Time Value Of Money: Engineering Economic

Time Value of Money Engineering Economic Annisa Uswatun Khasanah

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Introduction • When making decision in choosing the best alternatives, time is one important factor that must be considered. • There will be economic consequences if the alternatives are taken immediately (right away), in a short period or in a long period. • Money consequences of any alternative occur over a substantial period of time – time value of money

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Introduction • The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. • The time value of money explains the change in the amount of money over time for funds that are owned (invested) or owed (borrowed). • This is the most important concept in engineering economy. 3

Time value of money concept • You have won a cash prize! You have two payment options: A - Receive $10,000 now OR B - Receive $10,000 in three years. Which option would you choose?

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Time value of money concept • For option A: by receiving $10,000 today, you are poised to increase the future value of your money by investing and gaining interest over a period of time. • For Option B, you don't have time on your side, and the payment received in three years would be your future value

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Time value of money concept

• If you are choosing Option A, your future value will be $10,000 plus any interest acquired over the three years. • The future value for Option B, on the other hand, would only be $10,000. 6

Interest Concept • Interest is the manifestation of the time value of money. • Interest is the difference between an ending amount of money and the beginning amount. If the difference is zero or negative, there is no interest. • There are always two perspectives to an amount of interest— interest paid and interest earned. 7

Interest Concept

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Interest Concept • Interest is paid when a person or organization borrowed money (obtained a loan) and repays a larger amount over time. • Interest paid on borrowed funds (a loan) is determined using the original amount, also called the principal. Equation 1.1 Interest = amount owed now - principal

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Interest Concept • Interest is earned when a person or organization saved, invested, or lent money and obtains a return of a larger amount over time. • interest paid over a specific time unit is expressed as a percentage of the principal, the result is called the interest rate. Equation 1.2

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Interest Concept

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Terminology and Symbol P = value or amount of money at a time designated as the present or time 0. Also P is referred to as present worth (PW), present value (PV), net present value (NPV), discounted cash flow (DCF), and capitalized cost (CC); monetary units, such as dollars F = value or amount of money at some future time. Also F is called future worth (FW) and future value (FV); dollars A = series of consecutive, equal, end-of-period amounts of money. Also A is called the annual worth (AW) and equivalent uniform annual worth (EUAW); dollars per year, euros per month n = number of interest periods (The time unit of the rate); years, months, days i = interest rate per time period; percent per year, percent per month

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Example • You plan to make a lump-sum deposit of $5000 now into an investment account that pays 6% per year, and you plan to withdraw an equal end-of-year amount of $1000 for 5 years, starting next year. At the end of the sixth year, you plan to close your account by withdrawing the remaining money. Define the engineering economy symbols involved. 13

Example • All five symbols are present, but the future value in year 6 is the unknown. – P = $5000 – A = $1000 per year for 5 years – F = ? at end of year 6 – i = 6% per year – n = 5 years for the A series and 6 for the F value 14

Cash Flow • Cash flows are the amounts of money estimated for future projects or observed for project events that have taken place. • Cash inflows are the receipts, revenues, incomes, and savings generated by project and business activity • Cash outflows are costs, disbursements, expenses, and taxes caused by projects and business Cash flow activity. A negative or minus sign indicates a cash outflow.

R is receipts, and D is disbursements

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Cash Flow Cash inflows

(time)

Cash outflows

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Interest Concept 1. Simple interest 2. Compound interest

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Simple Interest • Simple interest is calculated using the principal only, ignoring any interest accrued in preceding interest periods

F = P(1+i.n) F = P + Pni

F=P+I 18

Simple Interest - Example • Green Tree Financing lent an engineering company $100,000 to retrofit an environmentally unfriendly building. The loan is for 3 years at 10% per year simple interest. How much money will the firm repay at the end of 3 years? – P = $ 100,000 – n = 3 years – i = 0,1 per year 19

Simple Interest - Example The interest for each of the 3 years is:

Interest per year = ($100,000)(0.10) = $10,000 Total interest for 3 years from is:

Total interest (I)

=Pni

Total interest (I)

= ($100,000)(3)(0.10) = $30,000

The amount due after 3 years is Total due (F)

=P+I

Total due (F)

= $100,000 + 30,000 = $130,000 20

Simple Interest - Example F = P(1+ i .n ) = $100,000 [1 + (0,1 x 3)] = $130,000

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Simple Interest - Example Year

0

Principal 100,000

Interest

Amount owned

Amount paid

0

100,000

0

1

10,000

110,000

0

2

10,000

120,000

0

3

10,000

130,000

130,000

P = 100,000

i = 10% n=3

F = 130,000

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Compound Interest • the interest accrued for each interest period is calculated on the principal plus the total amount of interest accumulated in all previous periods. • Compound interest reflects the effect of the time value of money on the interest also

F

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Compound Interest - Example • Assume an engineering company borrows $100,000 at 10% per year compound interest and will pay the principal and all the interest after 3 years. Compute the annual interest and total amount due after 3 years. – P = $ 100,000 – n = 3 years – i = 0,1 per year 24

Compound Interest - Example Interest, year 1: 100,000(0.10) = $10,000

Total due, year 1: 100,000 + 10,000 = $110,000 Interest, year 2: 110,000(0.10) = $11,000 Total due, year 2: 110,000 + 11,000 = $121,000

Interest, year 3: 121,000(0.10) = $12,100 Total due, year 3: 121,000 + 12,100 = $133,100 Or follow P(1+i)n

Year 1: $100,000(1+ 0,10) 1 = $110,000 Year 2: $100,000(1+ 0,10) 2 = $121,000 Year 3: $100,000(1+ 0,10) 3 = $133,100 25

Compound Interest - Example Year

Principal

Interest

Amount paid

0

100,000

0

1

10,000

110,000

0

2

11,000

121,000

0

3

12,100

133,100

133,100

0

100,000

Amount owned

P = 100,000

i = 10% n=3

F = 133,100

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The difference between Simple and Compound Interest $133,100 – 130,000 = $3100

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Single Payment Compound Factor single payments; they are used to find the present or future amount when only one payment or receipt is involved.

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Uniform Formula

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Uniform formula- Example • How much money should you be willing to pay now for a guaranteed $600 per year for 9 years starting next year, at a rate of return of 16% per year? A = $600 – A = $600 0 1 2 3 4 5 6 7 8 9 – n = 9 years – i = 16 % – P=? P=?

P = $2763.93 30

Uniform formula- Example • The president of Ford Motor Company wants to know the equivalent future worth of a $1000 capital investment each year for 8 years, starting 1 year from now. Ford capital earns at a rate of 14% per year. – – – –

A = $ 1000 n = 8 years i = 14% F=?

F = $13,232.80 31

Exercises (assignment 4) 1. A man deposit $500 in a credit union at the end of each year for five years. The credit union pays 5% compounded annually. At the end of five years, immediately following his fifth deposit, how much will he have in his account? 2. On January 1, a man deposits $5000 in acredit union that pays 8% interest compounded annually. He wishes to withdrawal all the money in five equal end of year sum, beginning December 31st of the first year. How should he withdraw each year?

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Exercises 3. If $500 were deposited in a bank saving account, how much would be in the account three years hence if the bank paid 6% interest compounded annually? 4. If you wish to have $800 in a saving account at the end of four years, and 5% interest compound was paid annually, how much should you put into the savings account now? 33

Exercises 5. Iselt Welding has extra funds to invest for future capital expansion. If the selected investment pays simple interest, what interest rate would be required for the amount to grow from $60,000 to $90,000 in 5 years?

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Exercises 6. A solid waste disposal company borrowed money at 10% per year interest to purchase new haulers and other equipment needed at the company owned landfill site. If the company got the loan 2 years ago and paid it off with a single payment of $4,600,000, what was the principal amount P of the loan? 35

0

1

2

3

4

5

Rp 3000 Rp 6000 Rp 8000 Rp 10000

Rp 12000

7.Perhatikan diagram alir kas tersebut jika tingkat bunga adalah 12%, hitunglah P, F pada akhir tahun ke 5 dan A! (untuk menghitung nilai P, tariklah semua nilai menjadi nilai P terlebih dahulu, kemudian tambahkan dengan Rp 6000. Baru hitung F dan A) 8.Banyaknya uang yang harus ditabungkan mulai tahun depan selama 6 tahun berturut-turut dalam jumlah yang sama agar pada akhir tahun ke 10, uang yang terkumpul sebesar Rp 20 juta, jika i = 10%/tahun adalah?

9. Banyaknya uang yang akan diperoleh 10 tahun yang akan datang, jika mulai tahun depan selama 5 tahun berturutturut ditabungkan uang sebanyak Rp 20 juta/tahun pada tingkat bunga 10%/tahun adalah?