FIN 614: Financial Management Larry Schrenk, Instructor

1.The Time Value of Money 2.Future Value (FV) 3.Present Value (PV)

‘Cash Flows’ Consider: $100 Today vs. $100 in 1 Year $100 Today vs. $110 in 1 Year $100 in 1 Year vs. $130 in 4 Years Project Comparison 123 Project A100 Project B0160

Factors Opportunity Cost Inflation Risk

Compounding One-Time Deposit If I invest $ today, how much will I have in… One Year? Ten Years? One Hundred Years?

How much is it worth after one year? Interest rate (r) is 10% $ × (1 + 10%) = $ × 1.1 = $ Reasoning: Multiply by 1  Still have Original Deposit Multiply by 0.10  Interest

How much do I have in two years? $ at t = 1 and r = 10% $ × (1 + 10%) = $ × 1.1 = $ YearCalculationValue 0$ $100.00(1.10) =$ $100.00(1.10)(1.10) =$ $100.00(1.10)(1.10)(1.10) =$ $100.00(1.10)(1.10)(1.10)(1.10) =$146.41

In Year 2 we have $ $100Original Deposit 10Interest on Deposit in Year 1 10Interest on Deposit in Year 2 1Interest on ‘Year 1 Interest’ in Year 2 $121Total ‘Interest on Interest’ Simple Interest: $120 in Year 2

Even better we can construct a formula: In practice, we will use our calculators.

$1 Compounded 100 Years = $131.50

Discounting Inverse of Compounding One-Time Future Cash Flow If I receive $ in… One Year Ten Years One Hundred Years How much is it worth today?

How much is it worth now? Interest rate (r) is 10% $100.00/(1 + 10%) = $100.00/1.1 = $90.91

As in compounding, we can repeat this algorithm for multiple years. YearCalculationValue 0$ $100.00/(1.10) =$ $100.00/[(1.10)(1.10)] =$ $100.00/[(1.10)(1.10)(1.10)] =$ $100.00/[(1.10)(1.10)(1.10)(1.10)] =$68.30

Even better we can construct a formula: In practice, we will use our calculators.

$100 Discounted100 Years = $0.76

FIN 614: Financial Management Larry Schrenk, Instructor