Chapter 5 Evaluating a Single Project

Chapter 5: Evaluating a Single Project Methods for evaluating a single project  Present worth (PW): most common method.  Future worth (FW).  Annual worth (AW).  Internal rate of return (IRR).  External rate of return (ERR).  Payback period: least common method. A project must provide a return that is equal to or greater than the minimum attractive rate of return (MARR). Present worth (PW) • All cash inflows and outflows are discounted to the present time at an interest rate (generally MARR). acceptable project (profit required by investors is satisfied or exceeded). Example: A project has a capital investment of $50,000 and returns $18,000 per year for 4 years. At a 12% MARR, is this a good investment? Example A new heating system is to be purchased and installed for $110,000. This system will save approximately 300,000 kWh of electric power each year for a 6-year period with no additional O&M costs. Assume the cost of electricity is $0.10 per kWh, and company’s MARR is 15% per year, and the market value of the system will be $8,000 at EOY 6. Using the PW method, is this a good idea? ⇒ Good investment Bond value: application of PW method - PW is used to determine the commercial value of a bond. Where: Example – bonds A bond has a face value of $10,000 and matures in 8 years. The bond stipulates a fixed nominal interest of 8% per year, but interest payments are made to the bondholder every 3 months. The bondholder wishes to earn 10% nominal annual interest (compounded quarterly). Assuming the redemption value is equal to the face value, how much should be paid for the bond now? Example – bonds A bond with a face value of $5,000 pays 8% interest per year. This bond will be redeemed at par value at the end of its 20-year life and the first interest payment is due one year from now. - How much should be paid now for this bond to receive a yield of 10% per year? - If this bond is purchased now for $4,600, what annual yield would the buyer receive? Capitalized worth - Capitalized worth (CW): special case of PW; where revenues or expenses occur over an infinite length of time. - If only expenses are considered, then it is called capitalized cost. Example: a bridge was constructed at a cost of $1,900,000 and the annual upkeep cost is $25,000. It is also estimated that maintenance will be required at a cost of $350,000 every 8 years. What is the capitalized worth of the bridge over its life assuming MARR = 8%? Future worth (FW). Example: A $45,000 investment in a new conveyer system is projected to improve throughput and increase revenue by $14,000 per year for five years. The estimated market value of the conveyer at the end of five years is $4,000. Using the FW method at a MARR of 12%, is this a good investment? PW? Annual worth (AW). • Equal annual series equivalent to the cash inflows and outflows at a specific interest rate (normally MARR). • AW is equivalent to PW and FW. • AW ≥ 0, project is economically justified. Example A project requires an initial investment of $45,000, has a salvage value of $12,000 after six years, incurs annual expenses of $6,000, and provides annual revenue of $18,000. Using a MARR of 10%, determine the AW of this project. Internal rate of return (IRR) • Most widely used rate of return method in engineering economic analysis. • Also called the investor’s method, the discounted cash flow method, and the profitability index. 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑜𝑜𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐ℎ 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑜𝑜𝑜𝑜 𝑐𝑐𝑐𝑐𝑐𝑐ℎ 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 Using PW: Example An equipment requires a capital investment of $345,000, has a salvage value of $115,000 after six years, annual expenses of $22,000, and provides annual revenue of $120,000. Using a MARR of 20%, is the purchase of this equipment a good decision according to the IRR method? IRR = 22.03% > MARR  Acceptable project. External rate of return (ERR) Example For the cash flows given below, find the ERR when the external reinvestment Payback (payout period) Two types of payback period: Example: An investment of $5,000,000 yields net annual revenue of $1,500,000. What is the simple payback period? Example: For the following cash flows, what is the simple and discounted payback periods at 𝑖𝑖 = 6%? 0 1 2 3 4 5 EOY -$42,000 $12,000 $11,000 $10,000 $10,000 $9,000 Net cash flow EOY 0 1 2 3 4 5 Net cash flow Cumulative PW at 0% Cumulative PW at 6% -$42,000 $12,000 $11,000 $10,000 $10,000 $9,000 -$42,000 -$30,000 -$19,000 -$9,000 $1,000 Keep calculating cumulative PW until reaching a positive value From the table: θ = 4 years and θ′ = 5 years -$42,000 -$30,679 -$20,889 -$12,493 -$4,572 $2,153