ECON 201 Lecture 4-5(a) Finance: Net Present Value & Benefit/Cost Analysis

Evaluating Projects Expansion project –Requires an initial investment, I o –Yields a flow of benefits and costs over time: B t, C t

The Net Benefits from an Investment The net benefit of an investment project is the difference between the revenue generated by the project and the project’s cost, including opportunity cost.

Interest Interest is an important part of the investment decision for two reasons: –First, interest must be paid to borrow funds. –Second, interest is the opportunity cost of using money to pay for an investment project. Money used to purchase capital could have been deposited in a bank to earn interest.

Interest (cont’d) Lenders charge interest: –To compensate themselves for not being able to use their own money to buy the things they want –To compensate themselves for the risk they assume when they make a loan –Because rising prices will reduce the purchasing power of the money when it is repaid

Present and Future Value The present value (PV) of money received in the future is equal to its value today. –In other words, it is the maximum amount that someone would pay today to receive the money in the future.

Present and Future Value (cont’d) The relationship between present and future value can be shown by the following equations:

Present and Future Value (cont’d) Examples: Suppose the interest rate is 5%. –What is the future value of $10,000 one year from now? FV = $10,000 x (1 +.05) = $10,500 –What is the present value of $10,000 received one year from now? PV = $10,000 / (1 +.05) = $9,524

Present and Future Value (cont’d) Discounting refers to the method used to calculate the present value of a stream of payments over time. –Example: Suppose a firm expects to earn $10,000 of revenue in each of the next 2 years.

Net Present Value (cont’d) Example: Suppose a firm is considering investing $8,000 in new equipment. As a result of the new equipment, the firm expects to earn revenues of $10,000 in each of the next 2 years. Since NPV is positive, the firm should undertake the investment.

Other Applications How do we determine the value of the firm –Flow of revenues and costs –B t = “expected” revenue stream –C t = “expected” expenses Stock price –NPV/(#shares)

Closer to Home Mortgage Payments

Washington State Lottery Jackpot Analysis For Washington MEGA Millions Draw Date: Tuesday, March 11, 2008 Jackpot is worth $47,000,000 Payment Options –Annuity 26 Annual Payments of $1,807,692 –Lump Sum $29,200,000

Lump Sum or Annuity?