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| Line 16: |
Line 16: |
| accumulating interest on an investment | | accumulating interest on an investment |
| over time to earn more interest. | | over time to earn more interest. |
|
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|
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| Calculating Future Value
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| • Future Value of $1:
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| FV =
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| • Future Value Factor: (1 + r)t
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| Future Value: Example #1
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| • You deposit $500 into a savings account.
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| You plan on withdrawing the money and
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| closing the account exactly two years from
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| today. Interest rates are 10%, compounded
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| annually, and will remain constant over the
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| two years.
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| Future Value: Example #1
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| • How much money will you have when you
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| close the account (Future Value)?
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| • How much simple interest did you
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| accumulate?
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| • How much compound interest did you
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| accumulate?
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|
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| The Effects of Compounding
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| • The effects/benefits of compounding:
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| – Increase with time.
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| – Increase with the frequency of compounding.
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| (more on the details of this later.)
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| Future Value: Example #2
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| • You are scheduled to receive $17,000 in
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| two years. When you receive it, you will
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| invest it for six more years at 6 percent per
| |
| year. How much will you have in eight
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| years?
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| Future Value: Example #3
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| • You are trying to save to buy a new
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| $60,000 Jaguar. You have $22,000 today
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| that can be invested at your bank. The
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| bank pays 4 percent annual interest on its
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| accounts. How long will it be before you
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| have enough to buy the car?
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| The Time Value of Money
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|
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| Future Value: Example #4
| |
| • Assume you are only willing to wait 15
| |
| years in the previous example. What rate
| |
| of return would you need to earn?
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| Some Present Value Definitions
| |
| • Present Value (PV): The current value of future
| |
| cash flows discounted at the appropriate discount
| |
| rate.
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| • Discount: Calculate the present value of some
| |
| future amount.
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| • Discount Rate: The rate used to calculate the
| |
| present value of future cash flows.
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| Calculating Present Value
| |
| • Present Value of $1 (i.e., $1 is the FV):
| |
| PV = =
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| • Present Value Factor:
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| 1
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| ----------------------------------------
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| (1 + r)t
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|
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| Present Value: Example #1
| |
| • You have five of the six Florida Lottery
| |
| numbers. Lottery officials offer you the
| |
| choice of the following alternative payouts:
| |
| – Alternative 1: $100,000 one year from now.
| |
| – Alternative 2: $200,000 five years from now.
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| Present Value: Still Example #1
| |
| • Which alternative would you choose if
| |
| interest rates are 12%?
| |
| • What rate makes the two alternatives
| |
| equally attractive?
| |
| Present Value: Example #2
| |
| • You have just received notification that
| |
| you have won the $1 million first prize in
| |
| the Centennial Lottery. However, the prize
| |
| will be awarded on your 100th birthday
| |
| (assuming you are around to collect), 80
| |
| years from now. What is the present value
| |
| of your windfall if the appropriate discount
| |
| rate is 15%?
| |
|
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| Present Value: Example #3
| |
| • Suppose you are still committed to owning
| |
| a $60,000 Jaguar. If you believe your
| |
| mutual fund can achieve a 9 percent annual
| |
| rate of return and you want to buy the car
| |
| in 10 years, how much must you invest
| |
| today?
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| Tips on Solving Present Value
| |
| and Future Value Problems
| |
| • Present value factor (PVF) is the reciprocal
| |
| of the future value factor (FVF).
| |
| • FVt = CF0 × (1 + r)t
| |
| • PV = CFt / (1 + r)t
| |
| • For multiple cash flows, just add up the
| |
| individual present (or future) values.
| |
| Tips on Solving Present Value
| |
| and Future Value Problems
| |
| • As t ↑, PV ↓ and FV ↑
| |
| • As r ↑, PV ↓ and FV ↑
| |
| • There are (currently) only 4 components:
| |
| PV, FV, t, and r
| |
| –With ANY 3 components, you can solve
| |
| for the 4th
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| The Time Value of Money
| |
| FINC 3610 -- Yost 7
| |
| Suggested Problems
| |
| • Critical Thinking and Concepts Review
| |
| – 1, 2, 3, 4, and 5
| |
| • Questions and Problems:
| |
| – 1, 6, 9, 13, 14, 15, 16, 18, 20, 22, 23, and 25
| |
| Additional Practice
| |
| $50,000 9 $25,000
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| $245,498 15% $15,000
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| $18,395 9% 13
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| 5% 7 $40,000
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| Future
| |
| Value
| |
| Interest
| |
| Rate Years Present
| |
| Value
| |
| Additional Practice
| |
| • You are offered an investment that requires
| |
| you to put up $13,000 today in exchange
| |
| for $40,000 twelve years from now. What
| |
| is the average annual rate of return on this
| |
| investment?
| |
| • Would you accept it if the appropriate
| |
| discount rate was 8%?
| |
|
| |
| Additional Practice
| |
| • You have the opportunity to make an
| |
| investment that costs $900,000. If you
| |
| make this investment now, you will receive
| |
| $120,000 one year from today, $250,000
| |
| and $800,000 two and three years from
| |
| today, respectively. The appropriate
| |
| discount rate for this investment is 12%.
| |
| Additional Practice (continued)
| |
| • Should you make the investment? What is
| |
| the net present value?
| |
| • If the discount rate is 10%, should you
| |
| invest?
| |
| Calculator Tips
| |
| • Make sure you set the number of payments
| |
| per year to 1.
| |
| • Clear when necessary.
| |
| • Either PV or FV must be negative.
| |
| • Enter the interest rate as a whole number.
| |
The Time Value of Money
Some Future Value Definitions
• Future Value (FV): The amount an
investment is worth after one or more
periods.
• Simple Interest: Interest earned only on
the original principal amount invested.
More Future Value Definitions
• Compound Interest: Interest earned on
both the initial principal and the interest
reinvested from prior periods.
• Compounding: The process of
accumulating interest on an investment
over time to earn more interest.
