Net Present Worth Review
• NPW can compare mutually exclusive projects or
prioritize investments (using Incremental Analysis)
• Criteria: Choose highest NPW
• NPW > 0 means that project beats the MARR
• Project Life equality is an issue:
• If projects are repeatable, use LCM:
•
Combine cycles into one, big CFD and analyze
(Civil E method works, but is time consuming)
•
Analyze one cycle, then create & analyze
simplified (repeated life) CFD
• Study period is an alternative if specified:
•
Requires that salvage value function is known
Equivalent Annual Worth Review
• EAW can compare mutually exclusive projects or
prioritize investments (using Incremental Analysis)
• Criteria: Choose highest EAW (lowest EAC)
• EAW > 0 means that project beats the MARR
• Project Life equality is NOT an issue:
• Compare on same payment frequency, though:
•
Move non-annual flows to present / future, then
annualize (NOT average!) over project life
•
Can use Opportunity Cost formulation to
simplify capital equipment: (P – S)(A/P,i,n) – S(i)
• IMPORTANT:
•
Land does not change in value (pt in 3-D space)
Perpetuity Review
• Perpetuity (Capitalized Cost) is used to fund projects
that will “last forever”
• Relationship: can live off of the period’s interest, but
can’t touch account principle: A = P(i)
• Steps:
• Separate non-recurring cash flows from the
recurring flows, then calculate CCNR:
•
Find net present value of all non-recurring flows
• For all the recurring flows, calculate CCR:
•
Find annual equivalent of one cycle of each
recurring flow, then combine to find net annual
•
Use perpetuity relationship to find present
value of the net annual equivalent
• Total capitalized cost is: CCT = CCNR + CCR
Bonds Review
• Bonds are used to acquire start-up capital early on, but
wait to pay back the bulk of the borrowing until the
production cash flow is realized (interest-only loan)
• Basically reusing two concepts:
• Solving CFD and finding Effective Interest Rates
• Use Bond Cash Flow Diagram to solve:
•
•
•
•
•
Translate Bond Terminology to CFD
Find ib and Dividend to flesh out the CFD
Solve CFD for unknown Price / Yield to Maturity
Yield to Maturity is i*, such that NPWBOND CFD = 0
Annual Yield: ia = (1 + i)m – 1
• Watch for Sunk Costs Trick:
•
Only worry about remaining cash flows!
CFD with Bond Terms…
ib =
Coupon Rate
Dividend Periods / Yr
Dividend = (Face Value) (ib) – or – Face Value
Coupon Rate
Dividend Periods / Yr
Face Value
Yield Rate = ia = (1+ ib) m – 1
Dividend
0
1
2
3
n periods
(to Maturity Date)
Bond Price
Yield to Maturity = i* such that NPW = 0
5
Internal Rate of Return Review
• IRR can compare mutually exclusive projects or
prioritize investments - MUST USE Incremental Analysis
• Criteria: Choose IRR that is greater than MARR
• IRR > 0 means that project makes money, but not
necessarily better than the safe investment rate
• Concepts:
• IRR is the interest rate (i*), such that NPW = 0
• Note: Can only have one sign change in net CFD,
otherwise there are multiple IRRs!
• Strategies:
• If only one table factor in CFD equation, solve for it and
use tables to find approximate IRR
• If more than one table factor involved, use divide &
conquer to find approximate IRR using tables
• Use spreadsheet and P/F or P/A factors if large problem
Incremental Analysis Review
• Incremental Analysis can be used to prioritize
investments (using NPW, EAW, or even NFW), but it
MUST be used when comparing relative measures
(IRR or Cost/Benefit Ratio)
• Caution: Equal lifetime issues (NPW and IRR)
• Steps:
• Order projects by increasing first costs
• Find first feasible project becomes current best
•
•
Compare with Doing Nothing if that is an option
If a Revenue Project, IRR > MARR (worth > 0)
• Pairwise Comparison on Incremental Cash Flow
•
•
•
Compare feasible options, & compare in–order!
If > 0 (IRR > MARR), then higher cost is better
If ≤ 0 (IRR ≤ MARR), then lower cost is better
Incremental Analysis Review
• Incremental Analysis comparison is like a single playoff
tournament:
• Seed the contenders on first costs, larger cost get byes
• Only have to win incremental game to move on
• Worthincr> $0 or if IRRincr > MARR  higher cost wins
• Worthincr ≤ $0 or if IRRincr ≤ MARR  current best wins
• Last one unbeaten is best choice
• Start over with beaten contenders to find next best, etc.
Do Nothing
Low $ Contender
Mid $ Contender
High $ Contender