EE1 PEEE Refresher Class Finance Notes notes by T. Ernst EE1 - Finance, Notes Page 1

Time is Money A dollar today is not equivalent to a dollar at some other date …. Due to interest! Financial analysis typically involves comparison between alternatives with varying cash flows occurring at different times. Page 2 EE1 - Finance, Notes

Financial Equivalence At 6%, all the cases are financially equivalent in a TVM sense. All cases will repay the loan at 6%. The cases are not equivalent at a rate other than 6%. Page 3 EE1 - Finance, Notes

TVM Equivalence Factors: Single Payment: Future value of a present value: [F/P] Present value of a future value: [P/F] F n P P n F Page 4 EE1 - Finance, Notes

TVM Equivalence Factors: Single Payment: Future value of a present value: [F/P]ni = (1+i)n Present value of a future value: [P/F]ni = 1/(1+i)n where: n = number of periods i = interest rate per period Page 5 EE1 - Finance, Notes

TVM Equivalence Factors: Uniform Series Payments: Future value of an annuity: [F/A] Annuity from a future value: [A/F] F A 1 A 2 A 3 A A n A 1 A 2 A 3 A A n F Page 6 EE1 - Finance, Notes

TVM Equivalence Factors: Uniform Series Payments: Present value of an annuity: [P/A] Annuity from a present value: [A/P] P A 1 A 2 A 3 A A n A 1 A 2 A 3 A A n P Page 7 EE1 - Finance, Notes

TVM Equivalence Factors: Uniform Series Payments: Future value of an annuity: [F/A]ni = [(1+i)n - 1]/i Annuity from a future value: [A/F]ni = i/[(1+i)n - 1] Present value of an annuity: [P/A]ni = [(1+i)n - 1]/i(1+i)n Annuity from a present value: [A/P]ni = i(1+i)n/[(1+i)n - 1] = i + (i/[(1+i)n - 1]) Page 8 EE1 - Finance, Notes

TVM Equivalence Factors: Uniform Gradients: Annuity from a gradient: [A/G] Present value of a gradient: [P/G] A 1 A 2 A 3 A A n g 2g (n-2)g (n-1)g P 1 2 3 n g 2g (n-2)g (n-1)g Page 9 EE1 - Finance, Notes

TVM Equivalence Factors: Uniform Gradients: Future value of a gradient: [F/G] F n 1 2 3 g 2g (n-2)g (n-1)g Page 10 EE1 - Finance, Notes

TVM Equivalence Factors: Uniform Gradients: Annuity from a gradient: [A/G]ni = (1/i) - (n/[(1+i)n - 1]) Present value of a gradient: [P/G]ni = [P/A]ni * [A/G]ni Future value of a gradient: [F/G]ni = [F/A]ni * [A/G]ni Page 11 EE1 - Finance, Notes

TVM Equivalence Factors: Geometric Inflation: Present value of inflation: [P/I] Future value of inflation: [F/I] P 1 2 3 n A(1+r) A(1+r)2 A(1+r)3 A(1+r)n F 1 2 3 n A(1+r) A(1+r)2 A(1+r)3 A(1+r)n Page 12 EE1 - Finance, Notes

TVM Equivalence Factors: Geometric Inflation: Present value of inflation: [P/I]n(i,r) = [P/A]nic Future value of inflation: [F/I]n(i,r) = [P/A]nic * [F/P]ni where: r = inflation rate ic = convenience rate = (i - r)/(i + r) Page 13 EE1 - Finance, Notes

Remember the $10,000 Loan? Cash Flow analysis of case 1: Page 14 EE1 - Finance, Notes

Remember the $10,000 Loan? Cash Flow analysis of case 2: Page 15 EE1 - Finance, Notes

Remember the $10,000 Loan? Cash Flow analysis of case 3: Page 16 EE1 - Finance, Notes

Remember the $10,000 Loan? Cash Flow analysis of Case 4: Page 17 EE1 - Finance, Notes

Page 18 EE1 - Finance, Notes