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

2024
Views:

205

Pages:

2
Author:

stud_ice13

The present value (PV) of a single amount is the value today of a sum to be received or paid in the future, discounted at a specified interest rate. The PV concept helps us compare current and future cash flows by adjusting for the effect of interest over time, often referred to as the “discount rate.” This concept is used widely in financial decision-making, especially for investments and loans. Key Concepts 1. Present Value Formula: The PV of a single future amount can be calculated with the formula: PV=FV(1+i)nPV = where: o o o o PV = present value (amount today) FV = future value (amount in the future) i = interest rate per period (discount rate) n = number of periods until the future amount is received This formula shows how the value today (PV) of a future amount (FV) decreases as the interest rate or the time period increases, due to the concept of interest or discounting. 2. Interest Table for Present Value: Present value tables simplify PV calculations by providing PV factors for a variety of interest rates and time periods. These tables assume a future value of 1, which is then adjusted for different future values by multiplication. For example, with an interest rate (i) of 8% over 6 periods (n), a PV factor of 0.6302 is used to find the PV of any future amount. 3. Illustrative Cases Using the PV Table: o Case 1: Finding PV given FV, i, and n. For instance, a future amount of $220 one period from now with an interest rate of 10% has a PV of $200 (since $220 × 0.9091 = $200). o Case 2: Finding n given PV, FV, and i. For example, if $13,000 today is to grow to $100,000 at a 12% rate, we can determine that it will take approximately 18 periods (years). o Case 3: Finding i given PV, FV, and n. For instance, if $60,000 today needs to grow to $120,000 in 9 years, an interest rate of about 8% is required. Example Calculation: For a company evaluating an investment that will yield $70,000 after six years, and aiming for an 8% return, the present value can be calculated as: PV=70,000×0.6302=44,114 This means the company would be willing to invest $44,114 today for a future return of $70,000 after six years at an 8% discount rate. Summary The PV concept enables effective financial planning and comparison of current versus future financial obligations or assets, adjusting for interest over different time periods and ensuring that decisions consider the time value of money.