eng'g economics lesson 3

8/12/2019 Eng'g Economics Lesson 3

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Concepts from theexample problems

( F / P, i, N) Prob lem 1

( P / F, i, N) Prob lem 2

( F / A , i, N) Prob lem 3( A / F, i, N) Prob lem 4

( P / A , i, N) Prob lem 5

( A / P, i, N) Prob lem 6( P / G, i, N) Prob lem 7

( A / G, i, N) Prob lem 8


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Example 1

How much w ould you have to deposi ttoday to have $2000 in 4 years i f you can

get a 12% interest rate compounded

annual ly?GIVEN:

F4= $2 000

i = 12%FIND P:

P = F4(P/F,i,n)

= 2 000(P|F,12%,4)

= 2 000(0.6355) = $1 271

0 1 2 3

n=4

P?

$2 000

DIAGRAM:


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Different Waysof Looking at P/F

From previous examp le, i f you can earn 12%

compounded annual ly, you need to depos i t

$1271 to have $2000 in 4 years.

You are ind ifferent between $1271 today and

$2000 in 4 years, assum ing you can earn areturn on your money o f 12%.

$1271 today and $2000 in 4 years are

equivalent, i f you can earn 12% on you r money.

The present wor th o f $2000 in 4 years is $1271(i = 12% cpd annually).

If you could get 13% on your money, would you

rather have the $1271 today, or $2000 in 4 years


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Example 2

Tui t ion costs are expected to inf late at the

rate of 8% per year. The first years

tu i t ion is due one year from now and w i ll

be $10,000. To co ver tui t ion cost fo r 4

years, a fund is to be set up today in an

accoun t that w i l l earn in terest at the rate

of 5% per year, compounded annual ly.

How much must be deposi ted in to thefund today in o rder to pay the 4 years o f

tu i t ion expenses?


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Present Given Gradient (Geometric)

gis the geometric gradient over the time period (time period: Time 0 to Time n, 1st flow at Time 1)

Pis the present value of the flow at Time 0

(n periods in the past)

i is the effective interest rate for each period

Note: cash flow starts with A1at Time 1, increases by constant g%

0 n

A1

P ?

1 2 3

P = A1(P/A,g,i,n)

11

1

1

( )

( )

( / , , , )

( )

n

g

iwhen i g

i g

P A g i n

nwhen i g

i

g = %


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Example 2

Tuit ion costs are expected to inf late at the rate of 8% peryear. The first years tuition is due one year from now and

w il l be $10,000. To co ver tuit ion cos t for 4 years, a fun d is

to be set up today in an acco unt th at wi l l earn interest at

the rate of 5% per year, com pou nded annual ly. How m uch

must be deposi ted into the fund tod ay in order to pay the 4years of tui t ion expenses?


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Example 2 - Concept

If you r r ich Aunt Edna wanted to put a

sum of money in the bank today to pay

for you r next four years o f tu i t ion, that

sum wou ld be $39,759 assum ing 5%

return on investment and tu i t ion that

begin s at $10,000 increasing by 8% per

year. This problem assumes tui t ion is

due at the end of the year.


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Complex Cash Flows

Complex Cash Flows B reak apart(or separate) complex cash f lows

into component cash f lows in order

to use the standard form ulas.

Remember: You can on ly combine

cash f low s i f they occu r at the same

po int in t ime.

(This is l ike bu i ld ing w ith LEGOs!)


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Problem 3A con struct ion f i rm is consider ing the purchase of an

air compresso r.

The comp ressor h as the fo l lowing expected end o f

year maintenance costs :

Year 1 $800

Year 2 $800Year 3 $900

Year 4 $1000

Year 5 $1100

Year 6 $1200

Year 7 $1300

Year 8 $1400

What is the present equivalent maintenance cost i f th e

interest rate is 12% per year compou nded annual ly?


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Problem 3 Alt Soln 1GIVEN:

MAINT COST1-8

PER DIAGRAM

i = 12%/YR, CPD ANNUALLYFIND P: P = PA+ PG + PF= A(P/A,i,n) + G(P/G,i,n) + F(P/F,i,n)

= $700(P/A,12%,8) + $100(P/G,12%,8)+ $100(P/F,12%,1)

= $700(4.9676) + $100(14.4715)+ $100(0.8929) = $5014

PA?

0

1 2 3 n=8

$700

4

NOTE: CAN BREAK INTO 3 CASH FLOWS:ANNUAL, LINEAR GRADIENT, AND FUTURE

DIAGRAM:

P ?

0

1 2 3 n=8

$700

$100

$700

4

$200$300

$100PG?

0

1 2 3 n=8

$100$700$200 $300

4 0 $100

PF?

n=1


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Problem 3 Alt Soln 2GIVEN:

MAINT COST1-8

PER DIAGRAMi = 12%/YR, CPD ANNUALLY

FIND P: P = PA+ P

G(P

PG)= A(P/A,i,n) + G(P/G,i,n-1)(P/F,i,1)

= $800(P/A,12%,8) + $100(P/G,12%,7)(P/F,12%,1)

= $800(4.9676) + $100(11.6443)(0.8929)= $5014DIAGRAM:

P ?

0

1 2 3 n=8

$800

$100

$600

4

$200

PA?

0

1 2 3 n=8

$800

4

PG?

0 1 2 n=73

$100

$600

$200NOTE: PGMUST BE OFFSET ONE YEARSOBRING THE OFFSET YEAR BACK TO TIME ZERO

0

PG?

PPG

?

1


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Problem 4A young coup le has decided to make advance plans for

financing their 3 year old daughters college education.Money can be deposited at 8% per year, com pou nded

annually.

What annu al depos it on each bir th day, from the 4thto the

17th(inc lus ive), mus t be made to p rov ide $7,000 on each

bir thd ay from the 18th

to th e 21s t

(inclu sive)?GIVEN:

WITHDRAWALS18-21

= $7 000i = r = 8%/YR, CPD YEARLY

FIND A4-17

:

17

21 yrs

$7 000

A ?

DIAGRAM:

4

180P17= A(F/A,i,n) = A(P/A,i,n)

= A(F/A,8%,14) = 7 000(P/A,8%,4)

= A(24.2149) = 7 000(3.3121)

A = $957

STRATEGY: CAN BREAK INTO 2 CASH FLOWS,SO PICK A CONVENIENT POINT IN TIME AND SETDEPOSITS EQUAL TO WITHDRAWALS

eng'g economics lesson 3

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