Corporate Finance I Flashcards
What are property rights
- Rights to use an asset - Rights to alienate those use rights Well defined and enforced property rights result in efficient allocation and generate the right incentives
What are the assumptions behind the CAPM
- Investors have mean-variance preferences 2. Investors have the same belifes about the distribution from which returns are drawn 3. Investors have a common investment horizon 3. No costs of trading in financial markets; easy to go short, all investors can borrow and lend at the risk-free interest rate
What should be used to calculate the expected return
a) The required investment amount
b) Market value of the project
Market value of the project
What variation of the CAPM should be used to evaluate cash flows
Certainty equivalent CPM
How does the certainty CAPM work on a very high level?
Instead of changing the discount rate to account for risk, the CE-CAPM adjusts the expected cash flow
Derive the CE-CAPM
What is to be thought of when choosing a risk free rate
Default risk, investment risk, inflation risk are all relevant
There may be several risk free rates
Heuristic: use either 90 T-bill yields or 10-year-T-bon
How do get the market risk premium
Generally, use historic data to estimate the future
Have investors’ risk preferences really not changed
A very long interval is needed to get a low S.E. of estimate
Can cost of debt be priced with the CAPM in general
Yes, the CAPM applies to all capital asset classes, including debt
The cost of debt equals the expected return on debt \mu_{Debt}
The conventional approach uses promised yield to maturity (YTM) to proxy
What is the problem of using the promised return as the cost of debt to opt out the debt beta ?
The expected return of debt does not equal to promised return. There is a risk of default that is not considered in the promised return.
Investors care about default even if they do not care about variance or risk
How big is the error when using the promised rate of return instead the expected return on debt?
What method (approximation) is applied here
Quick and Dirty formula
Derive the quick and dirty formula
What are the assumptions for the quick and dirty formula?
- Debt is perpetual
- Probability of default is the same in each period.
- If default occurs, bondholders receive gamma fraction of the face value of the bond plus accrued interest
- Bond is sold at par, i.e. the bonds initial price equals its principal value
- If the bond does not default, the bondholder receives the promised coupon payment
- Discount rates are constant over time
What is the payback period?
The payback period is the smallest number of periods over which the accumulated free cash flows exceed the initial investment outlay
What is the interpolated payback
Sometime payback is computed by interpolating between periods
Example
What is the Internal rate of return (IRR)
The internal rate of return IRR an interest rate at which the NPV is zero
NPV is what remains of free cash flow after paying investors a fair return on their capital
What are problems of the IRR
- IRR assumes that cash thrown off from the project can be reinvested at the IRR rate
- It is very hard to comapre projects using IRR
- When project cash flow change signs many times, the project can have many IRRs
What is the modified IRR and what kind of rates do we need for that criteria?
A financing rate is applied to outflows to push them to date
A reinvestment rate is applied to inflows to push them to date T
What is the MIRR from that example
What are the pro and cons of the MIRR
The advantage of MIRR is that it does not have the multiple root problem of IRR
Whereas the IRR does not have to assume a discount rate, the MIRR one needs to assume two rates of return
In total we need three discount rates for that method
What are potential problems with multiples
First, it is to say that multiple valuation is easy which is a plus point, but
Multiple generates relative values, they will not identify sectoral mispricing
NPV is fundamental, multiples are sometimes harder to justidy
Problems with irregular cash flows
How to value terminal project valuations
The terminal value at this horizon date is usually estimated by either
EBITDA multiples
Gordon growth formula
How does the gordon growth formula look like?
What are problems with terminal value estimates
(Gordon Growth, Multiples)
If gordon growth formula is used:
Terminal valuations are very sensitive to g
There is no lower bound for g, but a stable g cannot exceed the growth rate of the economy
If multiples are used:
The projects’s long run cash-flow matches industry norms
Today’s multiples are the same as those which will obtain at the end of planning horizon
What is a ex post project evaluation
Economic Value Added (EVA)
How is economic and accounting depreciation calculated
How is EVA calcualted?
Why is EVA not optimal as project evaluation per se?
EVA is a period by period snapshot of the value of an investment project. A project selection criterion is a overall valuation of the project over its whole life
NOPAT is not free cash flow
EVA of a positive NPV project need not be positive in every year of the project’s life
EVA of a negative NPV project need not be negative in every year of the project’s life
The PV of the EVAL of a project equals the project’s realized NPV
Why?
NPV is a single number that reflects the total effect of a project on firm value
EVA is a consequence, one for each period
Trying to compare EVA with NPV is like trying to compare 6 with 1 7 -2
The present value of EVA equals the realized NPV from the project
Show that the present value of EVA equals NPV
Begin with the equation
What are arguments for and against the use of EVA
Pro:
If your manager is sure to stick around for the life of the project
Compensating your manager with rewards proportional to EVA will lead to her make value maximising project choices
Cons:
Assumptions are not realistic
State the gordon growth formula for share prices in terms of the dividend payout ratio
What is the MM proposition I
Suppose that market are complete with perfect competition and no transaction costs that all agents have the same information that there are no costs of bankruptcy and no agency costs. Then in the absence of taxes, the value of a corporation is independent of its capital structure
Proofed by arbitrage
What is MM proposition II
Since FCF is independent of capital structure, the corporate cost of capital is independent of the capital structure
What does constant growth of cash flows ensure (thinking about discount rates)
We then will have constant rates of return
What are implications of the constant rate of growth assumption
The unlevered firm’s discount rate is constant and equal to r_u
The value of the unlevered firm in every period is a constant multiple of its current cash flows - These multiples are known constants at date 0
How is the tax shield valued at time t
What discount rate should we use when having a constant debt ratio in the WACC model
How do we value the tax shield when we have a constant debt level
Would you allocate:
Miles Ezzell policy
WACC policy
MM policy
to either Constant ratio policy or constant level policy
Constant ratio policy:
Miles Ezzell policy
WACC policy
Constant level policy
MM Policy
What are the two methods of the constant ratio policy and how are they used
How does the levered company discount rate/ beta compare against its unlevered counterpart in a constant level policy setting and why
What is the Capital Cash Flow approach
Applied when the company has a constant ratio policy. This approach values the tax shield separately using the cost of the unlevered company. The reason for that is that the tax shield has the same risk as the company’s cash flows
Using this equation of the CCF approach and show that this is equivalent to the WACC approach
How does the WACC look like if it is adjusted for taxes
Describe the Miles Ezzell on a very high level
The Miles-Ezzel ME formula obtains a cost of capital for free cash flows based on the unlevered cost of capital, constant over time, and the current cost of debt capital
What does the APV differently to the WACC valuation
The alternative to WACC valuation is to direclty value the tax shield, discount it at its own appropriate rate
How are equity betas and unlevered betas related under the constant ratio and constant level policies
Show how the relation between the unlevered beta and equity beta is arrived under the constant ratio assumption
Simply stating the weighted average beta of the company combined with the assumption that beta debt is equal to zero
Show how the relation between the unlevered beta and the equity beta is arrived under the constant level assumption
What is bankrupcty
It is the law that governs the way that the company’s assets are distributed in the wake of a failure to pay debt
What are direct and indirect costs of bankruptcy
Direct costs are out-of-the pocket expenses associated with bankruptcy proceedings
What are indirect costs of bankruptcy
- Industry performance
- Firm performance
- Short-term interest changes
- Firm leverage
What is the trade off theory of the tax shield and bankruptcy
Firms trade off the value of the tax shield against the increasing expected costs of bankruptcy until the two effects are the same at the margin
What is the Miller Equilibrium
The argument of Miller is that in equilibrium the marginal borrower derives no tax advantages from issuing debt rather than equity
How do you compare the lease and purchase options
Discount lease cash flows using a discount rate appropriate to each cash flow
Disocunt buy cash flows at a discount rate appropriate to each cash flow
Choose the option that produces the highest discounted value
What is a financial lease
A lease where essentially all of the economic value of the leased asset is transferred to the lessee
Lease term equals the economic life of the asset
Lease is non-callable
Lessee assumes all maintenance and upkeep costs associated with the asset
What is rule of Myers, Dill and Bautista regarding lease vs. buy
Discount after tax lease excluding lost debt tax shields at the after tax cost of debt capital. If the resulting present value is less than the purchase price, lease; otherwise buy
What are assumptions of MDB regarding the classic lease vs. buy formula
Lease obligations are identical to debt obligations with respect to risk
Lease obligations are perfect substitutes for debt in the firm’s capital structure
Firm follows a constant-debt-level policy
The firm can fully utilise all of its tax shields
Valuation of the firm is based on MM analysis with taxes
For which kind of leases is the lease obligation assumption made by MDB realistic?
Only for financial leases
Derive the classical lease formula given these parameters for the case when t < H and t >= H
If t >=H, future costs are 0, hence the cost of leasing is zero
The other case is described in the picture
If the MDB assumptions for leases do not hold why can the follwoing be problematic
- Risk of lease contract is not the same as risk of debt
- Debt and lease contracts are not perfect substitutes
- Not all tax shields can be utilisied
- Options built into lease
- Differential treatment in insolvency bankruptcy
- Insufficient taxable income
Explain every part of the formula and why it is there. Context: Financial leases
The first part of the equation is just the lease payment which is tax deductible and therefore we only count the part we actually pay
The second part is the tax benefit we lose because of not buying it and therefore also not depreciating the asset
The part afterwards is due to the fact that assuming we would have bought the asset with debt then we would have an increase in the tax shield
The last part is the future cost of lease. Here we have again the depreciation, the lease payment and the loss in the tax shield.
In the end we will iterate that process
What are common approaches for real options
Simple shoehorning
Fancy shoehorning
Simulation
Analytical modelling
What is simple shoehorning the context of real options
Fit the capital budgeting problem into the black scholes model for pricing european options
Try to find the current price of an underlying asset that drives the project’s payoff
What is fancy shoehorning in the context of real options
Exchange option formula: Consider an option of exchange of two assets X and Y paying max(X-Y,0)
Compound option models: Options where exercising one option provides the holder with another option on the same asset
Describe the simulation approach in the context of real options
Identify an underlying asset or use risk-adjusted discounting to value the project under the assumption that it undertaken
Use the black-scholes risk neutral valuation assumptions to generate random prize paths starting from the current value
Compute the payoff for each of these paths decision
Average the payoffs and discount back at the risk free rate
What is the analytical approach in the context of real options
Develop your own continous time pricing model tailor to your project
Solve the model in closed form
Input the parameters into your solution
Value the asset
When would the investor be indifferent between a tax-exempt municipial bond which offers a return r_0 and a corperate bond
What is the sum of the cash flow to investors given these variable definitions
Given these parameters, what is the Miller tax advantage?
What is the alternative to value bonds if the beta is not known but the value of the company in different states in the world is known as well as the discount rate for the company as a whole
Risk neutral Probabilities are applicable.
First we calculate the RNP through the company, and then we apply these probabilities on the bond itself
How do you calculate the nominal yield of a bond?
Why might that be incorrect as a measure of yield
What is the ‘correct’ way of calculating the required rate of return
Promised payment/ Price of the bond - 1
It does not price in the fact that default could occur
Expected Value of Cash flow / Price of the bond - 1
How can it be possible that two companies have the same probability of default but the required rate of return is different?
The probability of default can be related to the state of the economy or not related to the sate of the economy.
Let us consider the first case: If it is related than this risk is not diversifiable and investors should be compensated for that risk
In the other case, if it is not related to the state of the economy that risk is company specific and hence can be diversified. Investors should not get compensated for that
If the volatility of a project is 0.8, how do you calculate up and down probabilities?
Assuming the risk free rate is 5%
Assuming you have the option to sell an asset at date t=1 for 24. You know that your asset can either have an up movement or a down movement. How do you value that real option in basic terms.
Hint (Risk neutral probabilities)
Assume you have an option which entitles you to buy half of the company’s ownership for 2m. The company (which value at t=0 is denoted by V_0) can either have an up or a down movement which happen with the risk neutral probabilitiy q.
Furthermore, you can disregard the ‘down’ case as that would be negative
How would the valuation formula look like
Assume that the volatility of return is 0.95
Calculate the up and down movement multiplier
