Finance:Net Present Value

& Benefit/Cost Analysis

Lecture 10.1a

ECON 201

Jun 9, 2009

Evaluating Projects

• Expansion project– Requires an initial investment, Io

– Yields a flow of benefits and costs over time: Bt, Ct

1 10

0

...(1 ) (1 ) (1 )

nn n t t

o o on tt

B C B CB CNPV I B C I

r r r

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.

Net Present Value

• Firms focus on the net present value (NPV) of an asset when making investment decisions. – NPV = PV of the asset minus the PV of the

expenditures on the asset.

• If NPV > 0 then the investment is profitable.– All else equal, the sooner the benefits are received

and the lower the interest rate, the higher the NPV.

Other Decision Criteria

• Payback– Determine the number of years until revenues

= costs– Choose project with shortest payback period

• Accounting Rate of Return– average annual profit / initial outlay

Have to Choose 1 Project

Year A B C D (1+.1) t̂0 -1000 -1000 -1000 -1000 11 100 0 100 200 0.9092 900 0 200 300 0.8263 100 300 300 500 0.7514 -100 700 400 500 0.6835 -400 1300 1250 600 0.621

NPV -407.3 510.7 530.85 519.2Payback 2 4 4 3ARR -0.08 0.26 0.25 0.22NPV(B/C) 0.5927 1.5107 1.53085 1.5192

• Projects are mutually exclusive– E.g., SPU & Taylor Creek

• Several options to improve drainage; but can only do 1

NPV Decision Rules

• If only 1 project, or not capital constrained– NPV > 0

• If more than 1 project and capital constrained– If the same initial investment

• Choose project(s) with highest NPV

– If different investment levels• Choose project(s) with highest (NPV) Benefit to

Cost Ratio

Interest and the Demand for Capital

• The interest rate represents the opportunity cost of purchasing capital. Therefore, as the interest rate increases, the quantity of capital demanded will fall.

Figure 14.1 The Demand Curve for Physical Capital

Other Applications

• Evaluating benefit/cost of medical care that increases longevity (stop smoking)

– Found that NPV of increased life-span < increased costs of medical care

• Army Corp of Engineers– Always uses B/C analysis to evaluate projects

• Government Accounting Office– Required to evaluate congressional proposals

• Insurance premiums– B/C analysis + actuarial analysis

Other Applications

• How do we determine the value of the firm– Flow of revenues and costs

– Bt = “expected” revenue stream

– Ct = “expected” expenses

• Stock price– NPV/(#shares)

1 10

0

...(1 ) (1 ) (1 )

nn n t t

o o on tt

B C B CB CNPV I B C I

r r r

Closer to Home

• Mortgage Payments

1 (1 )12

ni

annuali

PAmount borrowed

r

Closer to Home

• Decision to refinance– Cost of refinancing

• Loan origination fees (~2% of the loan): -Io

• NPV of monthly payments at new interest rate

– Cost of Current loan• NPV of remaining payments at old (higher) interest

rate

JJ WentworthAnnuity through Inheritance • When Earl's mother passed away he inherited an annuity and chose

to continue receiving the monthly payments. However, Earl later realized that the payments were not having the impact that he had hoped. When an opportunity arose to expand his business, Earl wondered if there was a way for him to tap into his annuity and get the capital that his business needed.

• Read More • J.G. Wentworth: The Leading Purchaser of Structured

Settlement and Annuity Payments • At J.G. Wentworth, we understand it is hard to wait for future

payments from your structured settlement or annuity when you need to Get Cash Now. J.G. Wentworth's knowledgeable staff can help you get the cash you need in a lump sum payment by purchasing all or part of your monthly annuity or structured settlement payments.