EE 1 PEEE Refresher Class Finance Notes notes

EE 1 PEEE Refresher Class Finance Notes notes by T. Ernst EE 1 - 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. EE 1 - Finance, Notes Page 2

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%. EE 1 - Finance, Notes Page 3

TVM Equivalence Factors: Single Payment: • Future value of a present value: [F/P] F n P • Present value of a future value: [P/F] P n F EE 1 - Finance, Notes Page 4

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 period EE 1 - Finance, Notes Page 5

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

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

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]) EE 1 - Finance, Notes Page 8

TVM Equivalence Factors: Uniform Gradients: • Annuity from a gradient: [A/G] A A A 1 2 0 3 g n 2 g (n-2)g (n-1)g • Present value of a gradient: [P/G] P 1 0 2 3 g 2 g n (n-2)g EE 1 - Finance, Notes (n-1)g Page 9

TVM Equivalence Factors: Uniform Gradients: • Future value of a gradient: [F/G] F 1 0 2 3 g 2 g n (n-2)g EE 1 - Finance, Notes (n-1)g Page 10

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 EE 1 - Finance, Notes Page 11

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

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) EE 1 - Finance, Notes Page 13

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

Remember the $10, 000 Loan? Cash Flow analysis of case 2: EE 1 - Finance, Notes Page 15

Remember the $10, 000 Loan? Cash Flow analysis of case 3: EE 1 - Finance, Notes Page 16

Remember the $10, 000 Loan? Cash Flow analysis of Case 4: EE 1 - Finance, Notes Page 17

EE 1 - Finance, Notes Page 18