontier portfolios. Thus combining the GMVP and the efficient portfolio will give us the whole frontier. We do
Drawing the efficient frontier: By Proposition 2 of Chapter 9, the efficient frontier is the convex combination of any two frontier portfolios. Thus combining the GMVP and the efficient portfolio will give us the whole frontier. We do
0% 5% 10% 15% 20% 25%
-3%
-2%
-1%
0%
1%
2%
3%
4%
5% Portfolio Returns & Sigma
Standard deviation
Exp
ecte
d r
etu
rn
Solving an Unconstrained Portfolio Problem
Variance-covariance matrix Means
0.10 0.03 -0.08 0.05 8%0.03 0.20 0.02 0.03 9%
-0.08 0.02 0.30 0.20 10%0.05 0.03 0.20 0.90 11%
c 8.0% 3.00%
Optimal portfolio without short sale restrictions (Chapter 9, Proposition 1)
18.To set the scene, consider the following optimization problem, which is solved without any short-sale constraints. The spreadsheet shows a four asset variance-covariance matrix and associated expected returns. Given a constants c = 8 percent, find the optimal portfolio . By changing the value of c in the spreadsheet,to c = 3%, compute other portfolio; show the frontier as the expected return and standard deviation.
PORTFOLIO OPTIMIZATION ALLOWING SHORT SALESFollows Proposition 1, Chapter 9