examen Flashcards
What investment rule would you recommend and why?
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NPV is recommended because:
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-It compares the entire cash flow at a given discount rate and therefore takes into account the time
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-The discounted future cash flows are then compared to the initial investments I0.
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-Allows for comparison between projects with different risk profiles.
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- NPV > 0, concludes that the project should be initiated, since its returns > discount rate.
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-NPV may also be used in combination with IRR, which will provide a comparable interest for the project.
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- Finally, the discount rate relates the relative riskiness directly: High risk = High discount rate.
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- And NPV is easy to use, understand and communicate.
NPV=-Investment +sum vert år ( Cash flow/(1 + discount rate^år)
Drawback:
- Dependent on correct discount rate (therefore recommended to use together with IRR) and estimates on future cash flows.
What are the potential pitfalls associated with the Internal Rate of Return (IRR)?
Timing, scaling, multiple or no IRRs, cannot differ between lending and borrowing
What is a Monte Carlo simulation and how can you apply it to an investment analysis?
MC algorithm:
1. Identify the projects cash flows, formula for project NPV and its dependent input factors.
2. Estimate probability distr. for input factors, e.g. for the product price.
3. Draw from probability distributions in (2) and calculate NPV.
4. Repeat steps (2)-(3) several times (e.g. 100 000 times)
5. Calculate expected NPV from (4).
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-In a MC simulation a set of input factors are drawn in what can be understood as a complex “What-if” analysis. (1)
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-A set of input factors is chosen and each of the input factors is assigned a probability distribution. (2)
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- These input factors are then simulated, and this simulation is run thousands of times to create a probable outcome for the project’s NPV. (3-4)
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- This creates a probability distribution for the NPV and also an expected NPV. (5)
If the expected NPV > 0, the investment can be accepted.
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- However, an investor may assess the relative riskiness, e.g. whether the downside (and upside) of the investment is considerable…
- -Finally, a complex model may be too complex, and we may end up with something “exactly wrong” or GIGO = Garbage In, Garbage Out.
What is the Capital Asset Pricing Model (CAPM) and why is it important when evaluating a set of investments?
Assume a discount rate of 20%. Calculate the Net Present Value (NPV) and rank the 3 projects using NPV. Which project(s) should you invest in?
According to NPV, C is the best investment. Ranking: C > B > A
Since NPV > 0, all projects should be initiated.
how to calculate Profitability Index (PI)?
how to calculate Net Present Value (NPV)
Rank the 3 projects using the Profitability Index (PI). Which project(s) should you invest in?
According to PI, A is the best investment. Ranking: A > C > B
Since PI > 1, all projects should be initiated.
Calculate the Internal Rate of Return (IRR) for the projects. Which project(s) should you invest in and how does this compare to your answers in (a) and (b)?
This is solved by “try/fail” method, after setting NPV = 0:
Since IRR > discount rate, all projects should be initiated.
Ranking: A > C > B.
Note that due to different investment size and timing of cash flow, the ranking in c) differs from a).
If you can only invest 2 000, which project(s) should you invest in? Show your calculations.
Since NPV for C > NPV for A + B, the firm should invest in project C.
What is the expected net present value of this project?
The Company has the opportunity to postpone the investment to period 1.
What is the expected net present value as seen from period 0, if the firm decides to invest in period 1?
What is the value of the flexibility associated with the opportunity of waiting one period with the investment?
Draw a decision tree illustrating the investment opportunities. Also, list the typical real options to consider in an investment analysis.
Real options to consider are:
- Expand
- Abandon
- Delay
The company is going to invest in a new project that is an expansion of the company’s existing business. It is not going to be in a tax paying position for the duration of the project. What is the required rate of return on the project?
Required rate of return on equity is 6,44%
The company considers investing $100 million in another new project within its line of business. The project requires the company to loan 60% of the required capital. The interest rate is 7% because the lenders consider the company slightly risky. The company is now also in a tax position, and faces a tax rate of 28%. What is the Weighted Average Cost of Capital (WACC) for this project?
The cash flow (in millions) of the project is described in the following table. Should the project be initiated? Explain why/why not and discuss typical issues with your analysis and conclusion.
Year
0
1
2
3
4
Cash flow
-100
20
30
40
50
Explain real options.
Value of an option to adjust the project after it has been accepted.
E.g.:
- Option to abandon
- Option to expand
- Options of timing and scaling
Explain sensitivity analysis and its advantages/disadvantages.
Sensitivity analysis compares the outcome of a project by varying the value of one input at a time. e.g. a project that is dependent on oil price and construction cost, may choose to do sensitivity by varying the oil price by +/- 10% and 20% or vary the construction cost by +/- 10% and 20%, and study how the NPV of the project varies as the input varies.
Major disadvantage is that we only vary one variable at the time, while there is a chance many of the variable may experience changes at the same time due to correlation. Moreover, we do not know what change is more likely, e.g. is a reduction in oil price by 20% equally probable as a 10% increase in construction cost?
Explain Modigliani and Miller’s propositions I and II (without taxes).
MM proposition 1 (without taxes): The market value of any firm is independent of its capital structure. In other words: Financial managers (i.e. stockholders) should not worry about the financial leverage of the firm
MM proposition 2 (without taxes): Expected return on equity increases in proportion to the debt-equity ratio (D/E), expressed in market values, and the rate of increase depends on the spread between rA and rD:
Explain “tax shield” in financing, and how this changes the Modigliani and Miller’s theorem I and II (with taxes).
Interest Tax Shield:
Tax savings resulting from deductibility of interest payments
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MM proposition 1 (with taxes):
The market value of a company increases with debt due to the tax shield.
- In other words: Financial managers (i.e. stockholders) should increase debt/equity-ratio.
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MM proposition 2 (without taxes): Expected return on equity increases in proportion to the debt-equity ratio (D/E), expressed in market values, and the rate of increase, although reduced due to tax-shield compared to MMII (without taxes)
Explain Internal Rate of Return (IRR) and its potential pitfalls.
IRR provides us a discount factor where NPV = 0.
Pitfalls:
1. Cannot differ between borrowing/lending
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2.Timing of cash flows
- - With some cash flows the NPV of the project increases as the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. The IRR rule will only give the same answer as the NPV rule whenever the NPV of a project is a smoothly declining function of the discount rate, and for some project cash flows this is not the case.
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3. Size of investment
- - IRR sometimes ignores the magnitude of the project when we have mutually exclusive projects (ie. Can only undertake one of the projects).
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4. Multiple IRRs
- - Certain cash flows can generate NPV=0 at two different discount rates. It is possible to have no IRR and a positive NPV
How do Net Present Value (NPV) and Internal Rate of Return (IRR) complement each other?
NPV provides an estimate of a project’s profitability assuming a set discount factor.
NPV = Investment + Discounted future cash flows
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IRR provides a discount rate r where NPV = 0. Together, IRR and NPV provides valuable information about the project’s profitability and its vulnerability towards its correct discount rate. If IRR < or = project’s discount rate, the project is profitable. The bigger the difference between IRR and project’s discount rate the higher the profitability’s certainty.
Explain the 3 potential pitfalls associated with using IRR in selection of projects.
1.Cannot differ between borrowing/lending
2. Timing of cash flows
3. Size of investment
4. Multiple IRRs
Explain real options.
Real options are extra value to a project that occurs as possible adjustments after the project is initiated. It is important to include in a project’s evaluation, since it will only provide a positive (or at least = 0) addition to the project’s value.
Real option = NPV with flexibility - NPV without flexibility
The flexibility may be the option to:
- Abandon
- Expand
- Delay
Explain Monte Carlo simulation and its advantages/disadvantages.
Monte Carlo algorithm:
1.Identify NPV-formula and dependent variables
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2. Estimate/assume probability distributions for dependant variables
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3. Draw random numbers from probability distribution in (2). Calculate NPV.
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4. Repeat (3) for a number of times (e.g. 10 000 times).
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5. Sort results from (4) and construct the simulated NPV probability distribution.
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Advantages: Possibility to define advanced/complex NPV-estimations, and include correlation.
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Disadvantages: Relies on correct probability distribution in (2). May become too complex. Time consuming.
Explain the Capital Asset Pricing Model (CAPM).
A beta = 2 indicates that the asset is twice as risky compared to the market, and consequently the investors require twice the expected return.
Question 3 –Weighted Average Cost of Capital (25 %)
The total market value of Stavanger Real Estate Company (SREC) is $50 million, and the total value of its debt is $20 million. The treasurer estimates that the beta of the stock currently is 1.8 and the expected risk premium on the market is 8 percent. The risk free interest rate is 2 percent, and the company pays 5% in interest on its debt.
What is the required rate of return on SREC stock?
Compare Net Present Value (NPV) with Internal Rate of Return (IRR).
NPV discounts all cash flows and compare future cash flows with the initial investment. If NPV > 0 then project is profitable. Important to use correct discount rate which should reflect level of risk associated with project. High discount rate = high risk.
IRR is the discount rate where NPV = 0. This can then be compared to the company’s or project’s discount rate r. If IRR > r then project is profitable since NPV @r > 0. Has 3 pitfalls: scaling, timing and borrowing/lending.
IRR and NPV is often used together.
Explain risk aversion.
Risk aversion considers how an agent values risk. In general investors consider safe cash flows more valuable than uncertain cash flows. However, a risk lover (gambler) would prefer the extra uncertainty and perhaps the opportunity to win big over certainty and the possibility of a small safe bet. The opposite is true for a risk averse person. Finally, a risk neutral person would make decisions based only on the expected cash flow.
Explain sensitivity analysis and its advantages/disadvantages.
Sensitivity analysis compares the outcome of a project by varying the value of one input at a time. E.g. a project that is dependent on oil price and construction cost, may choose to do sensitivity analysis by varying the oil price by +/- 10% and 20% or vary the construction cost by +/- 10% and 20%, and study how the NPV of the project varies as the input varies.
Major disadvantage is that we only vary one variable at the time, while there is a chance many of the variable may experience changes at the same time due to correlation. Moreover, we do not know what change is more likely, e.g. is a reduction in oil price by 20% equally probable as a 10% increase in construction cost?
Explain the Capital Asset Pricing Model (CAPM).
And calculates the expected return of an asset i by using a risk premium against the market and the risk associated with the market, as defined by Beta.
A Beta of 2 means that the asset is twice as risky as the market, and with a 10% increase (decrease) in the market the asset will increase (decrease) with 20%.
Explain the opportunity cost of capital.
The opportunity cost of capital is the expected rate of return investors could earn in financial markets at the same level of risk as the asset to be valued.
Explain briefly the Capital Asset Pricing Model (CAPM).
CAPM describes the relationship between risk and the expected return. (formel 1)
rA is the return for the asset, which depends on the time value of money (risk free interest rate, rf) and the asset specific risk.
This asset specific risk is represented by the other half of the formula: Beta*(rM-rf), where rM-rf is called the market risk premium.
The asset specific risk represents how much the investor must be compensated when investing in the asset (compared to a risk-free investment and the market premium).
CAPM explains the risk/return trade-off: Higher risk = Higher returns.
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Beta represents the relative riskiness of an asset to the market: (formel 2)
A beta bigger than 1 represents an asset which is riskier than the market.
A beta smaller than 1 represents an asset which is less risky than the market.
In CAPM beta is the only risk the investor should receive an expected return higher than the risk-free interest rate.
CAPM assumes that investors have the same information and expectations.
Explain briefly Weighted Average Cost of Capital (WACC).
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The Weighted Average Cost of Capital (WACC) is one of the key inputs in discounted cash flow (DCF) analysis and is frequently the topic of technical investment banking interviews.
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The WACC is the rate at which a company’s future cash flows need to be discounted to arrive at a present value for the business. It reflects the perceived riskiness of the cash flows.
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Put simply, if the value of a company equals the present value of its future cash flows, WACC is the rate we use to discount those future cash flows to the present.
WACC Formula?
xplain briefly tax shield in financing and how this is important when calculating the Weighted Average Cost of Capital (WACC).
Notice in the Weighted Average Cost of Capital (WACC) formula above that the cost of debt is adjusted lower to reflect the company’s tax rate. For example, a company with a 10% cost of debt and a 25% tax rate has a cost of debt of 10% x (1-0.25) = 7.5% after the tax adjustment. That’s because the interest payments companies make are tax deductible, thus lowering the company’s tax bill. Ignoring the tax shield ignores a potentially significant tax benefit of borrowing and would lead to undervaluing the business.
Use Modigliani & Miller’s theorem and discuss briefly the importance of how a company or a project is financed.
MM I without taxes states that the company value is indifferent to how the company is financed, however MM II notes that the risk is increasing with increasing debt levels. However, this gearing also provides a higher expected return to equity holders.
With taxes, MM I advices to take on as much debt as possible due to the extra value added from the tax shield. The same tax shield reduces some of the risk, but risk still increases with increasing debt levels according to MMII.
What real options are important to consider when evaluating an investment?
Real options to consider is:
- Expand
- Abandon
- Delay
- Synergy/cannibalism
Risk aversion.
A risk averse individual or firm dislikes risk. It will accept a smaller amount of money with certainty than the amount that it could expect to receive in a gamble (i.e. expected wealth, E(W)). For a risk averse individual this means that the certainty equivalent wealth would be less than the expected wealth associated with the gamble (see answer to question c). In mathematical terms the von Neumann-Morgenstern utility function of a risk averse individual has a negative second derivative, i.e. U’‘(W)<0.
Use of net present value (NPV) vs. internal rate of return (IRR) in investment analysis.
IRR has 4 pitfalls:
- Multiple IRRs
- Borrowing/lending
- Scaling
- Timing
Can use incremental IRR to counter scaling issues.
Modigliani and Miller’s propositions I and II.
a) Which project will a risk neutral investor prefer? And, which project will a risk averse investor prefer?
Projects A and B are preferred by a risk neutral investor. Project B is preferred to project C by a risk averse investor, but one need more information on risk preferences to determine if A or B is preferred.
