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 CC NR : Find net present value of all non-recurring flows For all the recurring flows, calculate CC R : 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: CC T = CC NR + CC R

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 i b and Dividend to flesh out the CFD Solve CFD for unknown Price / Yield to Maturity Yield to Maturity is i*, such that NPW BOND CFD = 0 Annual Yield: i a = (1 + i) m – 1 Watch for Sunk Costs Trick: Only worry about remaining cash flows!

5 CFD with Bond Terms… n periods (to Maturity Date) Bond Price Dividend Face Value Yield Rate = i a = (1+ i b ) m – 1 Coupon Rate Dividend Periods / Yr i b = Coupon Rate Dividend Periods / Yr Dividend = (Face Value) (i b ) – or – Face Value Yield to Maturity = i* such that NPW = 0

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 Worth incr > $0 or if IRR incr > MARR  higher cost wins Worth incr ≤ $0 or if IRR incr ≤ 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