Steps in the Decision Economics Process Step 3: Select Interest Rates.

Steps in the Decision Economics Process

• Step 3: Select Interest Rates

Interest – money paid for the use of money

Rate of interest – The ratio between the interest payable at the end of a period of time, and the money owed at the beginning of that period (principle).

You borrow $10,000 and pay it off at the end of the year for $10,900. You pay $900 for the use of

the $10,000.

You borrow $10,000 and pay it off at the end of the year for $10,900. You pay $900 for the use of

the $10,000.

PrincipleInterestInterest rate

Unless otherwise stated, the interest rate used in problems is for one year, not months, weeks, days, etc.

How would you select the interest rate?

Use the rate that the owner (client, sponsor) has to pay to borrow the money, or perhaps investment such as government bonds.

Method Interest Paid Present Value Future Value

9% + Balloon $9,000.00 $10,000.00 $19,000.00

9% + $1000 $4,950.00 $10,000.00 $14,950.00

$1,558.20 $5,582.01 $10,000.00 $15,582.01

Balloon $13,673.64 $10,000.00 $23,673.64

Which is the best deal??Which is the best deal??

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,0001 $900 $10,900 $900 $10,0002 $900 $10,900 $900 $10,0003 $900 $10,900 $900 $10,0004 $900 $10,900 $900 $10,0005 $900 $10,900 $900 $10,0006 $900 $10,900 $900 $10,0007 $900 $10,900 $900 $10,0008 $900 $10,900 $900 $10,0009 $900 $10,900 $900 $10,000

10 $900 $10,900 $10,900 $0$9,000 $19,000

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,0001 $900 $10,900 $1,900 $9,0002 $810 $9,810 $1,810 $8,0003 $720 $8,720 $1,720 $7,0004 $630 $7,630 $1,630 $6,0005 $540 $6,540 $1,540 $5,0006 $450 $5,450 $1,450 $4,0007 $360 $4,360 $1,360 $3,0008 $270 $3,270 $1,270 $2,0009 $180 $2,180 $1,180 $1,000

10 $90 $1,090 $1,090 $0$4,950 $14,950

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,000.001 $900.00 $10,900.00 $1,558.20 $9,341.802 $840.76 $10,182.56 $1,558.20 $8,624.363 $776.19 $9,400.55 $1,558.20 $7,842.354 $705.81 $8,548.17 $1,558.20 $6,989.975 $629.10 $7,619.06 $1,558.20 $6,060.866 $545.48 $6,606.34 $1,558.20 $5,048.147 $454.33 $5,502.47 $1,558.20 $3,944.278 $354.98 $4,299.26 $1,558.20 $2,741.069 $246.70 $2,987.75 $1,558.20 $1,429.55

10 $128.66 $1,558.21 $1,558.21 $0.00$5,582.01 $15,582.01

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,000.001 $900.00 $10,900.00 $0.00 $10,900.002 $981.00 $11,881.00 $0.00 $11,881.003 $1,069.29 $12,950.29 $0.00 $12,950.294 $1,165.53 $14,115.82 $0.00 $14,115.825 $1,270.42 $15,386.24 $0.00 $15,386.246 $1,384.76 $16,771.00 $0.00 $16,771.007 $1,509.39 $18,280.39 $0.00 $18,280.398 $1,645.24 $19,925.63 $0.00 $19,925.639 $1,793.31 $21,718.93 $0.00 $21,718.93

10 $1,954.70 $23,673.64 $23,673.64 $0.00$13,673.64 $23,673.64

Method Interest Paid Present Value Future Value

9% + Balloon $9,000.00 $10,000.00 $19,000.00

9% + $1000 $4,950.00 $10,000.00 $14,950.00

$1,558.20 $5,582.01 $10,000.00 $15,582.01

Balloon $13,673.64 $10,000.00 $23,673.64

Which is the best deal??Which is the best deal??

From the viewpoint of the investor who has $10,000 to invest,the borrower will promise to repay the loan using any one of four different payments schedules.

From the viewpoint of the borrower the $10,000 is needednow, and any one of the payment schedules will provide the cash.

So we can see that a loan of $10,000 can be repaidwith several different methods.

To the investor the loan is the amount necessary to secure the promise of future payments. That amount is the present worth.

To the borrower, the present worth is the amount that can be obtained in exchange for the promise to make specific future payments.

Equivalence – all future payments or series of Equivalence – all future payments or series of payments that would repay the present sum with payments that would repay the present sum with interest at the stated rate are equivalent.interest at the stated rate are equivalent.

Engineering economy problems usually involve making aEngineering economy problems usually involve making achoice of several alternative plans for accomplishing anchoice of several alternative plans for accomplishing anobjective. objective.

In my 4 examples, it may not be obvious that allIn my 4 examples, it may not be obvious that allfour are equivalent. It is only obvious if all arefour are equivalent. It is only obvious if all areconverted to a single present worth or to an converted to a single present worth or to an equivalent uniform series.equivalent uniform series.

Steps in the Decision Economics Process

• Step 4: Put Costs and Benefits on a Comparable Basis & Calculate B:C or Least Cost

Much of the remaining material & homework will be directed to understanding the determination of a comparable basis.

Steps in the Decision Economics Process

• Step 5: Consider Intangible Benefits & Costs

The author uses the example of the intangible aesthetic value of a timber bridge vs. a steel bridge.

In the real world, be certain that a value is actually intangible.

Steps in the Decision Economics Process

• Step 6: Recommend Best Alternative

The “recommended best” alternative will depend on your confidence, valuation of intangibles, acceptance of that alternative by the community, permitting agency, and your mother-in-law.

DISCOUNTING FACTORS

Discounting factors are used to convert a set of discrete and continuous costs and revenues to a common point in time or a common period.

Discounting factors account for the time value of money, allowing “apples to apples” comparison.

Discounting Factors – p. 220 through 240 in (Walesh, 2000)

Single-Payment Simple-Interest Factor

Single-Payment Compound-Amount Factor-

Single-Payment Present-Worth Factor-

Series Compound-Amount Factor-

Series Sinking-Fund Factor-

Series Present-Worth Factor-

Capital-Recovery Factor-

Gradient-Series Present-Worth Factor-

Fig 8-16

HANDOUT

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,0001 $900 $10,900 $900 $10,0002 $900 $10,900 $900 $10,0003 $900 $10,900 $900 $10,0004 $900 $10,900 $900 $10,0005 $900 $10,900 $900 $10,0006 $900 $10,900 $900 $10,0007 $900 $10,900 $900 $10,0008 $900 $10,900 $900 $10,0009 $900 $10,900 $900 $10,000

10 $900 $10,900 $10,900 $0$9,000 $19,000

INTEREST ONLY

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,0001 $900 $10,900 $1,900 $9,0002 $810 $9,810 $1,810 $8,0003 $720 $8,720 $1,720 $7,0004 $630 $7,630 $1,630 $6,0005 $540 $6,540 $1,540 $5,0006 $450 $5,450 $1,450 $4,0007 $360 $4,360 $1,360 $3,0008 $270 $3,270 $1,270 $2,0009 $180 $2,180 $1,180 $1,000

10 $90 $1,090 $1,090 $0$4,950 $14,950

INTEREST + $1000 / YEAR

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,000.001 $900.00 $10,900.00 $1,558.20 $9,341.802 $840.76 $10,182.56 $1,558.20 $8,624.363 $776.19 $9,400.55 $1,558.20 $7,842.354 $705.81 $8,548.17 $1,558.20 $6,989.975 $629.10 $7,619.06 $1,558.20 $6,060.866 $545.48 $6,606.34 $1,558.20 $5,048.147 $454.33 $5,502.47 $1,558.20 $3,944.278 $354.98 $4,299.26 $1,558.20 $2,741.069 $246.70 $2,987.75 $1,558.20 $1,429.55

10 $128.66 $1,558.21 $1,558.21 $0.00$5,582.01 $15,582.01

CAPITAL RECOVERY

End of Interest Total Money Year- end Money owed

Year Due owed before Payment after year-

year- end end payment

payment

0 $10,000.001 $900.00 $10,900.00 $0.00 $10,900.002 $981.00 $11,881.00 $0.00 $11,881.003 $1,069.29 $12,950.29 $0.00 $12,950.294 $1,165.53 $14,115.82 $0.00 $14,115.825 $1,270.42 $15,386.24 $0.00 $15,386.246 $1,384.76 $16,771.00 $0.00 $16,771.007 $1,509.39 $18,280.39 $0.00 $18,280.398 $1,645.24 $19,925.63 $0.00 $19,925.639 $1,793.31 $21,718.93 $0.00 $21,718.93

10 $1,954.70 $23,673.64 $23,673.64 $0.00$13,673.64 $23,673.64

SINGLE-PAYMENT COMPOUND-AMOUNT

The example demonstrates single-payment compound-amount & capital-recovery. For homework, develop a spreadsheet for the other Discount Factors, p. 241, Fig 8-16. Ignore Gradient-Series Present-Worth.

P = $10,000

n = 10 years

i = 9%

F = ?

Email your .xls spreadsheet to me at [email protected] by Monday morning the 9th.

Turn in paper solutions (tabulations) during class on 10 Sept., next Tuesday.

Working in groups is OK (2 to 4 persons). I will ask some of you to explain each of the Discount Factors using your tables during the following classes.