Chapters 2&3: Decision Rules Flashcards
Three processes in any cash-flow analysis
- Identification
- Valuation
- Comparison
Conventions in representing cash flows
- Initial or ‘present’ period is always year 0
- Year 1 is one year from present year
- All amounts accruing during a period are assumed to fall on the last day of the period
Comparing costs and benefits
- We cannot compare dollar values that accrue at different points in time - to compare we use the concept “discounting”
- Reason: $1 today is worth more than $1 tomorrow
Discount Factor
1/(1+i)^n
Future Value
FV=PV*(1+i)^n
Present Value
PV=FV/(1+i)^n
Net Present Value
Found by subtracting the discounted value of project costs from the discounted value of project benefits
NPV Decision Rule: Accept vs Reject Decisions
If NPV =>0: accept
If NPV<0: reject
Choose larger NPVs
Changing the discount rate
As the discount rate increases, the NPV increases
IRR
the discount rate at which NPV=0
The IRR decision rule
Compare the IRR to the cost of borrowing funds to finance the project
- If IRR=>r: accept
NPV vs IRR
- With straightforward accept/reject decisions, the NPV and IRR will always give identical decisions
- Safer to use NPV rule when comparing or ranking mutually exclusive projects
Other problems with IRR
- Multiple solutions
- No solution
Using Annuity Tables
When there is a constant amount each period, we can use an annuity factor instead of applying a separate discount factor each period
Problems with NPV Rule
- Capital rationing (more projects may pass NPV test than you can fund) -> use profitability ratio
- Indivisible or “lumpy” projects -> compare combinations to maximise NPV
- Projects with different lives -> renew projects until they have common lives using LCM; use annual equivalent method (using annuity factors, convert stream into a constant annual amount)
Annual Equivalent Value
Divide present value by annuity factor at discount rate and number of years of project to convert any given amount or cash flow into an annuity
