SAMENVATTING: CAPITAL INVESTMENT POLICY
LECTURE 1:
What is “Capital Investment Policy”?
Any investment policy must embody one or more criteria by which to measure the relative economic
attributes of investment alternatives and decision rules for selecting “acceptable” investments!
➢ A strategy for value creation
A consistent and adequate investment policy has a double function:
➢ Short-term: indicate which investments should be chosen to achieve the financial objectives
of the corporation → the goal is to keep the shareholders happy
➢ Long-term: form the basis for identifying or developing investment alternatives that are likely
to match the policies selected → ex. banks adapt their alternatives to the company’s policy
A company should always keep these questions in mind:
1) What investments should we make? (the focus of investment policies)
2) How should we pay for these investments? Ex. what other assets should we sell?
The financial goal of the corporation:
A company = a group of projects → the role of the management is to choose the best projects
A project = a series of cash flows
A cash flow = an amount of money paid at a specific time
➢ A cash inflow represents revenue and stands for a positive amount (+)
➢ A cash outflow represents investments & expenses and stands for a negative amount (-)
The goal of a firm is determined by the firm’s owners, or in case of a corporation, by its shareholders
Large companies hire management to act on behalf of the “owners” → two problems may arise:
1) Definition of goals: shareholders can disagree among each other
2) Implementation of shareholder’s goals: agency conflicts arise when manager’s private
interests don’t align with shareholder’s objectives
➢ Agency costs arise when managers don’t maximize firm value or when shareholders
incur costs to monitor & constrain the managers
All shareholders – independent of their individual consumption preferences – can agree to assign one
objective to the manager: to maximize the current market value of shareholders’ investments in the
firm!
With functioning and competitive financial markets, wealth can then be put to whatever purpose
each shareholder wants → financial markets allow to transfer consumption over time!
It’s crucial that all shareholders have equal access to opportunities!
Maximizing shareholders value ≠ maximizing profits
➢ Increasing current profits by cutting back on long-term investments, such as maintenance and
training, may impair long-term value
➢ Not paying dividends and reinvesting additional cash in a mature company might increase
current profits but not shareholder value (a plateau has already been reached)
,Hurdle rate = cost of capital = the minimum rate of return at which shareholders would be happy with
an investment and not demand their money back
➢ Dependent on risk (opportunity cost)
Investment decisions and present value:
Corporate investment decisions are a way of creating value for the shareholders and the goal is to
choose the “most valuable” projects → cash flows should be comparable (at the same point in time)
𝐶 𝐶
➢ Present value (PV) of a future cash flow = (1+𝑟)
1
→ in year t: PV = (1+𝑟)
𝑡
𝑡
➢ Future value (FV) of a current cash flow = C0 x (1 + r)
1
➢ r is called the discount rate and (1+𝑟) is called the discount factor
𝐶
1 2𝐶 3 𝐶
Note: the PV of a stream of cash flows = (1+𝑟) + (1+𝑟) 2 + (1+𝑟)3 + ….
Principle: a project adds value if its return is higher than the return of comparable alternative
investments (hurdle rate)!
Investment decision rules:
𝐶
➢ Present value rule: invest if (1+𝑟)
1
> cost of investment C0
𝐶1
➢ Net present value (NPV) rule: invest if C0 + > 0 → often used by managers
(1+𝑟)
𝑝𝑟𝑜𝑓𝑖𝑡
➢ Rate of return rule: invest if >r
𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
A perpetuity = a financial instrument that pays C dollars per period forever, starting one period from
today → interest rate can be constant or growing
An annuity = a financial instrument that pays C dollars for T periods, starting one period from today
→ interest rate can be constant or growing
Summary of formulae:
1
FV of an annuity = C x 𝑟 x ((1 + r)N -1)
When choosing among projects, we always choose all projects with NPV > 0!
If due to resource restrictions we can’t pick all projects, we choose the ones with the highest NPVs!
Every time a firm invests in an NPV-positive project, it’s value increases by the NPV!
Principle: regardless of our preferences for cash today vs. cash in the future, we should always
maximize NPV first! (perfect capital market)
➢ If the capital market is not frictionless or does not exist, one needs to know an investor’s
consumption preferences to determine whether one project is superior to another
Ex. brand-new Lexus offered with discount vs. 5000 cash
,Alternative decision rules:
Alternative decision methods exist, but they might lead to different results and project rankings
➢ Any method producing results that differ from NPV is wrong, always trust the NPV-rule!
Internal Rate of Return (IRR): (most popular alternative method)
A project’s IRR = the interest rate that sets the NPV of cash flows equal to zero
𝐶1 𝐶2 𝐶3
Ex. 0 = C0 + + + + … → r can be found and is the IRR
(1+𝑟) (1+𝑟)2 (1+𝑟)3
Decision rule: only invest if IRR > the hurdle rate r
The difference between the cost of capital and the IRR is the highest estimation error in the cost of
capital estimate that can exist without altering the original decision
➢ IRR has complementary value: gives additional information on investment advice
Nevertheless, the IRR has many pitfalls:
1. Projects can have the same IRR, but not be equally desirable: lending vs. borrowing
2. The amount of CF sign changes = the max. amount of IRR’s → which IRR should we use???
3. IRR doesn’t consider the different scales of projects → can lead to wrong conclusions
4. Complex if the hurdle rates are time varying
5. Sometimes no real solutions for IRR exist: ex. imaginary number
So IRR only works if:
➢ There’s one discount rate for all periods
➢ The only negative CF takes place in period 0 and is followed by only positive CF’s
➢ There’s only one investment to consider
Conclusion: if given a choice, always use the NPV-rule!
The payback rule:
The payback period = the amount of time it takes to recover or pay back the initial investment
Decision rule: accept the project if the payback period is less than a pre-specified length of time
Pitfall: the rule ignores the time value of money → generally unreliable results
Efficient capital markets and no-arbitrage pricing:
Efficient capital markets have no taxes, no transactions costs and no differential information!
➢ Investors can borrow and lend at the same (risk-adjusted) rate
➢ Unlimited short-selling possible with full access to proceeds
➢ It’s impossible to “outsmart” the market: no arbitrage opportunities
Arbitrage opportunity = it’s possible to make a profit without taking any risk or making any
investment
• No arbitrage price of a security = PV of all CF’s paid by the security
• The NPV of buying/selling a security = 0 (goes for all financial investments)
To make money on the stock market, one needs to know more than the people who
set prices
, The law of one price = if equivalent investment opportunities trade simultaneously in different
efficient markets, they must trade for the same price in both markets
➢ Implication:
We have two securities A & B and security C has the same CF’s as A and B combined, then
security C is equivalent to a portfolio of the securities A and B
Value additivity: price(C) = price (A + B) = price(A) + price (B)
Even with transaction costs, arbitrage generally keeps prices of equivalent goods & securities close to
each other → prices can deviate, but not by more than the transactions costs of the arbitrage trade!
Complementary material: interest rates:
Effective Annual Rate (EAR) vs. Annual Percentage Rate (APR): 1 + EAR = (1 + APR/k)k
➢ EAR is the true annual interest rate
➢ APR only complete with the compounding frequency k
➢ k gets very large → continuous compounding: EAR = eAPR – 1
Real interest rate vs. nominal interest rate: (1 + rreal) x (1 + i) = 1 + rnominal
➢ A nominal CF is the number of dollars you pay out or receive (different purchasing power)
➢ A real CF is adjusted for inflation (always the same purchasing power)
𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝐶𝐹
➢ real CF =
(1 + 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒)𝑡
Rule: discount real CF with the real interest rate and nominal CF with the nominal interest rate!
LECTURE 1:
What is “Capital Investment Policy”?
Any investment policy must embody one or more criteria by which to measure the relative economic
attributes of investment alternatives and decision rules for selecting “acceptable” investments!
➢ A strategy for value creation
A consistent and adequate investment policy has a double function:
➢ Short-term: indicate which investments should be chosen to achieve the financial objectives
of the corporation → the goal is to keep the shareholders happy
➢ Long-term: form the basis for identifying or developing investment alternatives that are likely
to match the policies selected → ex. banks adapt their alternatives to the company’s policy
A company should always keep these questions in mind:
1) What investments should we make? (the focus of investment policies)
2) How should we pay for these investments? Ex. what other assets should we sell?
The financial goal of the corporation:
A company = a group of projects → the role of the management is to choose the best projects
A project = a series of cash flows
A cash flow = an amount of money paid at a specific time
➢ A cash inflow represents revenue and stands for a positive amount (+)
➢ A cash outflow represents investments & expenses and stands for a negative amount (-)
The goal of a firm is determined by the firm’s owners, or in case of a corporation, by its shareholders
Large companies hire management to act on behalf of the “owners” → two problems may arise:
1) Definition of goals: shareholders can disagree among each other
2) Implementation of shareholder’s goals: agency conflicts arise when manager’s private
interests don’t align with shareholder’s objectives
➢ Agency costs arise when managers don’t maximize firm value or when shareholders
incur costs to monitor & constrain the managers
All shareholders – independent of their individual consumption preferences – can agree to assign one
objective to the manager: to maximize the current market value of shareholders’ investments in the
firm!
With functioning and competitive financial markets, wealth can then be put to whatever purpose
each shareholder wants → financial markets allow to transfer consumption over time!
It’s crucial that all shareholders have equal access to opportunities!
Maximizing shareholders value ≠ maximizing profits
➢ Increasing current profits by cutting back on long-term investments, such as maintenance and
training, may impair long-term value
➢ Not paying dividends and reinvesting additional cash in a mature company might increase
current profits but not shareholder value (a plateau has already been reached)
,Hurdle rate = cost of capital = the minimum rate of return at which shareholders would be happy with
an investment and not demand their money back
➢ Dependent on risk (opportunity cost)
Investment decisions and present value:
Corporate investment decisions are a way of creating value for the shareholders and the goal is to
choose the “most valuable” projects → cash flows should be comparable (at the same point in time)
𝐶 𝐶
➢ Present value (PV) of a future cash flow = (1+𝑟)
1
→ in year t: PV = (1+𝑟)
𝑡
𝑡
➢ Future value (FV) of a current cash flow = C0 x (1 + r)
1
➢ r is called the discount rate and (1+𝑟) is called the discount factor
𝐶
1 2𝐶 3 𝐶
Note: the PV of a stream of cash flows = (1+𝑟) + (1+𝑟) 2 + (1+𝑟)3 + ….
Principle: a project adds value if its return is higher than the return of comparable alternative
investments (hurdle rate)!
Investment decision rules:
𝐶
➢ Present value rule: invest if (1+𝑟)
1
> cost of investment C0
𝐶1
➢ Net present value (NPV) rule: invest if C0 + > 0 → often used by managers
(1+𝑟)
𝑝𝑟𝑜𝑓𝑖𝑡
➢ Rate of return rule: invest if >r
𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
A perpetuity = a financial instrument that pays C dollars per period forever, starting one period from
today → interest rate can be constant or growing
An annuity = a financial instrument that pays C dollars for T periods, starting one period from today
→ interest rate can be constant or growing
Summary of formulae:
1
FV of an annuity = C x 𝑟 x ((1 + r)N -1)
When choosing among projects, we always choose all projects with NPV > 0!
If due to resource restrictions we can’t pick all projects, we choose the ones with the highest NPVs!
Every time a firm invests in an NPV-positive project, it’s value increases by the NPV!
Principle: regardless of our preferences for cash today vs. cash in the future, we should always
maximize NPV first! (perfect capital market)
➢ If the capital market is not frictionless or does not exist, one needs to know an investor’s
consumption preferences to determine whether one project is superior to another
Ex. brand-new Lexus offered with discount vs. 5000 cash
,Alternative decision rules:
Alternative decision methods exist, but they might lead to different results and project rankings
➢ Any method producing results that differ from NPV is wrong, always trust the NPV-rule!
Internal Rate of Return (IRR): (most popular alternative method)
A project’s IRR = the interest rate that sets the NPV of cash flows equal to zero
𝐶1 𝐶2 𝐶3
Ex. 0 = C0 + + + + … → r can be found and is the IRR
(1+𝑟) (1+𝑟)2 (1+𝑟)3
Decision rule: only invest if IRR > the hurdle rate r
The difference between the cost of capital and the IRR is the highest estimation error in the cost of
capital estimate that can exist without altering the original decision
➢ IRR has complementary value: gives additional information on investment advice
Nevertheless, the IRR has many pitfalls:
1. Projects can have the same IRR, but not be equally desirable: lending vs. borrowing
2. The amount of CF sign changes = the max. amount of IRR’s → which IRR should we use???
3. IRR doesn’t consider the different scales of projects → can lead to wrong conclusions
4. Complex if the hurdle rates are time varying
5. Sometimes no real solutions for IRR exist: ex. imaginary number
So IRR only works if:
➢ There’s one discount rate for all periods
➢ The only negative CF takes place in period 0 and is followed by only positive CF’s
➢ There’s only one investment to consider
Conclusion: if given a choice, always use the NPV-rule!
The payback rule:
The payback period = the amount of time it takes to recover or pay back the initial investment
Decision rule: accept the project if the payback period is less than a pre-specified length of time
Pitfall: the rule ignores the time value of money → generally unreliable results
Efficient capital markets and no-arbitrage pricing:
Efficient capital markets have no taxes, no transactions costs and no differential information!
➢ Investors can borrow and lend at the same (risk-adjusted) rate
➢ Unlimited short-selling possible with full access to proceeds
➢ It’s impossible to “outsmart” the market: no arbitrage opportunities
Arbitrage opportunity = it’s possible to make a profit without taking any risk or making any
investment
• No arbitrage price of a security = PV of all CF’s paid by the security
• The NPV of buying/selling a security = 0 (goes for all financial investments)
To make money on the stock market, one needs to know more than the people who
set prices
, The law of one price = if equivalent investment opportunities trade simultaneously in different
efficient markets, they must trade for the same price in both markets
➢ Implication:
We have two securities A & B and security C has the same CF’s as A and B combined, then
security C is equivalent to a portfolio of the securities A and B
Value additivity: price(C) = price (A + B) = price(A) + price (B)
Even with transaction costs, arbitrage generally keeps prices of equivalent goods & securities close to
each other → prices can deviate, but not by more than the transactions costs of the arbitrage trade!
Complementary material: interest rates:
Effective Annual Rate (EAR) vs. Annual Percentage Rate (APR): 1 + EAR = (1 + APR/k)k
➢ EAR is the true annual interest rate
➢ APR only complete with the compounding frequency k
➢ k gets very large → continuous compounding: EAR = eAPR – 1
Real interest rate vs. nominal interest rate: (1 + rreal) x (1 + i) = 1 + rnominal
➢ A nominal CF is the number of dollars you pay out or receive (different purchasing power)
➢ A real CF is adjusted for inflation (always the same purchasing power)
𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝐶𝐹
➢ real CF =
(1 + 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒)𝑡
Rule: discount real CF with the real interest rate and nominal CF with the nominal interest rate!
