University:
Grand Rapids Community College
Course:
Financial and Managerial Accounting: Information for Decisions - John J. Wild
Academic year:

2024
Views:

92

Pages:

2
Author:

stud_ice13

The present value (PV) of an annuity calculates the current worth of a series of equal payments made at regular intervals, such as loan payments, investments, or rental income. An ordinary annuity is specifically a series of equal payments made at the end of each period (e.g., end of each year). This calculation helps assess how much a future cash flow is worth today, factoring in a specific discount rate or interest rate. Key Concepts 1. PV of an Ordinary Annuity Formula: To compute the PV of an annuity, we find the PV of each individual payment and sum these values. The formula is: PV=PMT×(1−(1+i)−ni)PV = PMT where: o o o PMT = amount of each annuity payment i = interest rate per period n = total number of payments This formula provides the PV of a series of payments, adjusting for the effect of interest over time. 2. Using Present Value of Annuity Tables: A present value of an annuity table (e.g., Table B.3) simplifies these calculations by providing a single annuity factor for various combinations of n (number of periods) and i (interest rate per period). By multiplying this annuity factor by the payment amount (PMT), we obtain the PV of the annuity. For example, if an annuity involves three $100 payments at the end of each period with an interest rate of 15%, we locate n = 3 and i = 15% in the table to find a PV factor of 2.2832. Then, the PV of the annuity is: PV=100×2.2832=228.32PV = 100 3. Example Calculation: Suppose a company considers an investment with semiannual payments of $10,000 over three years, with the first payment received in six months. The company requires an 8% annual return, equating to a 4% semiannual rate. Given six total payments (n = 6) and i = 4%, the PV annuity factor is 5.2421. The PV of this annuity is: PV=10,000×5.2421=52,421PV = 10,000 This is the maximum amount the company is willing to invest today to achieve its required return. Summary The PV of an annuity is a practical tool for valuing consistent future cash flows in today’s terms. Annuity tables or formulas allow quick calculation by providing a PV factor based on interest rate and payment period. This concept applies broadly, from investment evaluations to financial planning decisions.