Net Present Worth Net Present Worth ReviewReview

Net Present Worth Net Present Worth ReviewReview

• 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 Equivalent Annual Worth ReviewReview

Equivalent Annual Worth Equivalent Annual Worth ReviewReview

• 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 ReviewPerpetuity ReviewPerpetuity ReviewPerpetuity 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 ReviewBonds ReviewBonds ReviewBonds 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• Annual Yield: ia = (1 + i)m – 1• Yield to Maturity is i*, such that NPWBOND

CFD = 0

• Watch for Sunk Costs Trick:• Only worry about remaining cash flows!

Internal Rate of Return Internal Rate of Return ReviewReview

Internal Rate of Return Internal Rate of Return ReviewReview

• 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 Incremental Analysis ReviewReview

Incremental Analysis Incremental Analysis ReviewReview

• 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

• If > 0 (IRR > MARR), then higher cost is better

• If ≤ 0 (IRR ≤ MARR), then lower cost is better• Compare feasible options, & compare in–order!

Incremental Analysis Incremental Analysis ReviewReview

Incremental Analysis Incremental Analysis ReviewReview

• 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 $ ContenderMid $ Contender

High $ Contender