Ch5 - Dr. Yi Ch 5: Advanced Topics on Time Value of Money...

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Ch 5: Advanced Topics on Time Value of Money Dr. Yi
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Outlines of Ch 4 and 5: Time Value of Money (TVM) Time is money ??? Piazza’s $91 million contract Time value of money = opportunity cost Solve TVM problems Basics Simple present / future value problem Simple vs. Compound Interest (Power of Compound) Compounding Frequency Annuity / Annuity Due / Perpetuity Uneven cash flow Amortization Table Effective annual rate
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Multiple CFs: Annuities and Perpetuities Defined Annuity – finite series of equal payments that occur at regular intervals Two conditions Equal cash flows spaced evenly apart Ordinary annuity: “at the end of each period” Annuity due: “at the beginning of each period” Perpetuity – infinite series of equal payments
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Perpetuity Definition infinite series of equal payments Perpetuity formula PV = C / i Example Valuing a share of stock with no definite maturity like preferred stock
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Does PV = C / i work fine? For example, you could invest $100 in a bank account paying 5% interest per year forever. Suppose you withdraw $5 (=$100*5%) per year and leave $100 intact. This means that you receive $5 perpetuity. That is, PV = $100, C = $5, i = 5%. PV * i = 100 * 5% = $5 = C PV = C / i
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Example 1 : Endowing a Perpetuity You want to endow an annual MBA graduation party at your name recognition. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first payment is in one year from now, how much will you need to donate to endow the party?
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Example 2: Money Machine Your buddy in mechanical engineering has invented a money machine. The main drawback of the machine is that it is slow. It takes one year to manufacture $100. However, once built, the machine will last forever and will require no maintenance. The machine can be built immediately, but it will cost $1000 to build. Your buddy wants to know if he should invest the money to construct it. If the interest rate is 9.5% per year, what should your buddy do? Hint: Find the PV of $100 perpetuity starting at year 1 at 9.5% and compare it to $1000.
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Growing Perpetuities Assume you expect the amount of your perpetual payment to increase at a constant rate, . (growing perpetuity) C PV i g = -
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Example 3: Endowing a Growing Perpetuity In the earlier example, you planned to donate $30,000 per year to fund an annual graduation party. Given an interest rate of 8% per year, the required donation was the present value of $375,000. Before accepting the money, however, the MBA student association asked that you increase the donation to account for the effect of inflation on the cost of the party in future years. Although $30,000 is adequate for next year’s party, the students
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This note was uploaded on 02/28/2012 for the course FIN 3313 taught by Professor Yi during the Spring '12 term at Texas State.

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Ch5 - Dr. Yi Ch 5: Advanced Topics on Time Value of Money...

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