1. EE1 PEEE Refresher Class Finance Notes notes by T. Ernst
EE1 - Finance, Notes
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2. 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.
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EE1 - Finance, Notes

3. 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%.
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EE1 - Finance, Notes

4. 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
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EE1 - Finance, Notes

5. 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
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EE1 - Finance, Notes

6. 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
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EE1 - Finance, Notes

7. 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
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EE1 - Finance, Notes

8. 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])
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EE1 - Finance, Notes

9. 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
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EE1 - Finance, Notes

10. 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
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EE1 - Finance, Notes

11. 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
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EE1 - Finance, Notes

12. 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
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EE1 - Finance, Notes

13. 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)
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EE1 - Finance, Notes

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

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

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

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

18. Page 18
EE1 - Finance, Notes