Chapter 11 Economis

Electric Submersible Pumps Mohamed Dewidar 2013

Chapter 11

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Economics

Table of Content

Section Content Page

1 Simple and compound interest 2

2 Present Value (PV) of Future Value (FV) 3

3 New income project 4

4 Rate Of Return (ROR) 4

Examples 5


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Economics

9.1. Simple and Compound Interest

Simple interest is the interest paid or received on the

original principal regardless the number of time period that

have passed. Interest rates are reported as annual percentage.

Interest = Principal x Rate x Time

Compound interest is applied to the principal at the end of

one period and added to the existing principal. The total is

then treated as principal again for the second interest period

and so on.

P = Principal : i = interest rate

P1 = Principal at end of 1st year = P[i+1]

P2 = Principal at end of 2nd year = p[i+1]+ p[i+1]*i= p[i+1]2

P3 = Principal at end of 3rd year = p[i+1]2 + p[i+1]2 * i =

p[i+1]2(i+1)=P[i+1]3

Interest = P[i+1]3-P = P([i+1]3-1)

Interest = P([i+1]n - 1)

Example

A sum of $2000 is invested in a saving account yielding an

annual interest rate of 12%. Compute the interest amount for

one year if:

a. The interest is compounded monthly

b. The interest is compounded quarterly

c. The interest is compounded annually

d. The interest is compounded semiannually

Solution

a. i = 0.12 ÷ 12 = 0.01 monthly compounding

Interest = 2000*([0.01+1]12-1) = $253.65

b. i = 0.12 ÷ 4 = 0.03 quarterly compounding

Interest = 2000*([0.03+1]4-1) = $251.02

c. I = 0.12

Interest = 2000*([0.12+1]1-1) = $240.00

d. I = 0.12 ÷ 2 = 0.06

Interest = 2000*([0.06+1]2-1) = $247.20


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9.2. Present Value (PV) of Future Sum (FV)

FV of Principal P (PV) of

1st year = P + Pi = P(i+1)

2nd year = P(i+1)+P(i+1)i=P(i+1)(i+1)=P(i+1)

2

3rd year = P(i+1)

2 + P(i+1)

2i = P(i+1)

3

and so on ……

FV = PV (i+1)n

PV = FV ÷ (i+1)n = FV * [1 ÷ (i+1)n]

The quantity of [1 ÷ (i+1)n] (is called discount factor

PV = FV * discount factor

Example

Compute PV for next 5 years of FV of $5,000 assuming interest

rate of 12% compounded. (a) Annually, (b) Semiannually

(a) PV = $5,000 ÷ (0.12+1)5 = $2,837.13

(b) i = 0.12/2 = 0.06 : n = 5 years x 2 period per year = 10

PV = $5,000 ÷ (0.06+1)10 = $2,791.97

FV = $2,837.13 x (0.12+1)5 = $5,000

PV = $2,791.97 x (0.06+1)10 = $5,000

9.3. New Income Project

Consider a typical new project in which an initial capital

outlay is required for plant. The financial history of such

project may be illustrated by the following graph where

cumulative profit, or loss is plotted vs time.

AB’ = investment time

BB’ = Total capital investment

DD’ = Final profit

B’C = Payout time

B’D’= Earning life of the project

AD’ = Life of the project


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9.4. Rate of Return (ROR)

To see how rate of return is defined, consider this graph.

As discount rate i increases the point D will approach D’ and

for some value R of the discount rate point D will coincide

with D’. This value R is defined as rate of return of the

project.


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To put another way, if the capital for a certain project is

borrowed from a bank and if profits from the venture are used

to reduce the outstanding debit, then the rate of return of

the project will equal the rate of interest the bank charges

on the outstanding loan if the final profit made at the end of

earning life is just sufficient to cover the final payment to

the bank.

Example 1

The capital cost of a certain project is $31,000, the earning

life of the project is 6 years, the income in these six years

are $5,000, $12,000, $13,000, $12,000, $12,000, and $8,000

respectively. calculate:

a. The undiscounted % profit

b. Discounted value based on discount rate of 10%/year

c. Payout time

d. Rate of return

Solution

a. Undiscounted % profit

Total income = $5,000+$12,000+$13,000+$12,000+$12,000+$8,000 =

$62,000

Undiscounted profit = $62,000-$31,000 = $31,000

Undiscounted % profit = $31,000 ÷ $31,000 = 100%

b. The discounted profit

PV = FV x discount factor (1 ÷ [i + 1]n)

i = discount rate per year

Discounted profit = $46,560 - $31,000 = $15,560

Discounted % profit = $15,554 ÷ $31,000 = 50.2%


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What does ROR = 23% mean?

It means that the, if the interest of the bank on the borrowed

money is equal 27.6%, the net profit of the project will be

0%. So, the interest of the bank must be much less than this

ROR.

Example 2

An oil well has reserve of 346,750 STB the life of the well is

5 years. The reserve is distributed among the five years as

following (i.e, cumulative production per year):

The 1st year will produce 109,500 STB

The 2nd year will produce 73,000 STB

The 3rd year will produce 54,750 STB

The 4th year will produce 54,750 STB

The 5th year will produce 54,750 STB

The expected average oil price is $80/bbl

The capital & operating cost during these 5 years are

$7,000,000 calculate Rate of return.

Capital & Operating cost = $7,000,000 DISCOUNT RATE

Reserve STB

Month

Undiscounted 20%

Undiscounted net income

Cumulative U.D.N.I.

Undiscounted

profit

Discounted factor

Discounted net income

Cumulative D.N.I.

Discounted profit

0 ($7,000,000) =1 ÷ (i+1)n

109,500 1 8,760,000 8,760,000 1,760,000 0.8333333 7,300,000 7,300,000 300,000

73,000 2 5,840,000 14,600,000 7,600,000 0.6944444 4,055,556 11,355,556 4,355,556

54,750 3 4,380,000 18,980,000 11,980,000 0.5787037 2,534,722 13,890,278 6,890,278

54,750 4 4,380,000 23,360,000 16,360,000 0.4822531 2,112,269 16,002,546 9,002,546

54,750 5 4,380,000 27,740,000 20,740,000 0.4018776 1,760,224 17,762,770 10,762,770


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Reserve STB

Month

Undiscounted 40%


Cumulative U.D.N.I.

Undiscounted

profit

Discounted factor


Cumulative D.N.I.

Discounted profit

0 ($7,000,000) =1 ÷ (i+1)

109,500 1 8,760,000 8,760,000 1,760,000 0.71428571 6,257,143 6,257,143 -742,857

73,000 2 5,840,000 14,600,000 7,600,000 0.5102041 2,979,592 9,236,735 2,236,735

54,750 3 4,380,000 18,980,000 11,980,000 0.3644315 1,596,210 10,832,945 3,832,945

54,750 4 4,380,000 23,360,000 16,360,000 0.2603082 1,140,150 11,973,095 4,973,095

54,750 5 4,380,000 27,740,000 20,740,000 0.1859344 814,393 12,787,487 5,787,487


Reserve STB

Month

Undiscounted 60%


Cumulative U.D.N.I.

Undiscounted

profit

Discounted factor


Cumulative D.N.I.

Discounted profit

0 ($7,000,000) =1 ÷ (i+1)

109,500 1 8,760,000 8,760,000 1,760,000 0.62500000 5,475,000 5,475,000 -1,525,000

73,000 2 5,840,000 14,600,000 7,600,000 0.390625 2,281,250 7,756,250 756,250

54,750 3 4,380,000 18,980,000 11,980,000 0.2441406 1,069,336 8,825,586 1,825,586

54,750 4 4,380,000 23,360,000 16,360,000 0.1525879 668,335 9,493,921 2,493,921

54,750 5 4,380,000 27,740,000 20,740,000 0.0953674 417,709 9,911,630 2,911,630


Reserve STB

Month

Undiscounted 80%


Cumulative U.D.N.I.

Undiscounted

profit

Discounted factor


Cumulative D.N.I.

Discounted profit

0 ($7,000,000)

109,500 1 8,760,000 8,760,000 1,760,000 0.5555556 4,866,667 4,866,667 -2,133,333

73,000 2 5,840,000 14,600,000 7,600,000 0.308642 1,802,469 6,669,136 -330,864

54,750 3 4,380,000 18,980,000 11,980,000 0.1714678 751,029 7,420,165 420,165

54,750 4 4,380,000 23,360,000 16,360,000 0.0952599 417,238 7,837,403 837,403

54,750 5 4,380,000 27,740,000 20,740,000 0.0529222 231,799 8,069,202 1,069,202


Reserve STB

Month

Undiscounted 100%


Cumulative U.D.N.I.

Undiscounted

profit

Discounted factor


Cumulative D.N.I.

Discounted profit

0 ($7,000,000)

109,500 1 8,760,000 8,760,000 1,760,000 0.5 4,380,000 4,380,000 -2,620,000

73,000 2 5,840,000 14,600,000 7,600,000 0.25 1,460,000 5,840,000 -1,160,000

54,750 3 4,380,000 18,980,000 11,980,000 0.125 547,500 6,387,500 -612,500

54,750 4 4,380,000 23,360,000 16,360,000 0.0625 273,750 6,661,250 -338,750

54,750 5 4,380,000 27,740,000 20,740,000 0.03125 136,875 6,798,125 -201,875


Chapter 11

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Chapter 11 Economis