ENGG 401 X2 Fundamentals of Engineering Management Spring 2008 Chapter 7: Present Worth Analysis

ENGG 401 X2ENGG 401 X2Fundamentals of Engineering ManagementFundamentals of Engineering Management

Spring 2008Spring 2008

Chapter 7:Chapter 7:

Present Worth AnalysisPresent Worth Analysis

Dave LudwickDave Ludwick

Dept. of Mechanical EngineeringDept. of Mechanical Engineering

University of AlbertaUniversity of Albertahttp://members.shaw.ca/dave_ludwick/

Dave Ludwick, Dept. of Mech. Eng.Ch 7 – Present Worth Analysis

Summer 20082

ENGG 401 X2 – Fundamentals of Engineering Management

Present WorthPresent Worth

• Equivalence says that we can shift any sum to an equivalent sum at some other point in time… the equivalent sum at the present time (right now) is called present worthpresent worth (PW).– PW is the comparable equivalent value at the present time of a

future sum or set of sums.– PW or NPV can be thought of as the difference between a future set

of cash inflows and cash outflows shifted to the present.• This is typical of any investment. You make a cash outlay expecting

future cash payments

• PW is also called net present valuenet present value (NPV), although that term is more often used when referring to the total present worth of a series of sums.


Summer 20083


Present Worth AnalysisPresent Worth Analysis

• Present worth analysisPresent worth analysis is when we compare the net present value of multiple mutually exclusive options.

• Present worth analysis considers only future incomes and expenditures.– Costs incurred in the past are called sunk costssunk costs and are irrelevant

when comparing future cash flows.– Sunk costs are in the past. You can’t undo them!

• FinancingFinancing and investmentinvestment activities are considered separate activities and then their NPVs combined.– The goal is to maximize the PW of investment benefits, minimize the

PW of financing costs, and maximize the NPV of a combination of financing and investment activities.


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Present Worth Analysis ExamplePresent Worth Analysis Example

• You can consider two types of equipment for your company, each with different costs, net annual benefits, useful lives, and salvage values:

#1 #2

Purchase cost $ 200k $ 700k

Annual benefit $ 95k $ 120k

Useful life 6 yrs 12 yrs

Salvage value $ 50k $ 150k

• Which option is best (assuming a 10% interest rate)?


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Capitalized CostsCapitalized Costs

• Capitalized cost analysisCapitalized cost analysis is a special kind of present worth analysis that chooses between several alternatives with infinite analysis periods.– The capitalized costcapitalized cost of an option is the NPV of a perpetual series

of cash flows.– Alternatively, capitalized cost is the present sum needed to provide

a perpetual series of cash flows that will support a capital project.

• The capitalized cost, P, that is needed to support a uniform perpetual annuity, A, is:

A

Pi


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Capitalized Costs ExampleCapitalized Costs Example

• Your municipality decides to invest in a long-term project that will cost $8 000 000, and need to be replaced every 70 years (at the same cost). If you estimate a 7% interest rate, what is the project’s capitalized cost?

0 70 140

$8M $8M$8M

0 1 2 3 4 5 70

A A A A AA

$8M $8M

210 240

0 70

$8M


Summer 20087


Present Worth Analysis using SpreadsheetsPresent Worth Analysis using Spreadsheets

• We can use (P/A, i, n) to calculate the present worth of a series of sums, but another method of doing so is with spreadsheets (e.g., MS Excel).

• Example: A = $1000, i = 10%, n = 10.n FV PV1 1,000.00$ 909.09$ 2 1,000.00$ 826.45$ 3 1,000.00$ 751.31$ 4 1,000.00$ 683.01$ 5 1,000.00$ 620.92$ 6 1,000.00$ 564.47$ 7 1,000.00$ 513.16$ 8 1,000.00$ 466.51$ 9 1,000.00$ 424.10$

10 1,000.00$ 385.54$ NPV 6,144.57$

/ , ,P A P A i n

$1000 / ,10%,10P A

$1000 6.145 $6145

Previous Method:Previous Method:


Summer 20088


Spreadsheet Example #1Spreadsheet Example #1

• How much would you pay for a contract that returns $580 per year for 15 years if you have the option of putting your investment into an account that pays 13% interest?


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Spreadsheet Example #2Spreadsheet Example #2

• What uniform annual payments would pay back a $25000 loan over 20 years with a 7% interest rate?

– Hint: We could use trial and error, but using the “goal seekgoal seek” feature in MS Excel will make this much easier.


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Problem 7.3(a) from Course NotesProblem 7.3(a) from Course Notes

• You are contemplating the purchase of a company that has a $600,000 “balloon payment” on a new 4-year loan with 8.5% interest. As part of your plan to purchase this company, you are contemplating paying off the debt early (i.e., today) in order to take out a larger long term debt with longer repayment provisions, at the current long term interest rate of 7.5%.

• Questions:– What payment would be a fair offer to repay the balloon payment,

assuming that you are going to refinance the new long term debt from the same financial institution at current rates?

– What if the company had an equivalent 4-year loan with uniform annual payments?


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Problem 7.3(a) from Course Notes (2)Problem 7.3(a) from Course Notes (2)

loan rate 8.5% loan rate 8.5%discount 7.5% discount 7.5%principal 600,000$ principal 600,000$

(A/P,8.5%,4) 0.305287893(A/P,7.5%,4) 0.298567509

n FV PV n FV PV1 51,000$ 47,441.86$ 1 183,173$ 170,393.24$ 2 51,000$ 44,131.96$ 2 183,173$ 158,505.34$ 3 51,000$ 41,052.99$ 3 183,173$ 147,446.83$ 4 651,000$ 487,469.14$ 4 183,173$ 137,159.84$

NPV 620,095.96$ NPV 613,505.26$

Balloon Payment Uniform Payments

ENGG 401 X2 Fundamentals of Engineering Management Spring 2008 Chapter 7: Present Worth Analysis

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