Chapter 3 Interest and Equivalence Copyright Oxford University Press 2009

Chapter Outline Time Value of Money Interest Calculations Cash Flow Equivalence Single Payment Compound Interest Formulas Copyright Oxford University Press 2009

Learning Objectives Understand the concept of “time value of money” Distinguish between simple and compound interest Understand the concept of “equivalence” of cash flows Solve problems using Single Payment Compound Interest Formulas Copyright Oxford University Press 2009

Computing Cash Flows Question: Would you rather Receive $1000 today or Receive $ years from today? Answer: Of course today! Why? I could invest $1000 today to make more money I could buy a lot of stuff today with $1000 Who knows what will happen in 10 years? Copyright Oxford University Press 2009

Computing Cash Flows Because money is more valuable today than in the future, we need to describe cash receipts and disbursements at the time they occur. Copyright Oxford University Press 2009

Example Problems Copyright Oxford University Press 2009

Time Value of Money Money has purchasing power Money has earning power Money is a valuable asset People are will to pay some charges (interests) to have money available for their use Copyright Oxford University Press 2009

Simple Interest Interest is computed only on the original sum, and not on accrued interest Copyright Oxford University Press 2009 (Eq. 3-1) Total interest earned = whereP = Principal i = Simple annual interest rate n = Number of years whereF = Amount due at the end of n years (Eq. 3-2)

Example Problem Copyright Oxford University Press 2009

Compound Interest Interest is computed on the unpaid balance, which includes the principal and any unpaid interest from the preceding period Common practice for interest calculation, unless specifically stated otherwise Copyright Oxford University Press 2009

Example 3-4 Compound Interest Calculation Loan of $5000 for 5 yrs at interest rate of 8% Year Balance at the Beginning of the yearInterest Balance at the end of the year 1 $5, $ $5, $ $5, $ $6, $ $6, $ $7, Copyright Oxford University Press 2009

Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #1: Pay $1000 principal plus interest due Yr Balance at the Beginning of YearInterest Balance at the end of Year Interest Payment Principal Payment Total Payment 1$5,000.00$400.00$5,400.00$400.00$1,000.00$1, $4,000.00$320.00$4,320.00$320.00$1,000.00$1, $3,000.00$240.00$3,240.00$240.00$1,000.00$1, $2,000.00$160.00$2,160.00$160.00$1,000.00$1, $1,000.00$80.00$1,080.00$80.00$1,000.00$1, Subtotal$1,200.00$5,000.00$6, Copyright Oxford University Press 2009

Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #2: Pay interest due at end of each year and principal at end of 5 years Yr Balance at the Beginning of yearInterest Balance at the end of year Interest Payment Principal Payment Total Payment 1$5,000.00$400.00$5,400.00$400.00$0.00$ $5,000.00$400.00$5,400.00$400.00$0.00$ $5,000.00$400.00$5,400.00$400.00$0.00$ $5,000.00$400.00$5,400.00$400.00$0.00$ $5,000.00$400.00$5,400.00$400.00$5,000.00$5, Subtotal$2,000.00$5,000.00$7, Copyright Oxford University Press 2009

Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #3: Pay in 5 equal end-of-year payments Yr Balance at the Beginning of yearInterest Balance at the end of year Interest Payment Principal Payment Total Payment 1$5,000.00$400.00$5,400.00$400.00$852.28$1, $4,147.72$331.82$4,479.54$331.82$920.46$1, $3,227.25$258.18$3,485.43$258.18$994.10$1, $2,233.15$178.65$2,411.80$178.65$1,073.63$1, $1,159.52$92.76$1,252.28$92.76$1,159.52$1, Subtotal$1,261.41$5,000.00$6, Copyright Oxford University Press 2009

Repaying a Debt Repay of a loan of $5000 in 5 yrs at interest rate of 8% Plan #4: Pay principal and interest in one payment at end of 5 years Yr Balance at the Beginning of yearInterest Balance at the end of year Interest Payment Principal Payment Total Payment 1$5,000.00$400.00$5,400.00$0.00 2$5,400.00$432.00$5,832.00$0.00 3$5,832.00$466.56$6,298.56$0.00 4$6,298.56$503.88$6,802.44$0.00 5$6,802.44$544.20$7,346.64$2,346.64$5,000.00$7, Subtotal$2,346.64$5,000.00$7, Copyright Oxford University Press 2009

A Closer Look at the 4 Repayment Differences: Repayment structure (repayment amounts at various points in time) Total payment amount Similarities: All interest charges were calculated at 8% They all achieved the same purpose of repaying the loan within 5 years Copyright Oxford University Press 2009

Equivalence If a firm believes 8% was reasonable, it would have no preference about whether it received $5000 now or was paid by any of the 4 repayment plans. The 4 repayment plans are equivalent to one another and to $5000 now at 8% interest Copyright Oxford University Press 2009

Use of Equivalence in Engineering Economic Studies Using the concept of equivalence, one can convert different types of cash flows at different points of time to an equivalent value at a common reference point Equivalence is dependent on interest rate Copyright Oxford University Press 2009