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COMM 121 (16)
Chapter 5

Chapter 5

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Department
Commerce
Course
COMM 121
Professor
Blair Robertson
Semester
Fall

Description
Chapter 5: The Time Value of Money The One Period Case  Future Value = Principle amount x (1 + interest rate)  Present Value is the value of a future cash stream discounted at an appropriate market interest rate o o This method tells us what a future amount of money is valued at today  The decision to buy this year and sell next year can be evaluated as the net present value o NPV = PV of future cash flows – PV of the cost of the investment The Multi-Period Case Future Value and Compounding  Compounding is the process of leaving money in the capital market and lending it for another year  Simple Interest is interest that only considers the principle amount o i.e. 10% on 100 for ten years only means $1 per year (no interest on past interest)  Compound Interest is when an interest payment is reinvested once it’s been received o o The return something after 2x years is the return after x years, squared (i.). Present Value and Discounting  The process of calculating the present value of a future cash flow is called discounting o The formula is the same as the one above  The portion is known as the present value factor  it is the factor used to calculate an estimate of PV of an amount to be received in a future period  The PV of a set of cash flows is equal to the sum of the PVs of the individual cash flows Finding the Number of Periods  What if you need $Xs at some interest rate and to want to know how long it will take to double it  same formula as PV except now you are solving for T Compounding Periods  Important to note that compounding can happen more than one time per year o Semi-annually, quarterly, monthly, etc  Each time the interest is compounded, it is referred to as one period  monthly = 12 p’s  Remember that interest rates are given annually (stated annual interest rate) so when finding PV or FV you have to divide that rate by the number of periods in one year o The exponent also changes reflecting the number of periods that have passed m  Effective annual interest rate = (1+r/m) -1  annual rate of return Compounding Over Many Periods  Future Value with Compounding = Initial investment(1+r/m) mT o R is the stated annual interest rate Continuous Compounding  Involves compounding for every instant in time  i.e. continuously o FV = Initial Investment x e rT o R i
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