Annuities I - Ordinary Annuity | Lecture Note - Edubirdie

University:
California State University, Northridge
Course:
ACCT 220 | Introduction to Financial Accounting
Academic year:

2024
Views:

278

Pages:

1
Author:

ekrasitrj5

Basic present value analysis is used to determine the present value of a single sum to be received (paid) some time in the future - for example, a note receivable. However, sometimes you expect to receive (or pay) a series of payments - interest on a bond or payments on a car loan, for example In that case we must deal with the following: • • • regular payments made or received at regular intervals at least once a year, but may be semi-annually (bond interest) or monthly (car payment) For example: • What is the present value of three payments of $100 each. The payments will be received at the end of each of the next three years. We want to earn 10% interest on our investment. Option 1 we could express and solve the question above as follows: receive PV Factor answer: $100.00 (10%,1) 0.9091 $90.91 $100.00 (10%,2) 0.8264 $82.64 $100.00 (10%,3) 0.7513 $75.13 $248.68 While this is certainly doable, it becomes very tiresome (imagine a 50 year bond with semiannual interest payments - you would have to the calculation 100 times! Instead, we can use Algebra (uuhh, there it is again!) - we factor out the constant ($100) $100 * (.9091 + . 8264 + .7513) = X Option 2: Restated question: $ 100 * 2.4868 = X = $248.68 Present value of an annuity: (PVa) (.9091 + . 8264 + .7513) = 2.4868 = Pva(10%, 3) While this is much nicer, it is still too boring. Instead just use the present value table for an ordinary annuity (D38 in Nikolai) 2.486852 for PVa (10%, 3). Or, use the appropriate function in a spreadsheet program or calculator (But not on the exam!): Option 3: $100 * PVa(3,10%) = $100*2.486852 = $248.69

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