Present Worth Analysis (Investopedia, 2017) CEE 4200 Fall 2017

Today’s Learning Objectives Formulate alternatives Use present worth to select project(s) to implement Equal service life projects Projects with different lives Infinite life projects (capitalized costs) Independent projects Revise and resubmit PBL-2

The Basic Approach (Mutually Exclusive Projects) Calculate the present worth for each project (all benefits and costs) Choose the project with largest present value (most positive, least negative) Project Present Worth ($) Alpha $105,000 Bravo $122,000 Charlie - $30,000

Example 1. Use present worth analysis to determine which heavy-duty lawnmower to purchase Attribute Gas-Powered Electric-Powered First cost ($) 2,500 3,300 Annual cost ($/year) 900 550 Salvage value ($) 350 200 Life (years) 5 MARR (%) 10%

Example 2. Which fence pickets to purchase? Attribute Pine Cedar First cost ($) 2,500 6,250 Annual cost ($/year) 300 75 Life (years) 3 9 MARR (%) 10%

Infinite Life Projects (capitalized cost) Draw cash flow diagram for 2 cycles Calculate present worth of all one-time costs/benefits Calculate equivalent annual worth for 1 cycle of recurring costs Divide #2 by the interest rate and add to #1

Example 3. What is the capitalized cost today to maintain the Golden Gate Bridge in perpetuity (8% MARR)? Maintenance Item Cost ($ Mill) Frequency Replace rivets $12 1 year Paint bridge $22 6 years Resurface deck $35 10 years

Independent Projects (can do one or more) Unlimited budget Select all projects with PW > 0 at MARR Budget constrained Calculate PW for all projects Chose projects with PW > 0 (Rate of Return > MARR) Identify project combinations (bundles) with total initial investment < budget Find PW for each bundle Select bundle with largest PW

Example 4. Which skis to add to your quiver if you have $900 to spend? Ski Type Initial Cost Present Value A. Resort – Powder $550 $1,700 B. Resort – Mogels $450 ($240) C. Resort - Groomers $610 $1,100 D. Backcountry – AT $670 $2,300 E. X-Country (stride) $200 F. Ski Swap (rock skis) $90 $250