FIN3109 Lecture Notes - Lecture 1: Arc Elasticity, Weighted Arithmetic Mean, Demand Curve
FIN3109 – Module One
- Present Value (PV) is the value today of a single future cash flow or series of cash flows
- Future Value (FV) is the amount to which a single cash flow or series of cash flows will grow
over a period of time when compounded at a given interest rate
- Compound interest is interest on interest
- Single interest is no interest on interest
- E.g. Suppose is $1000 deposited toady at 5% for 2 years
oFV with Simple Interest = $1000 + $50 + $50 = $1100 ($50 in the interest per year)
oFV with Compound Interest = $1000(1.05)2=$1102.50
oThe extra $2.50 comes from the extra interest earned on the first $50 interest
payment (5% x $50 = $2.50)
- Compound interest
oInterest rate per year = i
oInterest rate per period = r
oNumber of years = t
oNumber of periods = n
oNumber of compounding periods per year = m
oThere for: and
- FV and PV: Single Payment Example
oSupposed you invest $1000 for one year at 5% per year. Assume annual
compounding, i.e. m = 1. What is the future value in one year?
o
o
oWe could also express the relationship to show present value: Hence: 1000 =
- FV and PV: Double Payment Example
oSuppose you leave the money in for another year. How much will you have two
years from now?
o
o
oOr we can express the PV as: 1000 =
oHence, in general, its best to think in terms of periods and periodic rates rather than
years and annual rates
- Solving for the Periodic Rate of Interest
o
o
- Example of Periodic Rate of Interest
oSuppose you make an investment of $1000 that pays annual interest and promises
to double your money in 8 years. What is the annual interest rate?
- Solving for Present Value
oSuppose you have a choice between received a cash payment of (i) $50,000 today or
(ii) $60,000 in three years. If you could earn 7% on your investments, which would
you choose?
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PV of (i) = $50,000
PV of (ii) =
- Future Value and Present Value: Multiple Payments
oWhat is the future value of the following cash flow stream at the end of year 3?
Cash Flow 0: FV = 7,000(1.08)3 = 8,817.98
Cash Flow 1: FV = 4,000(1.08)2 = 4,665.60
Cash Flow 2: FV = 4,000(1.08) = 4,320
Cash Flow 3: FV = 4,000
Total value in 3 years = 8,817.98 + 4,665.60 + 4,320 + 4,000 = $21,803.58
- Future Value and Present Value: Multiple Payments
oWhat is the present value of the
following cash flow stream?
o
Cash Flow 1: FV = 200/(1.12) = 178.57
Cash Flow 2: FV = 400/(1.12)2 = 318.88
Cash Flow 3: FV = 600/(1.12)3 = 427.07
Cash Flow 4: FV = 800/(1.12)4 = 508.41
Total value = 178.57 + 318.88 + 427.07 + 508.41 = $1,432.93
- Effective Annual Interest Rate
o
o
oThis allows you to compare loans with different compounding differences
- Simple Versus Compound Interest
oSuppose you can earn 1% per month on $100 invested today. How much are you
effectively earning?
o
o
0 1 2 3
4,0004,0004,0007,000
8%
?
?
?
?
FV =
1 2
200
12%
3 4
600400 800
?
?
?
?
?
0
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Document Summary
Present value (pv) is the value today of a single future cash flow or series of cash flows. Future value (fv) is the amount to which a single cash flow or series of cash flows will grow over a period of time when compounded at a given interest rate. Compound interest: interest rate per year = i, interest rate per period = r, number of years = t, number of periods = n, number of compounding periods per year = m, there for: and. Fv and pv: single payment example: supposed you invest for one year at 5% per year. What is the future value in one year? o o: we could also express the relationship to show present value: hence: 1000 = Fv and pv: double payment example: suppose you leave the money in for another year. Solving for the periodic rate of interest o o.
