Providing an in-depth guide to FM213 lent term with all topics covered in this guide with question examples as well as comprehensive explanations. Seller achieved a first class in this module - common exam questions covered.
,1 Capital Budgeting and the NPV Rule
1.1 NPV
The NPV converts future cash flows into a single present value.
One invests if the NPV > 0
The calculation considers time value of money ↑ r for more distant
future
Compensation for bearing risk ↑ r for more volatile cash flows
NPV ( A+ B )=NPV ( A ) + NPV (B) if projects are independent,
present values are additive which makes it convenient.
1.2 Free Cash Flow (FCF)
Unlevered FCF ignores all financing side effects:
1. Depreciation a non-cash item that generates tax benefit (↑ FCF ¿
Depreciation tax shield = Depreciation·Tax rate
2. CAPEX investment is not claimed as a cost or expense; therefore,
investment expenditure doesn’t enter the net income calculation di-
rectly.
Investment is a cash expense, which lowers the FCF.
3. NWC captures how much liquidity is tied up by the operation
As NWC increases, FCF decreases as more resources are tied
up
∆ NWC=(∆ CA−∆ CL) or ¿)
4. Salvage Value recovery value of used productive capital
At the end of a project, used equipment can be sold at market
price
However, we need to pay tax on capital gain (book value
captures the remaining acquisition cost you have paid on your
investment:
Capital Gain=selling proceeds−book value
o
o Book value=orginial investment −cumulative depreciation
Cash flow from Salvage = selling proceeds−(t·capital gain)
Depreciable amount = original investment −salvage value
5. Operating Cash Flow Net Income+ Depreciation
1.3 Book Rate of Return
Average income divided by average book value over project life.
Book Income
Book rate of return =
Book Assets
, Invest if book rate of return is high enough
Rarely used to make decisions time value of money and risk are ig-
nored.
1.4 Payback Period
Number of years before cumulative forecasted cash flow=initial project outlay
Rule accept project that payback within desired time frame
Ignores the time value of money and risks, ignores valuable cash flow
after payback period
1.5 Internal Rate of Return (IRR)
The discount rate that makes NPV =0.
Hurdle Rate invest if IRR> opportunity cost of capital
Pitfalls:
Lending vs Borrowing pitfall if two streams of cash flow are ex-
act opposites of one another, then they must have the same IRR, but
you can only prefer one (NPV positive or negative): IRR method can-
not distinguish between the two.
Multiple Rates of Return pitfall Certain cash flows can generate
NPV =0 at many different discount rates
Non-Existence of IRR pitfall It is possible to have no IRR but
positive NPV; either project is too good or too bad
Scale of the Projects pitfall Ignored scale of the project. Smaller
projects may offer a higher IRR but lower NPV, whilst large projects
may do the opposite.
1.6 Applications of NPV
1. Profitability Index
NPV
PI =
Investment
Choose project with the highest weighted average PI (WAPI )
E.g.,
WAPI ( BC )=P I B ( totalBcash )+ P I ( totalCcash )+ 0.0( totalsparecash )
C
2. Inflation
Change in price of typical basket of goods affects the dis-
count rate
1+ nominal interest rate
1+real interest rate=
1+inflation rate
Nominal figure
Real figure=
1+ infaltion rate
, 3. Equivalent Annual Cost (EAC)
Cost per period with the same PV as the actual cost of the
project
PV of costs
EAC=
annuity factor
2 Real Options
2.1 Definitions
Real options are the right but not the obligation to modify projects in the fu-
ture.
This is very valuable as you can avoid bad projects
Waiting is costly if valuable opportunities are sacrificed like losing
dividend when delaying exercise of stock option lose x years of
cash flow
Decisions tree a diagram of sequential decisions (available actions and
timings) and possible outcomes (payoffs and timings) used to help identify
and describe real options
Intrinsic Value (of an option) the profit if the option is exercised now
Time Premium (of an option) the value of being able to wait to exer-
cise an option
Why are real options valuable? If the future is deterministic, flexibility is
meaningless; every decision can be made and optimized upfront. But, if the
future is random, flexibility is very valuable. The more volatile the future, the
more valuable real options are.
What are the two sources of risk when market-testing? The two
sources of risk are cash flow risks and market-type risks.
How does market research create a real option? With many choices,
we take the NPV of the expected projected cash flow. When we research, we
learn about choices before investment, and hence we take the NPV of the
expected projected cash flow conditional on our research information. Dis-
count back to research period using risk-free rate, because holding cash is
risk free.
What does option theory suggest about whether we should wait or
start the project immediately? Early exercise is never optimal for an
American call option on a non-dividend paying stock, but
early exercise may be optimal for a dividend paying stock. What are the
strengths and weaknesses of real options? Real options are valuable
because, with them, you can avoid bad projects. But waiting can be costly if
valuable production opportunities are sacrificed – this is similar to losing a
dividend payment when delaying the exercise of a stock option.
What is the motivation behind real options? Firms do not hold assets
passively till maturity managers do not just watch the future unfold.
2.2 Option to Abandon
An option to abandon may be exercised when the project is no longer prof-
itable.
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