Chapter 8 Flashcards
Net Present value
Present value of cash flows minus investment
Opportunity cost of capital
Expected rate of return given up by investing in a project rather than in the capital market
Risk and present value
A risky dollar is worth less than a safe one
Investors avoid risk when they can without sacrificing return
Choosing between alternative projects
When choosing between two mutually exclusive projects Pick the one that offers the highest NPV
The internal rate of return rule
Instead of NPV companies prefer to ask if the projects rate of return is higher or lower than the opportunity cost of capital
Rate of return = profit / investment = C1-investment/investment
E.g 400,000-350,000/350,000 = .1429 or 14.3%
Two rules for investment
NPV - invest in any project with a positive NPV when it’s cash flows are discounted at the opportunity cost of capital
IRR- invest in any project offering a rate of return higher that is higher than the opportunity cost of capital
Both rules set the same cut off point an investment that is on knifes edge will have a NPV of 0 or a rate of return equal to the opportunity cost of capital
Closer look at IRR rule
The rate of return is the discount rate at which NPV equals 0
If the opportunity cost of capital is less than the project rate of return then the NPV of the project is positive
If cost of capital is greater than the project rate of return then NPV is negative
Calculating the rate of return for long lived projects
The discount rate that gives the project a zero NPV is known as the projects internal rate of return, or IRR. It is also called the discounted cash flow (DCF)rate of return.
E.g. year 0 1 2 3 Cash flow(k) 375 +25 +25 475
NPV= -375,000 + 25,00/1+IRR + 25,000/(1+IRR)^2 + 475,000/ (1+IRR)^3 = 0
No method to find IRR use trial and error start with 0 first
When IRR = 0 un equation the NPV is 150,000
Next try 50% when put in IRR equals 1.50 (1+50%) NPV = -206,481
NPV turns negative so the IRR lies between 0-50%
IRR = 12.56
To find the answer you can plot a NPV profile or using special software
The rate of return rule tells you to accept a project if it’s rate of return exceeds that of the opportunity cost of capital
On the examples NPV profile it has a downward slopping curve meaning the project has a positive NPV aslong as the opportunity cost of capital is less than the projects 12.56% IRR
The rate of return rule will give the same answer as the NPV rule as long as the NPV of a project declined smoothly as the discount rate increases
Caution with the IRR
Some people confuse IRR with opp cost of capital
IRR measures the profitability of the project
the opp cost of capital is the standard to accept the project
It is equal to the rate of return offered by equivalent risk investments in the capital market
Pitfalls with IRR
1) mutually exclusive projects
Normally when choosing between mutually exclusive projects you take the highest NPV to maximise shareholders wealth
Does not make sense to take highest IRR as a project may have a higher NPV but lower IRR meaning if the IRR rule was used to justify the investment then shareholders wealth would not be maximised
1)a) mutually exclusive projects involving different outlays
A similar misranking may occur when comparing projects with same lives but different outlays . IRR may mistankenly
2) lending or borrowing ?
3) multiple rates of return
Capital rationing
Limit set on the amount of funds available for investment
Soft rationing - limits not imposed by investors but instead top management
Even if capital isn’t rationed other resources can be
Hard rationing - where the funds cannot be raised if needed e.g. state controlled
soft rationing should never cost the firm anything
If the rationing becomes so Tight that good projects are being passed on, then soft management should allow for funds to be raised
Hard
Profitability index
Net present value/initial investment
Measures the net present value of a project per dollar of investment
Also known as benefit cost ratio
Any project with a positive Profitability index must have a positive NPV
Pitfalls of profitability index
The PI is used sometimes to rank projects even when there is neither soft nor hard rationing, this can lead to favor small projects over larger projects with higher NPVs
Designed to measure most bang per buck
The payback rule
A project with a positive NPV is worth more than it costs, so when a firm invests in such a project it makes its shareholders better off
Pay back period - length of time until cash flows recover the initial investment in the project
The pay back rule states that a project should be accepted if it’s pay back period is less than a specified cut off period
Issues :
Can lead to nonsensical decisions
Gives equal weighting to all cash flows arriving before the cut off period despite the fact that more distant flows are less valuable
To use the rule The firm must pick an appropriate cut off point but if they use be same cut of point for projects with different lives then they will accept too many short lived projects and not many long lived ones
Rule Used for its simplicity
Discounted payback
Discounted payback period - number of periods before the present value of the prospective cash flows equal or exceeds the initial investment
Asks - how much must the project last in order to offer a positive NPV
If the discounted payback meets the companies cut off point the project should be accepted
ADV- Never accepts a negative NPV
DIS- takes no account of cash flows after the cut off date, so companies using this method risks rejecting good long term projects as easily misrank competing projects
Instead of rejecting projects managers can put a warning on them
