Physical Education
smathew1996
Referencenotes2.pptx5-1
MBA 906 –Financial Strategy and Governance
Dr. Kashif Saleem
E-mail: [email protected]
Office: Room 4.18, 4th floor
9-2
Net Present Value and Other
Investment Criteria
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9-3
Replace Expand
Maintenance
or
Obsolescence
Current Product
or
Current Service
Cost
Reduction
New Product or
New Service
Uses of Capital Budgeting
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9-4
Our Task:
To determine if we should invest in/purchase the project.
HOW?
9-5
Good Decision Criteria
For each of the criteria listed above, we need to ask following questions when evaluating capital budgeting decision rules:
Does the decision rule adjust for the time value of money?
Does the decision rule adjust for risk?
Does the decision rule provide information about wealth creation, that is, whether we are creating value for the firm?
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9-6
Payback Period
Definition: How long does it take to get the initial cost back in a nominal sense?
Computation:
Estimate the cash flows
Subtract the future cash flows from the initial cost until the initial investment has been recovered
9-7
Project Example Information
You are reviewing a new project and have estimated the following cash flows:
Year 0: CF = -165,000
Year 1: CF = 63,120; NI = 13,620
Year 2: CF = 70,800; NI = 3,300
Year 3: CF = 91,080; NI = 29,100
Average Book Value = 72,000
Your required return for assets of this risk level is 12%.
8.7
9-8
Project Example - Visual
R = 12%
$ -165,000
1
2
3
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
The required return for assets of this risk level is 12% (as determined by the firm).
Year 1: $165,000 – 63,120 = 101,880
We need to get to zero so keep going…
Year 2: $101,880 – 70,800 = 31,080
We need to get to zero so keep going…
Year 3: $31,080 – 91,080 = -60,000
We “passed” zero so payback is achieved
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9-9
Payback Decision
We need to know a “management’s number”. What does the firm use for the evaluation of its projects when they use payback?
Most companies use either 3 or 4 years.
Let’s use 3 in our numerical example
9-10
Payback Decision
Our computed payback was 3 years
The firm’s uses 4 years as it’s criteria, so…
YES, we Accept this project as we recover our cost of the project early.
9-11
Discounted Payback Period
Definition: How long does it take to get the initial cost back after you bring all of the cash flows to the present value.
Computation:
Estimate the present value of the cash flows
Subtract the future cash flows from the initial cost until the initial investment has been recovered
9-12
Discounted Payback Computation
56,357
56,441
64,829
R = 12%
$ -165,000
1
2
3
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
Year 1: 165,000 – 56,357 = 108,643; continue
Year 2: 108,643 – 56,441 = 52,202; continue
Year 3: 52,202 – 64,829 = -12,627; finished
9-13
Net Present Value
Definition: The difference between the market value of a project and its cost
Computation:
Estimate the future cash flows
Estimate the required return for projects of this risk level.
3. Find the present value of the cash flows and subtract the initial investment.
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9-14
NPV – Decision Rule
A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal, as measured in dollar terms.
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Project Example - NPV
R = 12%
$ -165,000
1
2
3
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
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9-16
Discounted Payback Computation
56,357
56,441
64,829
R = 12%
$ -165,000
1
2
3
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
177,627 = PV of all cash flows
NPV =$177,627 - $165,000 = $12,627
9-17
Net Present Value Decision
If the NPV is positive
(NPV > $0), then we ACCEPT the project. Conversely, if the NPV is negative, then we REJECT the project.
Thus in our case, the NPV is $12,627 so we ACCEPT the project.
9-18
Profitability Index
Definition: The PI measures the benefit per unit cost of a project, based on the time value of money. It is very useful in situations where you have multiple projects of hugely different costs and/or limited capital (capital rationing).
Computation: PI = PV of Inflows
PV of Outflows
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9-19
Profitability Index Example
PI = PV of Inflows
PV of Outflows
$177,627 = 1.0765
$165,000
A Profitability Index of 1.076 implies that for every $1 of investment, we create an additional $0.0765 in value. A PI >1 means the firm is increasing in value.
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9-20
Average Accounting Return
Definition: The AAR is a measure of the average accounting profit compared to some measure of average accounting value of a project. The AAR is then compared to a required return by the company.
Computation: AAR = Average Net Income
Average Book Value
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9-21
Project Example Information
You are reviewing a new project and have estimated the following cash flows:
Year 0: CF = -165,000
Year 1: CF = 63,120; NI = 13,620
Year 2: CF = 70,800; NI = 3,300
Year 3: CF = 91,080; NI = 29,100
Average Book Value = 72,000
Your required return for assets of this risk level is 25%.
8.21
9-22
Average Accounting Return
Using the figures of our previous example:
1. ($13,620 + 3,300 + 29,100) / 3
46,020/ 3 = $15,340
AAR = 15,340 /72,000 = .2131 or 21%
If we compare this to our firm’s requirement of 25%, then we would Reject this project as the AAR < 25%
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Internal Rate of Return
This is the most important alternative to NPV
It is often used in practice and is intuitively appealing
It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere
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Internal Rate of Return
Definition: It is the discount rate (or required return) that will bring all of the cash flows into present value time and total the exact value of the cost of the project.
Said another way, IRR is the return that will yield a NPV = $0.
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9-25
Computing IRR for the Project
If no Excel, then Trial & Error with linear interpolation
Step1: Start off with an initial guess and compute NPV.
Step2: If NPV >0, take a second guess that would give a negative NPV (if NPV<0, second guess should have a positive NPV).
Step3: Once we have two opposing NPV values, use linear interpolation to find the approximate IRR value
IRR = 16.30 % > 12% required return:
thus we ACCEPT the project.
iL: Lower of i
NPVL: NPV computed using iL.
iU: Upper value of i
NPVU: NPV computed using iU.
Where:
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IRR – Decision Rule
If the IRR of a project is greater than the firm’s cost of capital, then we would accept the project
Since our goal is to increase owner wealth, IRR is a direct measure of how well this project will meet our goal, as measured in interest rate terms.
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Mutually Exclusive Projects
Mutually exclusive projects:
If you choose one, you can’t choose the other
Example: You can choose to attend graduate school at either Harvard or Stanford, but not both
Intuitively, you would use the following decision rules:
NPV – choose the project with the higher NPV
IRR – choose the project with the higher IRR
9-28
Mutually Exclusive Projects
| Period | Project A | Project B |
| 0 | -500 | -400 |
| 1 | 325 | 325 |
| 2 | 325 | 200 |
| IRR | 19.43% | 22.17% |
| NPV | $64.05 | $60.74 |
If the required rate of return for the firm is 10% and Projects A and B are both of equal risk, which project would you select?
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9-29
NPV vs. IRR
NPV and IRR will generally give us the same decision
Exceptions:
Nonconventional cash flows – cash flow signs change more than once
Mutually exclusive projects
Initial investments are substantially different (issue of scale)
Timing of cash flows is substantially different
Non-conventional Cash Flows
Suppose an investment will cost $90 thousand initially and will generate the following cash flows (in thousands):
Year 1: 132
Year 2: 100
Year 3: -150
The required return is 15%.
Should we accept or reject the project?
Using the NPV rule, the answer is YES, for NPV>0.
NPV = 132,000 /1.15 + 100,000 /(1.15)2 – 150,000 /(1.15)3 – 90,000 = 1,769.54
Using Excel to get IRR, the answer is NO, for IRRx<15%.
If we just blindly use Excel without recognizing the uneven cash flows, we get IRR = 10.11%, ( the first number that comes out) leading to a decision to reject the project.
Chp.9&10 - 30
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9-31
Conflicts Between NPV and IRR
NPV directly measures the increase in value to the firm.
Whenever there is a conflict between NPV and another decision rule, you should
always use NPV!
9-32
Capital Budgeting Decision Criteria Comparison
| Technique | Units | Accept if: |
| Payback | Time | Payback < Mgt’s # |
| Discounted Payback | Time | Payback < Mgt’s # |
| Net Present Value | $ | NPV > $0 |
| Profitability Index (PI) | None | PI > 1.0 |
| Average Acct. Return | % | AAR > Mgt’s # |
| Internal Rate of Return | % | IRR > R |
| Modified Internal Rate of Return (MIRR) | % | IRR > R |
9-33
Capital Budgeting In Practice
Most managers use the techniques of capital budgeting as part of their job.
Payback is a commonly used secondary investment criteria and is used when the project costs are small
NPV and IRR are the most commonly used primary investment criteria and especially when the project costs are large
10-34
Capital Budgeting and Cash Flows
10-35
Capital Budgeting and Cash Flows
In the previous session we focused on multiple techniques of capital budgeting to evaluate projects.
This Session is all about how each of the cash flows (CF’s) are determined.
10-36
Project Example - Visual
R = 12%
$ -165,000
1
2
3
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
The required return for assets of this risk level is 12% (as determined by the firm).
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37
Pro Forma Statements and Cash Flow
Capital budgeting relies heavily on pro forma accounting statements, particularly income statements
Computing Net Cash Flows (NCFs):
1. Initial Cash Outlay = Project Cost + Change in NWC
2. Operating Cash Flows (OCFs)
Tax Shield Approach:
OCF = (Sales - Costs) (1 - T) + Depreciation * T
(OCF = EBIT + Depreciation –Taxes)
3. Terminal Cash Flow = Salvage Value – Taxes + Recovery of NWC
Cash Flow From Assets (CFFA) =
OCF – net capital spending (NCS) – changes in NWC (ΔNWC)
9.37
Operating cash flow – students often have to go back to the income statement to see that the two definitions of operating cash flow are equivalent when there is no interest expense.
10-38
Most common financial calculation for OCF is:
OCF = EBIT + Depreciation – Taxes
The top-down approach to calculating OCF yields:
OCF = Sales – Costs – Taxes
Do not subtract non-cash deductions
The tax-shield approach is:
OCF = (Sales – Costs).(1 – tC) + tC . Depreciation
The bottom-up approach is:
OCF = Net income + Depreciation
All four methods for OCF should always give same answer.
Different Ways to Compute OCFs
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Example
Sales=108,000, Variable Cost= 51,000, Depreciation = 6800 Tax=35%
Most common financial calculation for OCF:
OCF = EBIT + Depreciation – Taxes
OCF = $50,200 + 6,800 – 17,570 = $39,430
Top-down approach:
OCF = Sales – Costs – Taxes (Depreciation is NOT deducted here)
OCF = $108,000 – 51,000 – 17,570 = $39,430
Tax-shield approach:
OCF = (Sales – Costs)(1 – T) + T.Dep.
OCF = ($108,000 – 51,000)(1 – .35) + .35(6,800) = $39,430
Bottom-up approach :
OCF = NI + Dep.
OCF = $32,630 + 6,800 = $39,430
10-40
Getting Started: The Project
You have been thinking about starting a new project to produce mobile phone plastic cases. Your business plan can be summarized as follows:
You estimate you can sell 50,000 pieces @ $4 each. Production cost is $2.5 per unit. Project is expected to have a life a three years. The machine needed would cost $90,000 and will be fully depreciated over the life of the project.
Fixed costs (for rent of production facility and other) are estimated at $12,000
The project is expected to require an initial investment in net working capital of $20,000.
Similar projects offer a 20% rate of return
Tax rate on income =34%
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10-41
Getting Started: Project Pro Forma Income Statement
| OCF = EBIT + Dep - Tax = | 51,780.00 |
Cash Flow From Assets (CFFA) =
OCF – net capital spending (NCS) – changes in NWC (ΔNWC)
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Projected Total Cash Flows
+ Purchase price of the new asset
– Selling price of the asset replaced (if applicable)
+ Costs of site preparation, setup, and startup
+(-) Increase (decrease) in tax liability due to sale of old asset at other than book value
Capital spending at the time of project inception (i.e., the “initial outlay”) includes following items:
NCS =
OCF
– ΔNWC
– NCS
=
CFFA
9.42
10-43
Project Example - Visual
R = 20%
$ -110,000
1
2
3
CF1 = 51,780
CF2 = 51,780
CF3 = 71,780
The required return for assets of this risk level is 20% (as determined by the firm).
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10-44
What’s Your Decision?
So...What do you think? Deal or No Deal?
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10-45
Computing Depreciation
Straight-line depreciation
D = (Initial cost – salvage) / number of years
Very few assets are depreciated using the straight-line method for tax purposes
MACRS (Modified Accelerated Cost Recovery System)
the basic idea under MACRS is that every asset is assigned to a particular class. An asset’s class establishes its life for tax purposes. Once an asset’s tax life is determined, the depreciation for each year is computed by multiplying the cost of the asset by a fixed percentage.
The expected salvage value (what we think the asset will be worth when we dispose of it) and the expected economic life (how long we expect the asset to be in service) are not explicitly considered in the calculation of depreciation.
To compute depreciation expense:
First need to know which asset class is appropriate for tax purposes
Multiply percentage given in table by the initial cost
Depreciate to zero
9.45
MACRS (Modified ACRS Depreciation)
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10-47
After-tax Salvage
If the salvage(market) value is different from the book value of the asset, then there is a tax effect
CF to consider is AT Salvage:
Book Value =
Initial cost – accumulated depreciation
After-tax salvage =
Salvage – T*(Salvage – BV@ time of sale)
10-48
Example: Depreciation and After-tax Salvage
You purchase equipment for $100,000, and it costs $10,000 to have it delivered and installed.
Based on past information, you believe that you can sell the equipment for $17,000 when you are done with it in 6 years.
10-49
Example: Depreciation and After-tax Salvage
The company’s marginal tax rate is 40%.
What is the depreciation expense and the after-tax salvage (AT-Salvage) in year 6 for each of the following scenarios?
Straight line Depreciation
MACRS 6 years
$ -110,000
6
Sell =
$17,000
5
4
3
2
1
0
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10-50
A: Straight-line
D = (110,000 – 17,000) / 6 = 15,500 every year for 6 years
BV in year 6 = 110,000 – 6(15,500) = 17,000
AT-Salvage = 17,000 - 0.4.(17,000 – 17,000) = 17,000
Book Value = Initial cost – accumulated depreciation
After-tax salvage =
Salvage – T*(Salvage – BV@ time of sale)
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B: 6-Year MACRS
| Year | MACRS Percent | Depreciation Per year |
| 1 | .1429 | .1429(110,000) = D1=$15,719 |
| 2 | .2449 | .2449(110,000) = D2=$26,939 |
| 3 | .1749 | .1749(110,000) = D3=$19,239 |
| 4 | .1249 | .1249(110,000) = D4=$13,739 |
| 5 | .0893 | .0893(110,000) = D5= $ 9,823 |
| 6 | .0892 | .0892(110,000) = D6= $ 9,812 |
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B: 6-year MACRS
Book Value at year 6 = 110000-95271=$14,729
After-tax salvage value:
17,000 - .40 (17,000 – 14,729) = $16,091.60
After-tax salvage =
Salvage – T*(Salvage – BV@ time of sale)
Book Value = Initial cost – accumulated depreciation
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Example: Cost Cutting
Your company is considering a new computer system with initial cost =$1 million.
It will generate $300,000 per year cost savings.
System expected to last for 5 years and will be depreciated using 3-year MACRS.
System expected to have a salvage value of $50,000 at the end of year5.
There is no impact on NWC.
The marginal tax rate is 40%.
The required return is 8%.
9.53
10-54
Cost Cutting - Analysis
| Initial Cost | 1,000,000 |
| Savings | 300,000 |
| Tax Rate | 40% |
| Expected Salvage | 50,000 |
| Discount Rate | 8% |
5-55
Introduction to Risk and Return
Expected Returns
Expected returns are based on the probabilities of possible outcomes
In this context, “expected” means average if the process is repeated many times
The “expected” return does not even have to be a possible return
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Example: Expected Returns
Suppose you have predicted the following returns for stocks C and T in three possible states of the economy.
1. What is the probability of “Recession”?
State Probability C T
Boom 0.3 15% 25%
Normal 0.5 10% 20%
Recession ??? 2% 1%
Probabilities add up to 100% (or 1.0) thus 1.0 – 0.3 – 0.5 = 0.2 or 20%
Example: Expected Returns
Suppose you have predicted the following returns for stocks C and T in three possible states of the economy.
2. What are the expected returns?
State Probability C T
Boom 0.3 15% 25%
Normal 0.5 10% 20%
Recession 0.2 2% 1%
RC = .3(15%) + .5(10%) + .2(2%) = 9.9%
RT = .3(25%) + .5(20%) + .2(1%) = 17.7%
Example: Expected Returns
The three states of the economy still apply to stocks C and T.
3. If the risk-free rate is 4.15%, what is the risk premium for C & T?
RC = .3(15%) + .5(10%) + .2(2%) = 9.9%
RT = .3(25%) + .5(20%) + .2(1%) = 17.7%
Stock C’s risk premium: 9.9 - 4.15 = 5.75%
Stock T’s risk premium: 17.7 - 4.15 = 13.55%
Variance and Standard Deviation
Variance and standard deviation measure the volatility of returns
Using unequal probabilities for the entire range of possible outcomes
Weighted average of squared deviations
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Example: Variance and Standard Deviation
State Probability C T
Boom 0.3 15% 25%
Normal 0.5 10% 20%
Recession 0.2 2% 1%
Expected return 9.9% 17.7%
Considering the previous example of stocks C and T:
What are the variance and St. Dev of Stock C?
2 = .3(15%-9.9%)2 + .5(10%-9.9%)2 + .2(2%-9.9%)2 = 0.2029%
= 4.50%
Example: Variance and Standard Deviation
What is the variance and standard deviation for T?
Stock T
2 = .3(25%-17.7%)2 + .5(20%-17.7%)2 + .2(1%-17.7%)2 = 0.7441%
= 8.63%
State Probability C T
Boom 0.3 15% 25%
Normal 0.5 10% 20%
Recession 0.2 2% 1%
Expected return 9.9% 17.7%
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Portfolios
A portfolio is a collection of assets
An asset’s risk and return are important in how they affect the risk and return of the portfolio
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Portfolios
The risk/return trade-off for a portfolio is measured by the portfolio’s expected return and standard deviation, just as with individual assets
Risk
Return
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Example: Portfolio Weights
Suppose you have $15,000 to invest and you have purchased securities in the following amounts:
$2000 of DCLK
$3000 of KO
$4000 of INTC
$6000 of KEI
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Example: Portfolio Weights
What are your portfolio weights in each security?
$2,000 of DCLK
$3,000 of KO
$4,000 of INTC
$6,000 of KEI
$15,000
DCLK: 2/15 = .133
KO: 3/15 = .200
INTC: 4/15 = .267
KEI: 6/15 = .400
15/15 = 1.000
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Portfolio Expected Returns
The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio
You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities
Example: Expected Portfolio Returns
Consider the portfolio weights computed previously. The individual stocks have the following :
DCLK: 19.69%
KO: 5.25%
INTC: 16.65%
KEI: 18.24%
Example: Expected Portfolio Returns
1. What is the expected return on this portfolio?
Return Weight
DCLK: 19.69% .133
KO: 5.25% .200
INTC: 16.65% .267
KEI: 18.24% .400
E(RP) = .133(19.69%) + .2(5.25%) + .267(16.65%) + .4(18.24%)
= 15.41%
Portfolio Variance
Compute the expected portfolio return, the variance, and the standard deviation using the same formula as for an individual asset
Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm
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Example: Portfolio Variance
Consider the following information:
State Probability A B
Boom .4 30% -5%
Bust .6 -10% 25%
Example: Portfolio Variance
Consider the following information:
State Prob. A B
Boom .4 30% -5%
Bust .6 -10% 25%
What is the expected return for asset A? VarA, St. DevA?
E(RA) = .4(30%) + .6(-10%) = 6%
Variance(A) = .4(30% - 6%)2 + .6(-10% - 6%)2 = 3.84%
Std. Dev.(A) = 19.6%
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Example: Portfolio Variance
Consider the following information:
State Prob. A B
Boom .4 30% -5%
Bust .6 -10% 25%
What is E(RB) ? VarB? St. DevB?
E(RB) = .4(-5%) + .6(25%) = 13%
Variance(B) = .4(-5%-13%)2 + .6(25%-13%)2 = 2.16%
Std. Dev.(B) = 14.7%
Example: Portfolio Variance
Consider the following information:
State Probability A B
Boom .4 30% -5%
Bust .6 -10% 25%
If you invest 50% of your money in Asset A, what is the expected return for the portfolio?
If 50% of the investment is in Asset A, then 50% (100% - 50%) must be invested in Asset B as the total asset allocation must be 100%
∑Wi = 100%
Example: Portfolio Variance
Consider the following information:
State Prob. A B..
Boom .4 30% -5%
Bust .6 -10% 25%
E(R) 6% 13%
Sigma 19.6% 14.7%
If you invest 50% of your money in Asset A,
what is the expected return for the portfolio If a boom? If a bust?
What is expected return for the whole portfolio (that is, considering both states of the economy)?
a. E(RP_Boom) = .5(30%) + .5(-5%) = 12.5%
E(RP_Bust) = .5(-10%) + .5(25%) = 7.5%
b. E(RP) = .4 (12.5% ) + .6(7.5%) = 9.5%
Example: Portfolio Variance
Another way of computing Portfolio returns :
Exp. portfolio return = .5(6%) + .5(13%) = 9.5%
E(RP) = WA E(RA) + WB E(RB) + WC E(RC) + …. + WN E(RN)
N: number of assets in the portfolio
Wi : weight of asseti in the portfolio
Consider the following information:
State Prob. A B..
Boom .4 30% -5%
Bust .6 -10% 25%
E(R) 6% 13%
Sigma 19.6% 14.7%
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Example: Portfolio Variance
What is the variance of the portfolio?
Variance of portfolio =
.4(12.5%-9.5%)2 + .6(7.5%-9.5%)2
= 0.06%
Standard deviation = 2.45%
77
Expected vs. Unexpected Returns
Realized returns are generally NOT equal to expected returns
There is the expected component and the unexpected component
At any point in time, the unexpected return can be either positive or negative
Over time, the average of the unexpected component is zero
Announcements and News
Announcements and news contain both an expected component and a surprise component
It is the surprise component that affects a stock’s price and therefore its return
79
Announcements and News
This surprise is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated
80
Systematic Risk
Risk factors that affect a large number of assets
Also known as non-diversifiable risk or market risk
Includes such things as changes in GDP, inflation, interest rates, etc.
Unsystematic Risk
Risk factors that affect a limited number of assets
Also known as unique risk and asset-specific risk
Includes such things as labor strikes, part shortages, etc.
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Diversification
Portfolio diversification is the investment in several different asset classes or sectors
Diversification is not just holding a lot of assets
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Diversification
For example, if you own 5 airline stocks, you are not diversified
However, if you own 50 stocks that span 20 different industries, then you are diversified
84
Total Risk
Total risk = systematic risk + unsystematic risk
The standard deviation of returns is a measure of total risk
For well-diversified portfolios, unsystematic risk is very small
Consequently, the total risk for a diversified portfolio is essentially equivalent to just the systematic risk
Diversification
The Principle of Diversification
Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns
This reduction in risk arises because worse-than-expected returns from one asset are offset by better-than-expected returns from another
However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion
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The Capital Asset Pricing Model (CAPM)
The capital asset pricing model defines
the relationship between risk and return:
E(Ri,t) = Rf + i(E(Rm,t) – Rf)
Ri,t = return on asset i at time t.
rf = return of riskless asset at time t.
Rm,t = return on the market portfolio at time t.
βi = Measure of systematic risk
The Capital Asset Pricing Model (CAPM)
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The CAPM assumes only one source of systematic risk: Market Risk.
• Systematic risk:
(1) Cannot be diversified
(2) Has to be hedged
(3) In equilibrium it is compensated by a risk premium
If we know an asset’s systematic risk, we can use the CAPM to determine its expected return
The Capital Asset Pricing Model (CAPM)
5-90
Interpreting the CAPM
Equity beta – a measure of systematic risk
Cov(re, rm)/Var(rm)
Positive beta contributes to portfolio variance
Negative beta reduces portfolio variance
Measuring Systematic Risk
How do we measure systematic risk?
We use the beta coefficient
What does beta tell us?
A beta of 1 implies the asset has the same systematic risk as the overall market
A beta < 1 implies the asset has less systematic risk than the overall market
A beta > 1 implies the asset has more systematic risk than the overall market
91
The Capital Asset Pricing Model (CAPM)
5-92
Recipe for the cost of equity capital
Get data on the market portfolio return, the equity returns on security j, and the T-bill interest rate (rf)
Determine the market risk premium – the expected excess return on the market portfolio [E(rm) – rf]
Obtain an estimate of β
Compute the expected return on security j
E(rj) = rf + βjm [E(rm) - rf]
Total vs. Systematic Risk
Consider the following information:
St.Dev Beta
Security C 20% 1.25
Security K 30% 0.95
1. Which security has more total risk?
K because the standard deviation
is greater than C
2. Which security has more systematic risk?
C because the beta is larger than K
93
Total vs. Systematic Risk
Consider the following information:
St.Dev Beta
Security C 20% 1.25
Security K 30% 0.95
3. Which security should have the higher expected return?
C because a well diversified investor cares about systematic risk. These investors would require higher returns for higher risk, and beta is higher for C
94
Example: Portfolio Betas
Consider the previous example with the following four securities:
Security Weight Beta
DCLK .133 2.685
KO .2 0.195
INTC .267 2.161
KEI .4 2.434
What is the portfolio beta?
.133(2.685) + .2(.195) + .267(2.161) + .4(2.434)
= 1.947
95
Example - CAPM
| Security | Beta | Expected Return |
| DCLK | 2.685 | 4.15 + 2.685(8.5) = 26.97% |
| KO | 0.195 | 4.15 + 0.195(8.5) = 5.81% |
| INTC | 2.161 | 4.15 + 2.161(8.5) = 22.52% |
| KEI | 2.434 | 4.15 + 2.434(8.5) = 24.84% |
Consider the betas for each of the assets given earlier. If the risk-free rate is 4.15% and the market risk premium is 8.5%,
What is the expected return for each?
96
MT_A
| MCQs: 30 marks: 2.5 each | MCQs | 30 | |||||||||||
| Q.1 | 12 | ||||||||||||
| 1. (12 marks: 4-6-2) Divia has Dh1250 ready for investment. The bank offers an APR =8%. | Q.2 | 8 | |||||||||||
| a. How much will she have in four years if annual compounding? | Q.3 | 3 | |||||||||||
| b. How much will she have in 4 years if quarterly compounding? If monthly compounding? | Q.4 | 4 | |||||||||||
| c. What do you notice? | Q.5 | 6 | |||||||||||
| Q.6 | 10 | ||||||||||||
| PV | 1250 | 1250 | 1250 | PV | 1250 | 1250 | 1250 | Q.7 | 8 | ||||
| APR | 8% | 8% | 8% | APR | 8% | 8% | 8% | Q.8 | 9 | ||||
| N | 4 | 4 | 4 | N | 4 | 4 | 4 | Total | 90 | ||||
| m | 1 | 4 | 12 | m | 1 | 4 | 12 | ||||||
| FV= | 1,700.61 | 1,715.98 | 1,719.58 | EAR | 8.00% | 8.24% | 8.30% | ||||||
| The higher the compounding times, the higher the FV | FV= | 5,632.64 | 5,652.92 | 5,657.66 | |||||||||
| 2. (8 marks: 2 each) Which bank would you pick for a loan to buy a new car? | |||||||||||||
| - Bank1 charges 6.1% with annual compounding. | |||||||||||||
| - Bank2 charges 5.95% with monthly compounding. | |||||||||||||
| - Bank3 charges 5.9% with daily compounding. | |||||||||||||
| - Bank4 charges 5.8% with continuous compounding. | |||||||||||||
| APR | m | EAR | |||||||||||
| 6.10% | 1 | 6.10% | |||||||||||
| 5.95% | 12 | 6.115% | |||||||||||
| 5.90% | 365 | 6.077% | |||||||||||
| 5.85% | exp | 6.02% | |||||||||||
| 3. (3 marks) What is the rate that would allow your money to double in 8 years? | |||||||||||||
| N | 8 | 7 | 6 | 9 | 11 | 12 | 13 | 16 | |||||
| FV/PV= | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |||||
| r= | 9.05% | 10.41% | 12.25% | 8.01% | 6.50% | 5.95% | 5.48% | 4.43% | |||||
| 9.00% | 10.29% | 12.00% | 8.00% | 6.55% | 6.00% | 5.54% | 4.50% | ||||||
| 4. (4 marks) You borrow AED9,250 and promise the bank to pay 1,900 each year. How long will it take you to pay off the loan if the bank’s APR=10%? | |||||||||||||
| PVA | 9,250.00 | ||||||||||||
| C | 1900 | ||||||||||||
| r | 10% | ||||||||||||
| $0.51 | |||||||||||||
| n= | 7 | $1.95 | |||||||||||
| 5. (6 marks: 2-2-2) You need to accumulate Dh100,000 ten years from now. APR = 6%. | |||||||||||||
| a. How much do you need to invest today (lump-sum) in order to accumulate 100,000 in ten years, if monthly compounding? | |||||||||||||
| b. How much would you need to deposit each year to accumulate 100,000 and rates compounding monthly? | |||||||||||||
| c. What would the annual deposit to be made if interest was compounded continuously? | |||||||||||||
| FVA | 100000 | ||||||||||||
| APR | 6.00% | ||||||||||||
| N | 10 | nper | 120 | ||||||||||
| m | 12 | per rate | 0.005 | ||||||||||
| PV = FV/(1+r)^n= | 54,963.27 | ||||||||||||
| Since annual pmts and periodic rate, compute EAR | |||||||||||||
| Monthly compounding | |||||||||||||
| EAR= | 6.17% | ||||||||||||
| C = FVA/FVIFA | 7,527.22 | 100,000.00 | |||||||||||
| Continuous compounding | |||||||||||||
| EAR= | 6.1837% | ||||||||||||
| C = FVA/FVIFA | 7,521.61 | 100,000.00 | |||||||||||
| $13.30 | |||||||||||||
| $7,521.61 | |||||||||||||
| 6. (10 marks: 3-3-4) ABC Inc. just paid a dividend of AED1.95 per share. Dividends are expected to grow at 10% year 1 to 3, then 8% for another 3 years, then settle at 3% in perpetuity. r =15%. | |||||||||||||
| a. Draw the CFTL | g1-3 | 10% | |||||||||||
| b. Compute Dividdends for years 1 to 7 | g4-6 | 7% | |||||||||||
| c. Compute value of shares today. | g7 + | 4% | |||||||||||
| D0= | 1.95 | R | 15% | ||||||||||
| g | Year | Div | P6 | PV | |||||||||
| 10% | 1 | 2.145 | 1.8652173913 | ||||||||||
| 10% | 2 | 2.3595 | 1.784120983 | ||||||||||
| 10% | 3 | 2.59545 | 1.7065505055 | ||||||||||
| 7% | 4 | 2.7771315 | 1.5878339486 | ||||||||||
| 7% | 5 | 2.971530705 | 1.4773759348 | ||||||||||
| 7% | 6 | 3.1795378543 | 30.0610851684 | 14.370838638 | |||||||||
| 4% | 7 | 3.3067193685 | 22.79 | ||||||||||
| 10% | 8% | 3% | |||||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||
| D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | ||||||
| P6 | |||||||||||||
| 7. (8 marks: 3-3-2) You are interested in the following bonds for investment. Compute the value of each bond: | |||||||||||||
| a. An annual-coupon bond that matures in 7 years. Par value =$25,000, CR=8%. YTM=7.5%. | |||||||||||||
| b. A 10-year zero-coupon bond with Par = $20,000. YTM=7% | |||||||||||||
| c. A perpetual bond that pays $25 each quarter. YTM = 6% | |||||||||||||
| Par | CR | YTM | freq | Mat | Quote | Price | |||||||
| a. | 25000 | 8% | 7.50% | 1 | 1/1/07 | 102.64830 | 25,662.08 | 2000 | 25662.0751651702 | ||||
| b. | 20000 | 0 | 7% | 1 | 1/1/10 | 50.83493 | 10,166.99 | 10,166.99 | |||||
| c. | 1000 | 10% | 6% | 4 | ∞ | 1,666.67 | |||||||
| 1,666.67 | |||||||||||||
| 8. (9 marks: 3-3-3) You need to buy new furniture for AED10,000 and are considering a two-year loan. | |||||||||||||
| - Bank A uses the fixed payment method, paid semiannually. | |||||||||||||
| - Bank B uses the fixed principal method, paid semiannually. | |||||||||||||
| - Bank C uses the ‘interest-only-loan method, paid semiannually | |||||||||||||
| Which one would you chose knowing that all have an APR of 8%? | |||||||||||||
| Loan | 10000 | ||||||||||||
| APR | 8% | ||||||||||||
| m | 2 | ||||||||||||
| N | 2 | ||||||||||||
| Fixed Pcpl | Beg Bce | Pcpl | Int | EndBce | Fixed Pmt | Interest only | |||||||
| 1 | 10000 | 2500 | 400 | 7500 | C = PVA/PVIFA | 2754.900453648 | semiannual interest | 400 | |||||
| 2 | 7500 | 2500 | 300 | 5000 | Total pmt = | 11019.6018145921 | Total interest | 1600 | |||||
| 3 | 5000 | 2500 | 200 | 2500 | Interest | 1019.6018145921 | |||||||
| 4 | 2500 | 2500 | 100 | 0 | |||||||||
| 1000 |
MT_B
| MCQs: 30 marks: 2.5 each | MCQs | 30 | ||||||||||
| Q.1 | 8 | |||||||||||
| 1. (8 marks: 2 each) Which bank would you pick for a loan to buy a new car? | Q.2 | 4 | ||||||||||
| - Bank1 charges 7.1% with annual compounding. | Q.3 | 12 | ||||||||||
| - Bank2 charges 6.95% with monthly compounding. | Q.4 | 3 | ||||||||||
| - Bank3 charges 6.9% with daily compounding. | Q.5 | 6 | ||||||||||
| - Bank4 charges 6.85% with continuous compounding. | Q.6 | 10 | ||||||||||
| Q.7 | 8 | |||||||||||
| APR | m | EAR | Q.8 | 9 | ||||||||
| 7.10% | 1 | 7.10% | Total | 90 | ||||||||
| 6.95% | 4 | 7.13% | ||||||||||
| 6.90% | 12 | 7.12% | ||||||||||
| 6.85% | exp | 7.09% | ||||||||||
| 2. (4 marks) You borrow AED8,275 and promise the bank to pay 1,900 each year. How long will it take you to pay off the loan if the bank’s APR=10%? | ||||||||||||
| PVA | 8,275.00 | |||||||||||
| C | 1900 | |||||||||||
| r | 10% | 0.5645 | ||||||||||
| 1.77 | ||||||||||||
| n | 6.00 | 6.00 | ||||||||||
| Note: Log and Ln give the same results | ||||||||||||
| 3. (12 marks: 4-6-2) hana has Dh1550 ready for investment. The bank offers an APR =6%. | ||||||||||||
| a. How much will she have in four years if annual compounding? | ||||||||||||
| b. How much will she have in 4 years if semi-annual compounding? If quarterly compounding? | ||||||||||||
| c. What do you notice? | ||||||||||||
| PV | 1550 | 1550 | 1550 | |||||||||
| APR | 6% | 6% | 6% | 93 | ||||||||
| N | 4 | 4 | 4 | |||||||||
| m | 1 | 2 | 4 | |||||||||
| FV= | 1,956.84 | 1,963.49 | 1,966.93 | |||||||||
| The higher the compounding times, the higher the FV | ||||||||||||
| EAR | 6.000% | 6.090% | 6.136% | |||||||||
| FV= | 1,956.84 | 1,963.49 | 1,966.93 | |||||||||
| 4. (3 marks) What is the rate that would allow your money to double in 6 years? | ||||||||||||
| N | 6 | |||||||||||
| FV/PV= | 2 | 0.1224620483 | ||||||||||
| r= | 12.25% | |||||||||||
| 5. (6 marks: 2-2-2) You need to accumulate Dh100,000 ten years from now. APR = 6%. | ||||||||||||
| a. How much do you need to invest today (lump-sum) in order to accumulate 100,000 in ten years, if monthly compounding? | ||||||||||||
| b. How much would you need to deposit each year to accumulate 100,000 and rates compounding monthly? | ||||||||||||
| c. What would the annual deposit to be made if interest was compounded continuously? | ||||||||||||
| FV/A | 100,000.00 | |||||||||||
| APR | 6.00% | |||||||||||
| N | 10 | nper | 120 | |||||||||
| m | 12 | per rate | 0.005 | |||||||||
| a. | PV = | 54,963.27 | ||||||||||
| b. | Since annual pmts and periodic rate, compute EAR | |||||||||||
| Monthly compounding | ||||||||||||
| EAR= | 6.17% | |||||||||||
| C = FVA/FVIFA | 7,527.22 | |||||||||||
| c. | Continuous compounding | |||||||||||
| EAR= | 6.1837% | |||||||||||
| C = PVA/PVIFA | 7,521.61 | |||||||||||
| 6. (10 marks: 3-3-4) ABC Inc. just paid a dividend of AED1.95 per share. Dividends are expected to grow at 10% year 1 to 3, then 8% for another 3 years, then settle at 3% in perpetuity. r =15%. | ||||||||||||
| a. Draw the CFTL | g1-4 | 8% | ||||||||||
| b. Compute Dividdends for years 1 to 7 | g5-6 | 6% | ||||||||||
| c. Compute value of shares today. | g7 + | 4% | ||||||||||
| D0= | 3.2 | R | 12% | |||||||||
| g | Year | Div | P6 | PV | ||||||||
| 8% | 1 | 3.46 | 3.0857142857 | |||||||||
| 8% | 2 | 3.732 | 2.9755102041 | |||||||||
| 8% | 3 | 4.031 | 2.8692419825 | |||||||||
| 8% | 4 | 4.354 | 2.7667690546 | |||||||||
| 6% | 5 | 4.615 | 2.6185492838 | |||||||||
| 6% | 6 | 4.892 | 63.592 | 34.6957780101 | ||||||||
| 4% | 7 | 5.087 | P0= | 49.01 | ||||||||
| a. | 8% | 6% | 4% | |||||||||
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||||
| D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | |||||
| P6 | ||||||||||||
| 27.5 | ||||||||||||
| 7. (8 marks: 3-3-2) You are interested in the following bonds for investment. Compute the value of each bond: | ||||||||||||
| a. An annual-coupon bond that matures in 7 years. Par value =$25,000, CR=8%. YTM=7.5%. | ||||||||||||
| b. A 10-year zero-coupon bond with Par = $20,000. YTM=7% | ||||||||||||
| c. A perpetual bond that pays $25 each quarter. YTM = 6% | ||||||||||||
| Par | CR | YTM | freq | Mat | Quote | Price | ||||||
| a. | 25000 | 7% | 7.50% | 1/1/07 | 97.3516993393 | 24337.9248348298 | Coupon = | 1750 | 15068.8725224471 | |||
| b. | 20000 | 0 | 8% | 1/1/10 | 46.3193488085 | 9263.8697616937 | 9263.8697616937 | 1875 | ||||
| c. | 1000 | 10% | 8% | 4 | 1250 | |||||||
| 1250 | ||||||||||||
| 8. (9 marks: 3-3-3) You need to buy new furniture for AED10,000 and are considering a two-year loan. | ||||||||||||
| Which one would you chose knowing that all have an APR of 8%? | ||||||||||||
| Loan | 20000 | |||||||||||
| APR | 6% | |||||||||||
| m | 2 | |||||||||||
| N | 2 | |||||||||||
| Fixed Pcpl | Beg Balance | Pcpl | Int | EndBce | Fixed Pmt | Interest only | ||||||
| 1 | 20000 | 5000 | 600 | 15000 | C = PVA/PVIFA | 5380.5409038616 | semiannual interest | 600 | ||||
| 2 | 15000 | 5000 | 450 | 10000 | Total pmt = | 21522.1636154466 | Total interst | 2400 | ||||
| 3 | 10000 | 5000 | 300 | 5000 | Interest | 1522.1636154466 | ||||||
| 4 | 5000 | 5000 | 150 | 0 | ||||||||
| 1500 |
IRR Approxim
| iL | iU | |||||||
| 5% | 10% | |||||||
| CF0 | -100000 | -100000 | irr = 0.05 + [(0.1-0.05)(6378.51)] / [6378.51--4904.04] | |||||
| CF1 | 30000 | 30000 | irr = 0.05 + [(0.05)(6378.51)] / [11282.55] | |||||
| CF2 | 40000 | 40000 | irr = 0.05 + 318.9255 / 11282.55 | |||||
| CF3 | 30000 | 30000 | irr = 0.05 + 0.0283 | |||||
| CF4 | 30000 | 30000 | irr = 0.0783 | |||||
| 15,448.81 | 3,360.43 | irr = 7.83% | ||||||
| 11.56% | ||||||||
| IRR = iL + [(iU-iL)(npvL)] / [npvL-npvU] | ||||||||
| 11.390% | ||||||||
| �Year 0: | CF | |||||||
| �Year 1: | CF | NI = 13,620 | ||||||
| �Year 2: | CF | NI = 3,300 | ||||||
| �Year 3: | CF | NI = 29,100 | ||||||
| �Average Book Value = 72,000 | ||||||||
| iL | iU | |||||||
| 12% | 18% | |||||||
| 0 | -165,000 | -165,000 | ||||||
| 1 | 63,120 | 63,120 | ||||||
| 2 | 70,800 | 70,800 | ||||||
| 3 | 91,080 | 91,080 | ||||||
| NPV= | $11,274.48 | ($4,429.59) | ||||||
| IRR≈ | 16.308% | |||||||
| $676.47 | ||||||||
| $15,704.07 | ||||||||
| 16.308% |
Sheet1
| Year | CFs | CFs | |||
| Year | 1 | 132 | 155 | ||
| Year | 2 | 100 | -100 | ||
| Year | 3 | -150 | |||
| Rate | NPV | ||||
| -5% | ($15.20) | ($7.65) | |||
| 0% | ($8.00) | ($5.00) | |||
| 5% | ($3.16) | ($3.08) | |||
| 10% | ($0.05) | ($1.74) | |||
| 15% | $1.77 | ($0.83) | |||
| 20% | $2.64 | ($0.28) | |||
| 25% | $2.80 | $0.00 | |||
| 30% | $2.44 | $0.06 | |||
| 35% | $1.68 | ($0.05) | |||
| 40% | $0.64 | ($0.31) | |||
| 45% | ($0.61) | ($0.67) | |||
| 50% | ($2.00) | ($1.11) | |||
| 55% | ($3.50) | ($1.62) | |||
| 60% | ($5.06) | ($2.19) | |||
| 65% | ($6.66) | ($2.79) | |||
| Rate | NPV | ||||
| 20% | ($0.28) | ||||
| 22% | ($0.14) | ||||
| 24% | ($0.04) | ||||
| 26% | $0.03 | ||||
| 28% | $0.06 | ||||
| 30% | $0.06 | ||||
| 32% | $0.03 | ||||
| 34% | ($0.02) | ||||
| 40% | ($0.31) | ||||
| 42% | ($0.44) | ||||
| 44% | ($0.59) | ||||
| 46% | ($0.75) | ||||
| 48% | ($0.92) | ||||
| 50% | ($1.11) | ||||
| 52% | ($1.31) | ||||
NPV -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55000000000000004 0.6 -15.201924478786992 -8 -3.1584062196306917 -5.2592036063103365E-2 1.769540560532576 2.6388888888888999 2.7999999999999972 2.4351388256713591 1.6811461667428773 0.64139941690963553 -0.605600885645174 -2 -3.4960222886106749 -5.05859375 NPV 0.2 0.22 0.24 0.26 0.28000000000000003 0.3 0.32 0.34 0.4 -0.27777777777778567 -0.13705993012631268 -3.6420395421430385E-2 2.7714789619551539E-2 5.859375E-2 5.9171597633138617E-2 3.213957759412267E-2 -2.0049008687898606E-2 -0.306 12244897958618
Sheet2
Sheet3
Sheet1
| Sales (50,000 units at $4.00/unit) | $200,000 | ||||
| Variable Costs ($2.50/unit) | 125,000 | ||||
| Gross profit | $75,000 | ||||
| Fixed costs | 12,000 | ||||
| Depreciation ($90,000 /3) | 30,000 | ||||
| EBIT | $33,000 | ||||
| Taxes (34%) | 11,220 | ||||
| Net Income | $21,780 | ||||
| INPUT Data | Proforma Income Statement | ||||
| Q | 50,000.00 | Sales | 200,000.00 | ||
| P | 4 | Variable Costs | 125,000.00 | ||
| vc | 2.5 | Gross profit | 75,000.00 | ||
| N | 3 | Fixed costs | 12,000.00 | ||
| FC | 12,000.00 | Depreciation | 30,000.00 | ||
| Cost of the Machine | 90,000.00 | EBIT | 33,000.00 | ||
| T | 34% | Taxes (34%) | 11,220.00 | ||
| Net Income | 21,780.00 | ||||
| OCF= | 51,780.00 | ||||
Sheet2
Sheet3
Sheet1
| Sales (50,000 units at $4.00/unit) | $200,000 | ||||
| Variable Costs ($2.50/unit) | 125,000 | ||||
| Gross profit | $75,000 | ||||
| Fixed costs | 12,000 | ||||
| Depreciation ($90,000 /3) | 30,000 | ||||
| EBIT | $33,000 | ||||
| Taxes (34%) | 11,220 | ||||
| Net Income | $21,780 | ||||
| INPUT Data | Proforma Income Statement | ||||
| Q | 50,000.00 | Sales | 200,000.00 | ||
| P | 4 | Variable Costs | 125,000.00 | ||
| vc | 2.5 | Gross profit | 75,000.00 | ||
| N | 3 | Fixed costs | 12,000.00 | ||
| FC | 12,000.00 | Depreciation | 30,000.00 | ||
| Cost of the Machine | 90,000.00 | EBIT | 33,000.00 | ||
| T | 34% | Taxes (34%) | 11,220.00 | ||
| Net Income | 21,780.00 | ||||
| OCF= | 51,780.00 | ||||
Sheet2
Sheet3
Sheet1
| Sales (50,000 units at $4.00/unit) | $200,000 | |||||
| Variable Costs ($2.50/unit) | 125,000 | |||||
| Gross profit | $75,000 | |||||
| Fixed costs | 12,000 | |||||
| Depreciation ($90,000 /3) | 30,000 | |||||
| EBIT | $33,000 | |||||
| Taxes (34%) | 11,220 | |||||
| Net Income | $21,780 | |||||
| INPUT Data | Proforma Income Statement | |||||
| Q | 50,000.00 | Sales | 200,000.00 | |||
| P | 4 | Variable Costs | 125,000.00 | |||
| vc | 2.5 | Gross profit | 75,000.00 | |||
| N | 3 | Fixed costs | 12,000.00 | |||
| FC | 12,000.00 | Depreciation | 30,000.00 | |||
| Cost of the Machine | 90,000.00 | EBIT | 33,000.00 | |||
| T | 34% | Taxes (34%) | 11,220.00 | |||
| Net Income | 21,780.00 | |||||
| OCF = NI + Dep | 51,780.00 | |||||
| OCF = EBIT + Dep - Tax = | 51,780.00 | |||||
| 110000 | ||||||
| Year | MACRS percent | |||||
| 1 | 0.3333 | 36663.00 | ||||
| 2 | 0.4445 | 48895.00 | ||||
| 3 | 0.1481 | 16291.00 | ||||
| 4 | 0.0741 | 8151.00 | ||||
| 110000.00 | ||||||
| Year | ||||||
| 0 | 1 | 2 | 3 | |||
| OCF | $51,780 | $51,780 | $51,780 | |||
| –ΔNWC | ($20,000) | 0 | 0 | 20,000 | ||
| –Net CS | ($90,000) | |||||
| =CFFA | -$110,00 | $51,780 | $51,780 | $71,780 | ||
Sheet2
Sheet3
Sheet1
| Sales (50,000 units at $4.00/unit) | $200,000 | |||||
| Variable Costs ($2.50/unit) | 125,000 | |||||
| Gross profit | $75,000 | |||||
| Fixed costs | 12,000 | |||||
| Depreciation ($90,000 /3) | 30,000 | |||||
| EBIT | $33,000 | |||||
| Taxes (34%) | 11,220 | |||||
| Net Income | $21,780 | |||||
| INPUT Data | Proforma Income Statement | |||||
| Q | 50,000.00 | Sales | 200,000.00 | |||
| P | 4 | Variable Costs | 125,000.00 | |||
| vc | 2.5 | Gross profit | 75,000.00 | |||
| N | 3 | Fixed costs | 12,000.00 | |||
| FC | 12,000.00 | Depreciation | 30,000.00 | |||
| Cost of the Machine | 90,000.00 | EBIT | 33,000.00 | |||
| T | 34% | Taxes (34%) | 11,220.00 | |||
| Net Income | 21,780.00 | |||||
| OCF = NI + Dep | 51,780.00 | |||||
| OCF = EBIT + Dep - Tax = | 51,780.00 | |||||
| 110000 | ||||||
| Year | MACRS percent | |||||
| 1 | 0.3333 | 36663.00 | ||||
| 2 | 0.4445 | 48895.00 | ||||
| 3 | 0.1481 | 16291.00 | ||||
| 4 | 0.0741 | 8151.00 | ||||
| 110000.00 | ||||||
| Year | ||||||
| 0 | 1 | 2 | 3 | |||
| OCF | $51,780 | $51,780 | $51,780 | |||
| –ΔNWC | ($20,000) | 0 | 0 | 20,000 | ||
| –Net CS | ($90,000) | |||||
| =CFFA | -$110,00 | $51,780 | $51,780 | $71,780 | ||
Sheet2
Sheet3
Sheet1
| Sales (50,000 units at $4.00/unit) | $200,000 | |||||
| Variable Costs ($2.50/unit) | 125,000 | |||||
| Gross profit | $75,000 | |||||
| Fixed costs | 12,000 | |||||
| Depreciation ($90,000 /3) | 30,000 | |||||
| EBIT | $33,000 | |||||
| Taxes (34%) | 11,220 | |||||
| Net Income | $21,780 | |||||
| INPUT Data | Proforma Income Statement | |||||
| Q | 50,000.00 | Sales | 200,000.00 | |||
| P | 4 | Variable Costs | 125,000.00 | |||
| vc | 2.5 | Gross profit | 75,000.00 | |||
| N | 3 | Fixed costs | 12,000.00 | |||
| FC | 12,000.00 | Depreciation | 30,000.00 | |||
| Cost of the Machine | 90,000.00 | EBIT | 33,000.00 | |||
| T | 34% | Taxes (34%) | 11,220.00 | |||
| Net Income | 21,780.00 | |||||
| OCF = NI + Dep | 51,780.00 | |||||
| OCF = EBIT + Dep - Tax = | 51,780.00 | |||||
| 110000 | ||||||
| Year | MACRS percent | |||||
| 1 | 0.3333 | 36663.00 | ||||
| 2 | 0.4445 | 48895.00 | ||||
| 3 | 0.1481 | 16291.00 | ||||
| 4 | 0.0741 | 8151.00 | ||||
| 110000.00 | ||||||
| Year | ||||||
| 0 | 1 | 2 | 3 | |||
| OCF | $51,780 | $51,780 | $51,780 | |||
| ΔNWC | ($20,000) | 0 | 0 | 20,000 | ||
| Net CS | ($90,000) | |||||
| CFFA | -$110,00 | $51,780 | $51,780 | $71,780 | ||
| 110000 | ||||||
| Year | MACRS Percent | Depreciation | ||||
| Per year | ||||||
| 1 | 0.1429 | 15719 | ||||
| 2 | 0.2449 | 26939 | ||||
| 3 | 0.1749 | 19239 | ||||
| 4 | 0.1249 | 13739 | ||||
| 5 | 0.0893 | 9823 | ||||
| 6 | 0.0892 | 9812 | ||||
| 95271 | ||||||
| Ending BV = | 14729 | |||||
| AT Salvage = | 16091.6 |
Sheet2
| Year | 1 | 2 | 3 | 4 | 5 | ||
| Cost Savings | 50,000 | 50,000 | 50,000 | 50,000 | 50,000 | ||
| Depr. | |||||||
| New | 49,995 | 66,675 | 22,215 | 11,115 | 0 | ||
| Old | 9,000 | 9,000 | 9,000 | 9,000 | 9,000 | ||
| Increm.Depr | 40,995 | 57,675 | 13,215 | 2,115 | -9,000 | ||
| EBIT | 9,005 | -7,675 | 36,785 | 47,885 | 59,000 | ||
| Taxes | 3,602 | -3,070 | 14,714 | 19,154 | 23,600 | ||
| NI | 5,403 | -4,605 | 22,071 | 28,731 | 35,400 | ||
| OCF | 46,398 | 53,070 | 35,286 | 30,846 | 26,400 | ||
| 150000 | |||||||
| Year | MACRS % | Deprec. | |||||
| 1 | 0.3333 | 49,995.00 | |||||
| 2 | 0.4445 | 66,675.00 | |||||
| 3 | 0.1481 | 22,215.00 | |||||
| 4 | 0.0741 | 11,115.00 | |||||
| 5 | 0 | - 0 | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | |
| OCF | 46,398 | 53,070 | 35,286 | 30,846 | 26,400 | ||
| NCS | -89,000 | -10,000 | |||||
| DNWC | 0 | 0 | |||||
| CFFA | -89,000 | 46,398 | 53,070 | 35,286 | 30,846 | 16,400 | |
| NPV= | 54,801.74 | ||||||
| IRR = | 36.28% |
Sheet3
| Old Machine | |||
| Initial cost | 100,000 | ||
| Annual depreciation | 9,000 | ||
| Purchased 5 years ago | |||
| Book Value | 55,000 | ||
| Salvage today | 65,000 | ||
| Salvage in 5 years | 10,000 | ||
| New Machine | |||
| Initial cost | 150,000 | ||
| Life | 5 | years | |
| Salvage in 5 years | 0 | ||
| Cost savings | 50,000 | a year | |
| 3-year MACRS depreciation |
Solutions
| Initial Cost | 1,000,000 | ||||||
| Savings | 300,000 | ||||||
| Tax Rate | 40% | ||||||
| Expected Salvage | 50,000 | ||||||
| Discount Rate | 8% | ||||||
| MACRS Depreciation Schedule | |||||||
| Year | 1 | 2 | 3 | 4 | 5 | BV year 5 | |
| Percentage | 33.33% | 44.45% | 14.81% | 7.41% | No MoreDep. | ||
| Depreciation Expense | 333,300 | 444,500 | 148,100 | 74,100 | 0 | 0 | |
| AT-Salvage = | 30,000 | ||||||
| Income Statement-OCF | |||||||
| Year | 1 | 2 | 3 | 4 | 5 | ||
| Cost Savings | 300,000 | 300,000 | 300,000 | 300,000 | 300,000 | ||
| Depr | 333,300 | 444,500 | 148,100 | 74,100 | 0 | ||
| EBIT | -33,300 | -144,500 | 151,900 | 225,900 | 300,000 | ||
| Taxes | -13320 | -57800 | 60760 | 90360 | 120000 | ||
| NI | -19,980 | -86,700 | 91,140 | 135,540 | 180,000 | ||
| OCF | 313,320 | 357,800 | 239,240 | 209,640 | 180,000 | ||
| CFFA | |||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | |
| OCF | 313,320 | 357,800 | 239,240 | 209,640 | 180,000 | ||
| NCS | -1,000,000 | 30,000 | |||||
| Δ NWC | 0 | 0 | |||||
| CFFA | -1,000,000 | 313,320 | 357,800 | 239,240 | 209,640 | 210,000 | |
| NPV | $83,797.50 | ||||||
| IRR | 11.45% | ||||||
| Depreciation Expense | = initial cost * percentage | ||||||
| Operating Cash Flow | =(sales - costs)*(1 - tax rate) + depreciation*tax rate | ||||||
| note that sales = 0 and a cost savings is -costs |
Sheet1
| State | Probability | C | T | ||||||
| Boom | 0.3 | 15% | 25% | 0.260% | 0.533% | ||||
| Normal | 0.5 | 10% | 20% | 0.000% | 0.053% | ||||
| Recession | 0.2 | 2% | 1% | 0.624% | 2.789% | ||||
| 9.90% | 17.70% | 0.2029% | 0.7441% | ||||||
| 4.50% | 8.63% | ||||||||
| State | Probability | ABC, Inc. (%) | |||||||
| Boom | 0.25 | 15% | 0.483% | ||||||
| Normal | 0.5 | 8% | 0.000% | ||||||
| Slowdown | 0.15 | 4% | 0.164% | ||||||
| Recession | 0.1 | -3% | 1.221% | ||||||
| 8.05% | 0.267475% | ||||||||
| 5.17% | |||||||||
| State | Prob. | A | B | Portfolio | |||||
| Boom | 0.4 | 30% | -5% | 12.50% | 5.760% | 3.240% | 0.090% | ||
| Bust | 0.6 | -10% | 25% | 7.50% | 2.560% | 1.440% | 0.040% | ||
| E(R)= | 6.0% | 13.0% | 9.5% | 3.8400% | 2.1600% | 0.0600% | |||
| Var | 3.8% | 2.2% | 0.060% | ||||||
| St.Dev | 19.60% | 14.70% | 2.45% |
