FM213: Principles of Finance - Lent Term Lecture Notes

1. Capital Budgeting and NPV Rule


NPV Rule
£ [ FCF ' ] £ [ FCFZ ] £ [ FCFN]
+
Npyo =
fcfo + + + . . .


Accept if NPVO > 0
It RAS sets ( It r Assets } (I + r Assets )N


Advantages
1. Precision : NPV considers

-

Time value of Money
-




higher discount for more distant with

compensation nor risk higher discount for more volatile cashflow
-
-




2. convenience :
Prs are additive

-


NPVCA + B) =
NPVCA ) + NPVIB ) it projects A and B are independent


free cash flows
FCF =
(I -

E) ✗ C- BIT +
Depreciation -



Change in NWC -
CAPE ✗ +
salvage (after tax )




c- BIT =
Earnings before interest and taxes = Revenue Operating Expenses ( COGS , overhead expenses , D8A )
-


.




t =
corporate marginal tax rate
(I -
E) ✗ C- BIT =
Net Income ( after tax -

profit)


Investment ICAPEXI Depreciation
Not a cost or expense
-

does not mean business Reduction in value of an asset overtime due to wear and tear

is
doing badly → does not affect Net income ,
Net Income = a- E) ( Profit -

costs -

Depreciation )

but is a cash expense → trfcf . Subtract depr . mom Net Income and add back in fcf , as

it is a non -

cash item that generates tax benefit .




Networking capital Depr .
tax shield =
Depr . ✗ Tax rate

=
current Assets -

current liabilities ( CL)

=
Account Receivables +
Inventory
-
CL Salvage
I0U money owed by used by company to
'
manufacture and sell
Book value of an asset after all depreciation has been
customers to me
company products .




TAR → Towedto him →cash ↑ inventory → %ehd→↓fCf fully expense d.
must pay tax on diff .




between sale price and
A measure of to resold at market price
a
company 's ability pay Equipment can be
-




-
boon value


off its short term liabilities with short -



salvage of =

selling proceeds
-


tax rate ✗
capital gain .




assets ✓
term Ca
selling proceeds Book value
= -

.




cumulative
↑ NWC →
more cash tied up → trfcf original investment -




depreciation
' '
Book value captures me
remaining acquisition cost




Incremental cash flows Project depends on all ADDITIONAL cash flows

Include Exclude

Incidental Effects (e. g. introduction of new product decreasing sunk costs
-
-




sales of
existing products .




Networking capital changes
-




opportunity cost ( best alternative use )
-

,Alternatives to NPV
Book Rate of Return IBRR) Accept it BRR > r


Average income divided book value over Reflects lax and not cash flow
by average ✗
accounting figures ,



the project 's life . ✗
Ignores time value of money and risk
BOOK Income
BRR =

BOOK Assets




Payback Period Accept it project pays back within desired timeframe .




Number of years before the cumulative additional ✗
Ignores TVM

cashflows equal the initial outlay .
✗
Ignores cash flows after payback period .




Internal Rate of Return IIRR ) Accept it IRR >
opportunity cost of capital
The discount rate that makes NPV = 0

Problems :




Lending Borrowing
✗
us .




streams of cash Hours
1- preferred
It two are
exactly opposite to
0/
-




to B
each other, have the same IRR
they .




✗
Multiple Rates of Return
-


certain cash flows ( usually negative future cash flows ) can generate NP40 at multiple discount rates .




↑
cashflow with IRR at 3.5%
and 19.54%




✗ NO Internal Rate of Return
-

It is possible to have no IRR and NPV > 0

Usually because project is too good bad
-


or




✗ scale of the Projects
-

IRR
ignores scale of the projects
IRR Chooses f- despite a offering
→
a


higher absolute NPV Of cash flows .




Applications of NPV

Profitability Index Inflation Equivalent Annual cost CEAC)
NPV
PI =
Affects me discount rate The cost per period with the same
investment
I + nominal r
1 + real r = PV as the actual cost of the project .




I + inflation

Choose highest weighted avg.pl
investment Unused PV of costs
WAPI =
§ P/ i ✗
cash available
+ 0 ✗
cash avail .
£ At =


Annuity factor

, 2. Real Options


Real option The
right but not the obligation to
modify the project in the culture .




make money '
? /
Why are real options valuable future is uncertain →
volatility → ↑ value of
flexibility avoid loss .




Decision Trees Build



Diagram of sequential decisions and possible outcomes .
serneiey
0.8
~
Build


"' Build
Cleveland


Types of Real Options •
Build




1. Option to Abandon

abandon to avoid losses
Project no
longer profitable → .




Temporary Abandonment Permanent Abandonment

e. g. Abandon it prices are too low ,
CFCO e.
g. Abandon it NPVA of continuation cashflow
→ cash flows on decision tree
-
< 0 become 0 < value of abandoning ✗
'
Backwards
calculate NPV with new Cfs find where NPVA abandonment ✗
→ →
.
at <

Induction




/
→
Remove subsequent decision three branches for these

scenarios and replace him × .




2. Optionto Expand
investment more provable man expected →
invest more




/
PV of not option date
e. g. Invest more it PV of investment at option date >
investing at backwards
induction .




→
replace decision tree branches
following decision with me higher NPV choice

→
calculate NPV of project with new Cfs .




3. Option to wait
NPV > 0 now , but it implemented in me lutnve ,
NPV will be even
higher .




profit it exercised now value of
waiting ^
option
Option value =
Intrinsic Value + Time Premium price

intrinsic
option value
value


↑ time premium
>
0
stock price



Timing
Even projects with NPV > 0
may be more valuable if deterred .




later
Net future value as of date
Current value =
Peter it RHS > LH5 .




)t