APPLY THE CONCEPTS: Present value of a single amount in the future As it is impo
ID: 2449035 • Letter: A
Question
APPLY THE CONCEPTS: Present value of a single amount in the future
As it is important to know what a current investment will yield at a point in the future, it is equally important to understand what investment would be required today in order to yield a required future return. The following displays what present investment would be required in order to yield $8,000 three years from now, assuming annual compounding at 5%.
The most straightforward method for calculating the present value of a future amount is to use the Present Value Table. By multiplying the future amount by the appropriate figure from the table, one may adequately determine the present value.
Instructions for using present value tables
+ Present Value of a Future Amount
Using the previous table, enter the correct factor for three periods at 5%:
You may want to own a home one day. If you are 20 years old and plan on buying a $700,000 house when you turn 30, how much will you have to invest today, assuming your investment yields an 8% annual return? If required, round your answers to the nearest cent. $
APPLY THE CONCEPTS: Present value of an ordinary annuity
Many times future sums of money will not come in one payment but in a number of periodic payments. For example, imagine that you want to buy a house and know that you will have periodic mortgage payments and you need to know how much you would have to invest today in order to facilitate all of those payments into the future. This is called an ordinary annuity and it says that a certain value today at a stated interest rate is equal to a certain number of future payouts for a given amount per payment. The following timeline displays how an ordinary annuity pays out when distributed in three equal payments at an annually compounded interest rate of 5%.
The most simple and commonly used method of determining the present value of an ordinary annuity is to multiply the incremental payout by the appropriate rate found on the present value of an ordinary annuity table.
+ Present Value of an Ordinary Annuity
Using the previous table, enter the correct factor for three periods at 5%:
The controller at Ross has determined that the company could save $4,000 per year in engineering costs by purchasing a new machine. The new machine would last 10 years and provide the aforementioned annual monetary benefit throughout its entire life. Assuming the interest rate at which Ross purchases this type of machinery is 10%, what is the maximum amount the company should pay for the machine? $ (Hint: This is basically a present value of an ordinary annuity problem as highlighted above.)
Assume that the actual cost of the machine is $18,000. Weighing the present value of the benefits against the cost of the machine, should Ross purchase this piece of machinery? SelectYesNoNot enough information
Future Value: $8,000 Year 1 Year 2 Year 3 Present Value: ?Explanation / Answer
1. Present Value factor for 3 Years at 5%: 0.8640
Future value = 8,000
Present Value = 8,000 x 0.8640 = $6,912
Present Value factor at 8% for 10 Years = 0.4632
Future Value = $700,000
Present Value = 700,000 x 0.4632 = $324,240
So, the amount that is required to be deposited today is $324,240
Present value of an Ordinay Annuity:
Present value factor for an ordinary annuity at 5% for 3 Years: 2.7233
Present value of an annuity of $5,000 for 3 years = 6,000 x 2.7233 = $16,338
Present value of $4,000 at 10% for 10 Years =
PV Factor for 10 Years at 10% = 6.14457
PV = 4,000 X 6.14457 = $24,579
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.