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# Module09 - Principles of Engineering Economy Economic...

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Principles of Engineering Economy Economic Equivalence with Loans, Bonds and Stock

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Key Concepts Last Module: Principles of Economic Equivalence This Module: Examples of Economic Equivalence Loans, Bonds and Stock provide a wonderful way to illustrate economic equivalence and also illustrate how engineering firms raise capital to grow.
Examples of Economic Equivalence Raising Capital Capital is another word for “money” generally used to invest Buy companies Build plants Buy equipment Companies must continuously raise capital to grow Get loans, Issue Bonds, Issue Stock Provides excellent equivalence examples

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Loans Contract in which funds are exchanged in an agreed upon fashion Key components: Principal Interest rate Payment plan
Loan Conditions Payments generally follow: Equal total payment plan Equal principal payment plan The total payment, An , made from the borrower to the lender at time n is comprised of an interest payment, IPn, and a principal payment, PPn.

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Important Equations Total payment: An= IPn + PPn Loan balance, where Bn is the balance at time n : B0= P Bn= Bn-1 – PPn Interest payment for any time period IPn=iBn-1
True Cost of a Loan The interest rate that equates the borrowed money to the payments (interest, principal and fees) is the true cost of the loan It is generally equal to the interest rate of the loan If payments are specified (no interest rate), it must be calculated

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Example Sao Martinho, a Brazilian sugar and ethanol group, obtained a loan of 288.6 million Brazilian Reals from the Brazilian Development Bank to expand a mill. Assuming an annual interest rate of Source: Jelmayer, R., “Brazil’s Sao Martinho Obtains \$162M Loan from BNDES,” Dow Jones International News , December 22, 2009.
Equal Principal Payments 288.6/9 years = 32.07 million reals per year.

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Equal Principal Payments 288.6/9 years = 32.07 million reals per year. =(R\$288.6M/9)
Equal Principal Payments 288.6/9 years = 32.07 million reals per year. =(R\$288.6M/9) =(0.0468)(R\$288.6M)

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Equal Principal Payments 288.6/9 years = 32.07 million reals per year. =(0.0468)(R\$288.6M) =R\$13.51M+R\$32.07M =(R\$288.6M/9)
Equal Principal Payments 288.6/9 years = 32.07 million reals per year. =(R\$288.6M/9) =(0.0468)(R\$288.6M) =R\$288.6M-R\$32.07M =R\$13.51M+R\$32.07M

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Equal Total Payments A=288.6M( A/P,4.68%,9 )=288.6M(.1387)=40.03M reals
Equal Total Payments A=288.6M( A/P,4.68%,9 )=288.6M(.1387)=40.03M reals =From above

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Equal Total Payments A=288.6M( A/P,4.68%,9 )=288.6M(.1387)=40.03M reals =From above =(0.0468)(R\$288.6M)
Equal Total Payments A=288.6M( A/P,4.68%,9 )=288.6M(.1387)=40.03M reals =From above =(0.0468)(R\$288.6M) =R\$40.3M-R\$13.51M

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Equal Total Payments A=288.6M( A/P,4.68%,9 )=288.6M(.1387)=40.03M reals =From above =(0.0468)(R\$288.6M) =R\$40.3M-R\$13.51M =R\$288.6M-R\$26.52M
Payment Plan TPn =R\$ 0, 10, 20, 30, 40, 50, 60, 70, 80 million

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Module09 - Principles of Engineering Economy Economic...

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