the time value of money module 24. opening why is a dollar today, worth more than a dollar a year...
TRANSCRIPT
The Time Value of Money
Module 24
Opening
• Why is a dollar today, worth more than a dollar a year from now?
• Would you lend a friend $100 now for a repayment of $115 in 4 years?
The Time Value of Money1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Money in the present is worth more than money in the future
The interest rate represents a payment to help compensate the lender, who would otherwise be repaid in dollars worth less than those borrowed.
Why We Charge Interest1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Opportunity Costs– If we decide to loan a friend money, we
face the opportunity costs of what we could use that money for
– So, interest is what compensates us for the delayed gratification
The Time Value of Money1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Purchasing Power– We know that due to inflation, the
purchasing power of the dollar will most likely decrease.
– Charging interest allows us to maintain that purchasing power
Present and Future Value1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Present value– The value of a future sum in today’s
dollars– How much is $1 received a year from
now worth today?
Future Value– The value in the future of money
invested today– How much is $1 invested today going to
be worth in a year?
Present and Future Value1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Present valueThe present value of $1 received t years from now is:
$1/(1+r)t
t= yearsr=
interest rate
Future ValueThe future value of $1 invested today in t years is:
$1 × (1+r)t
Present and Future Value1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Example– If our friend offered to give us $115 in four
years for $100 today, how do we know it’s worth it?
– Depends on the prevailing interest rate:
• At 4% interest rate, the present value of $115 in four years is
$115/(1+.04)4 = $98.30
• At 2% interest rate, the present value of $115 in four years is
$115/(1+.02)4 = $106.48
Present and Future Value1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Example– You could also compare the future value
to the $115:
• At 4% interest rate, the future value of $100 invested in four years is
$100 × (1+.04)4 = $116.99
• At 2% interest rate, the present value of $115 in four years is
$100 × (1+.02)4 = $108.24
Choosing Between Options1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present& Future Value - Explanation - Calculation
3) Choosing Between Options
If you are given a choice of several options where up front costs and future payoffs might vary, you choose the one that maximizes net present value
Choosing Between Options1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
A hotel manager needs to replace all of the light bulbs and has heard about these new compact fluorescents. Each CFL costs $15 and each regular incandescent bulb costs $1. The hotel has 1000 fixtures.
The energy bill will be $800 if you use the CFL’s and $4800 if you use the incandescent. They will both last 4 years.
Which is the better choice?
Choosing Between Options1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
• It seems like the CFLs are the best bet, but what else could we do with that $14,000?
Choosing Between Options1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
• As interest rates get higher, the present value of the savings realized from switching to CFL’s decreases
Choosing Between Options1) Why we charge interest - Opportunity Costs - Purchasing Power
2) Present & Future Value - Explanation - Calculation
3) Choosing Between Options
Suppose that a person only lives 2 years and has 2 choices. She can go to school in next year, or go straight into the work force. If a person immediately starts working, she will earn $20,000 in both years 1 and 2. If a person goes to school in year 1, she must pay $5,000, but she would earn $47,500 in year 2. If the interest rate is 5%, calculate the present value of a person who goes to school and a person who does not.
• School:PV = -5,000/(1.05) + 47,500/(1.05)2 = $38,322.00
• Workforce:PV = 20,000/(1.05) + 20,000/(1.05)2 = $37,188.21