net present value/ARR

NPV equation

NPV (A+ B) = NPV (A) + NPV (B)

discount factor

1 / r - 1

What is NPV dependent on?

It is dependent soley on the forecasted cash flows from the project and the opportunity cost of capital

when do you accept the NPV

you accept the NPV if the value is greater than zero

when do you reject the NPV

if the NPV is less than zero

what does it mean if the NPV is positive

if the NPV is positive, it means the rate of return will be above the discount rate

what are the rules of NPV (2)

1. If the NPV is greater than zero you accept it
2. if the NPV is less than zero you reject it

what is NPV used for?

* NPV analysis is used to determine how much an investment project is worth.
* Used in decision-making process such as acquisition

strengths of NPV

1. Uses cash flows - cash flows are better than earnings
2. uses all cash flows - other approaches ignore cash flows beyond a certain date
3. discount cash flows - fully incorporates the time value of money as a dollar today is worth more than a dollar tomorrow

drawbacks of NPV

1. Relies heavily on inputs, estimates and long term projections
2. hard to calculate manually especially for projects with many years of cash flow
3. doesn’t consider project size or return on investment

Average accounting return is also known as

Book rate of return

Book rate of return

Average income divided by average book value over project life.

book rate of return equation

book income / book assets

book rate of return

1. Determine average net income - then divide by number of years
2. determine average investment - work out the amount the investment at beginning of the x amount of years and worth at the beginning of the next year, every year the investment will depreciate hopefully the question will give you this./divide by number of years (add an additional year)
3. determine average accounting return - book income/ book assets

strengths of book rate of return

1. Simple return based measure

weakness of book rate of return

1. Does not use cash flows
2. Does not use time value of money
3. arbitrary target rate

payback period

the payback period of a project is the number of years it takes before the cumulative forecasted cash flow equals the inital outflow

the payback period rules

1. Accept it if the payback period is less than the benchmark
2. reject it payback period is more than the benchmark

strengths of payback period

1. simple to understand
2. very small scale investments
3. firms with severe capital rationing

drawbacks of payback period

1. timing of cash flows
2. flawed method as it ignores the later cash flow years and the PV of future cash flows

discounted payback period strengths

1. uses time value of money
2. simple to understand

discounted payback period drawbacks

1. arbitrary benchmark
2. ignores cashflows beyond benchmark

discounted payback period rules

1. accept if the payback period is less than benchmark
2. reject if payback period is more than the benchmark

internal rate of return

discount rate has to be at 0, using trial and error. You use the same method as NPV expect the IRR is guessed until you reach 0

internal rate of return equation an example

\-400 + 200/(1+r)^1 + 300/(1+r)^2 = 0

incremental cash flow

project A-B

incremental cash flow

NPV = A-B 0

internal rate of return rules

1. IRR < R reject
2. IRR > R accept

if the first cash flow is negative and the remaining cash flows are positive

IRR > R accept

IRR < R reject

if the first cash flow is postive and the remaining cash flows are negative

IRR > R reject

IRR < R accept

the general IRR rule

invest in any project offering a rate of return that is higher than the opportunity cost of capital

profitability index

NPV / investment

profitability index rule

the highest PI or highest weighted Pi can indicate which projects to select

why is the profitability index useful

the profitability index provides a tool for selecting among various project combinations and alternatives

which profitability indexes to accept and reject

PI > 1 accept

PI < 1 reject

real discount rate formula

( 1 + norminal rate / 1 + inflation ) - 1

equivalent annual cost annuity formula

present value of cash flows / annuity factor

what are the three elements of project cash flows

total cash flow = cash flow from capital investment + operating cash flow + cash flow from working capital

3 methods of calculating operating cash flows

1. revenues - expenses - taxes
2. net income + depreciation
3. (revenue - expenses) x (1-taxes) + (tax percentage x depreciation)

Operating leverage

The degree to which costs are fixed

operating leverage formula

1. 1 + (fixed costs + depreciation) / profit
2. % change in profits / % change in sales

economic income in year t

Ct + (PVt - PVt-1)

economic rent

economic income - cost of shareholders’ capital

what is economic income

when the realised economic income is more than the income that shareholders required the firm is said to earn economic rent

positive NPV projects

are those that earn economic rents

rules of ARR

accept if ARR is greater than target rate

reject if ARR is less than target