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Summary Capital Investment Policy 20/21 TEW KU Leuven
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Summary of the course CIP 2020/2021 For 2nd & 3rd bach
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LECTURE 1INTRODUCTION & CIP DEFINITION
Any company had to answer 2 broad questions:
1. What investments should it make?
2. How should it pay for these investments?
o We primarily focus on 1.
THE FINANCIAL GOAL OF THE CORPORATION
A company is a group of projects, role of management is to choose the best projects
A project is a series of cashflows
o Cash inflows represent revenue
o Cash outflows represent initial investment and expenses
Cash flow is an amount of money paid at a specific time
All shareholders – independent of their individual preferences – can agree to assign one objective to the
manager: to maximize the current market value of shareholders’ investments in the firm
o With functioning financial markets, the wealth can then be put to whatever purpose each shareholder
wants
o Maximizing shareholder value =/= maximizing profits
Managers’ private interests might not be aligned with the shareholders’ objective; such diverging objectives
cause agency problems
Agency costs are incurred when managers do not attempt to maximize firm value, or when shareholders incur
costs to monitor and constrain managers’ actions
NPV RULE
Present Value rule: invest if PV(benefits) > PV(costs)
Net Present Value: invest if NPV > 0
Rate of Return rule: invest if Rate of Return = profit / investment > r
A perpetuity is a financial instrument that pays C dollars per period forever, starting one period from today
o If the interest rate is constant, the PV is: 𝑃𝑉 = ∑
o The PV of a growing perpetuity: 𝑃𝑉 = ∑
An annuity is a financial instrument that pays C dollars for T periods, starting one period from today
o It has the following PV formula: 𝑃𝑉 = ∑ [1 − ( ) ]
( )
o A growing annuity: 𝑃𝑉 = ∑ [1 − ( )
]
Regardless of our preferences for cash today versus cash in the future, we should always maximize NPV first
,ALTERNATIVE DECISION RULES
IRR: INTERNAL RATE OF RETURN
A projects IRR is defined as the interest rate that sets the NPV of cashflows equal to zero. Given 𝐶 , 𝐶 , … , 𝐶
the IRR is the r solving the equation: 𝐶 + + + +⋯+( ) = 0
( ) ( ) ( )
Accept project if IRR > hurdle rate
In general, the difference between the cost of capital and the IRR is the maximum amount of estimation error
in the cost of capital estimate that can exist without altering the original decision
o If the difference is very small, a very precise estimate is needed
Pitfalls of the IRR-method:
o Lending or borrowing: IRR assumes a negative cashflow in t=0 and a positive cashflow in t=1, however,
if this is the other way around (negative NPV), IRR still assumes it is a good project
o Multiple IRR values: not always an unique solution
o Mutually exclusive projects: ignores the scale of the project
o Time varying interest rates: way too difficult
o No real solutions exist
THE PAYBACK RULE
The payback method is the amount of time it takes to recover or pay back the initial investment. If the payback
period is less than a pre-specified length of time: you accept the project.
o Does not always give a reliable decision since it ignores the time value of money
INTEREST RATES
INTEREST QUOTES AND COMPOUNDING
Suppose we earn 3% interest every 6 months.
Effective Annual Rate (EAR) = effectieve interest = 6,09%
Annual Percentage Rate (APR) = schijnbare/nominale interest = 2x3% = 6%
Converting between k times per year and annual rates: 1 + 𝐸𝐴𝑅 = (1 + )
As k gets very large, we converge to continuous compounding: 𝐸𝐴𝑅 = 𝑒 −1
INFLATION: NOMINAL VS REAL INTEREST RATES
A nominal cashflow is the number of dollars you pay out or receive (includes inflation) will have different
purchasing power at different dates
A real cashflow is adjusted for inflation always has the same purchasing power
To convert, we use: 𝑅𝑒𝑎𝑙 𝐶𝐹 =
( )
Or (a general rule): (1 + 𝑟 )(1 + 𝑖) = 1 + 𝑟
, LECTURE 2
INTRO & CAPTIAL RATIONING
Pitfall to using the NPV rule: Capital rationing
We can see that project A has the highest NPV,
however, we could also invest in project B AND C
this will lead to a better NPV (16 + 12 = 28) than
project A
How should the firm decide when it is resource constrained? by using the profitability index
PROFITABILITY INDEX
Is used to identify the optimal combination of feasible projects to undertake:
𝑁𝑃𝑉
𝑃𝐼 =
𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑
If we apply this to the previous example, we retrieve:
We should select B first, then C, then A
(from highest to lowest)
Shortcomings of the profitability index:
o The set of selected projects must exhaust all capital/resources
o There is only one resource constraint (often there are multiple resource constraints such as capital,
#employees)
o These conditions need to be satisfied
OUTSIDE FINANCING UN DER MORAL HAZARD
The outside financing problem (Holmstrom & Tirole):
Entrepreneur has a project that requires investment I in t=0, but only had liquid assets of A < I
To implement this project, the entrepreneur has to raise I – A from outside investors
Moral hazard: Project success depends on entrepreneur’s unobservable and privately costly effort
The project succeeds (CF R > 0) or fails ( CF = 0) with the probability of success 𝑝
o If the entrepreneur works (exert effort/pick a good project): 𝑝 = 𝑝
o If the entrepreneur shirks (no effort/misbehave/bad project): 𝑝 = 𝑃 < 𝑃 , but has a private
benefit of 𝐵 > 0 (by effort being saved for example)
Assumption: NPV positive if entrepreneur works, negative else:
o Necessary & sufficient condition for financing: 𝐴 ≥ 𝐴 ∶= 𝐵 − (𝑃 𝑅 − 𝐼)
o Only lend to the rich: Credit rationing
despite positive NPV if 𝐴 ≤ 𝐴
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