lecture 7 Flashcards
how to reduce the uncertainty of future cash flows using a probabilistic approach?
with the standard deviation
Risk Adjusted Discount Rate (RADR)
sum total of the risk-free rate and the risk premium
CAPM is relevant for the security market, but is it relevant for capital budgeting projects?
yeee bruuuv
SML is relevant for selecting securities, but is it relevant for selecting capital budgeting projects?
why?
yeee bruuuuv
we can use SML to determine the discount rate
–> each project should be evaluated with its own cost of capital
when do we accept using the SML project?
when it lies on the SML or above
when do we reject using the SML project?
when it lies below the SML
when do we use the WACC as the discount rate?
the appropriate discount rate for capital budgeting only if the project evaluated has the same risk as that of the firm as a whole
–> both financial risks and business risks of the project and company must be similar
when is a project j acceptable using the SML
When ERj (kj) = or > than RF + Bj · (ERM - RF)
when can we ensure that the beta of a project is the same as the beta of its firm
Financial Risk of Project = Financial Risk of Company
Business Risk of Project = Business Risk of Company
Financial Risk of Project = Financial Risk of Company
the debt/equity ration after accepting the project should remain the same as before
risk due to leverage (borrowing) as D/E increases
measured by degree of financial leverage
Business Risk of Project = Business Risk of Company
the level of fixed assets for the project compared with total assets must remain approximately the same as before the project’s acceptance
–> measured by degree of operating level
when a company uses WACC for discount rate, what do they tend to do when using the SML too?
they tend to do incorrect acceptances and rejections
say a project only needs 12% as a discount rate using the SML but actually achieves a 14% return
–> company that uses a WACC of 15% would incorrectly reject it because 15% > 14% even though the project is sexy as fuck
say a project only needs 17% as a discount rate using the SML but actually achieves a 16% return
–> Using the WACC of 15% would tell us to incorrectly accept it because 16% > 15% even tho the project is trash
formula for the Beta of equity
Beta of project · (Beta of project - Beta of debt) · D/E
but since debt is usually quite small and future cash flows from debt are know ahead of time
Beta of equity = Beta of project · (1 + D/E)
–> Beta of equity will increase as the D/E increases
Beta of equity will increase as the Beta of project increases
what is the risk shareholders face
risk due to leverage (debt level)
–> risk due to leverage (borrowing) as D/E increases
–> measured by degree of financial leverage
risk due to level of capital employed (level of fixed assets)
–> business risk
–> measured by degree of operating level (D. O. L.)
degree of operating level (DOL) formula
DOL: ((P - VC) · Q) / ((P - VC) · Q) - TFC)
P: Price per unit
Vc: variable cost per unit
TFC: total fixed cost
so when TFC increases, so does the DOL
–> higher level of fixed assets, higher TFC, higher business risk for a firm
degree of financial leverage formula (DFL)
DFL: EBIT / (EBIT - I)
or
(Q · (P - VC)) / (Q · (P - VC) - TFC - I)
I: interest payments
–> as interest payments increase, so does the DFL
—-> risk increase for shareholders
degree of total leverage (DTL)
the total risk of a firm
Business Risk and Financial risk
degree of total leverage (DTL) formula
((change in EPS) / EPS) / ((Change in Q) / Q)
or
DOL · DFL
so when does the beta of equity increase
increases with the firm’s business Risk and Level of fixed assets
increases with the firms level of debt (Financial Risk)
how do we calculate the Beta of a project j
(COV (j, M)) / σ^2M
5 methods other than the RADR to adjust for project risk
1) certainty equivalent method (CEQ)
2) the subjective approval
3) sensitivity and scenario analysis
4) decision trees (real options)
5) Monte Carlo model
certainty equivalent method (CEQ)
cash flow is certain (there is no risk)
investor would be happy with the RF as a discount rate
CEQ / (1 + RF) = PV = C1 / (1 + k)
(1 + k) / (1 + RF) = C1 / CEQ
(1 + k) / (1 + RF) > 1
C1 > CEQ
CEQt = Ct · ((1 + RF) / (1 + k))^t
PV = (at · Ct) / (1 + RF)^t
at = CEQt / Ct = ((1 + RF) / (1 + k))^t
certainty equivalent method (CEQ) various formulas
PV = CEQ / (1 + RF) = C1 / (1 + k)
(1 + k) / (1 + RF) = C1 / CEQ
(1 + k) / (1 + RF) > 1
C1 > CEQ
CEQt = Ct · ((1 + RF) / (1 + k))^t
PV = (at · Ct) / (1 + RF)^t
at = CEQt / Ct = ((1 + RF) / (1 + k))^t
subjectively adjusted discount rate
discount rate adjusted based on rules of thumb
–> the greater the risk, the higher the adjusted discount rate, the lower the NPV
subjectively adjusted discount rate formula
kj = WACC + Subjective Risk Premium
when is the Subjective Risk Premium positive?
kj > WACC
when is the Subjective Risk Premium negative?
kj < WACC
what are the assumptions when using CAPM to find an appropriate discount rate of a project?
the Beta of the project is constant and know over the project’s life
risk free rate remains the same
market risk premium remains the same
what do we do when the assumptions when using CAPM to find an appropriate discount rate don’t hold?
to apply different rates at different stages of a project’s life or to recast the problem into certainty equivalents
what are the scenario and sensitivity analysis used for?
tools available to identify potential errors when calculating the NPV of a project
scenario analysis
define a base case and then change certain variables to come up with different scenarios
ex: good or bad scenarios inspired by the base scenario
sensitivity analysis
only one variable is changed each time
decision trees
convenient way to set out possible consequences of future decisions
forced open the underlying strategy of a given project, revealing the ling between today and tomorrow’s decisions
–> help the financial manager find the strategy with the highest NPV
used in options
–> abandonment value
–> expansion value
subsequent decisions
depend on those made today
formula to find which level of EBIT would make the issue of bonds better than the issue of shares
((EBIT - I) · (1 - Tc)) / (# of shares outstanding with bonds issued)
=
((EBIT - I) · (1 - Tc)) / # of shares outstanding with more shares issued)
