Your company will generate $68,000 in an- nual revenue each year for the next seven years from a new information database. If the appropriate interest rate is 8.5 percent, what is the present value of the savings?
I'm going to use the BAII Plus calculator for my answer. So hopefully it makes sense.
PMT = 68,000
I/Y = 8.5
N = 7
Compute the PV to get = $340,058.92
As a note, the number will come out negative in the calculator. That's fine, it's just considering this as a cashflow out, but you want to write it as positive.
I'm dumb as @#%& and typed the PV in wrong. It's supposed to be:
$348,058.92
Sorry....
To calculate the present value of the savings, we need to use the formula for the present value of an annuity:
PV = PMT x [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
PMT = Annual Revenue
r = Interest Rate
n = Number of Years
In this case, the annual revenue is $68,000, the interest rate is 8.5% (or 0.085 in decimal form), and the number of years is 7.
Substituting the values into the formula:
PV = $68,000 x [1 - (1 + 0.085)^(-7)] / 0.085
Calculating the exponent first:
(1 + 0.085)^(-7) = 0.50843
PV = $68,000 x [1 - 0.50843] / 0.085
Simplifying further:
PV = $68,000 x 0.49157 / 0.085
PV = $396250
Therefore, the present value of the savings is $396,250.
To calculate the present value of the savings, we need to use the present value formula, which is commonly used in finance to determine the value of future cash flows in today's dollars.
The present value formula is:
PV = FV / (1 + r)^n
Where:
PV - Present Value
FV - Future Value
r - Interest Rate
n - Number of Time Periods (in this case, the number of years)
In this case, the future value (FV) is the annual revenue of $68,000 for each of the next seven years. The interest rate (r) is provided as 8.5 percent (or 0.085 as a decimal). The number of time periods (n) is seven.
Now let's plug these numbers into the formula and calculate the present value:
PV = $68,000 / (1 + 0.085)^7
First, simplify the expression inside the parentheses:
(1 + 0.085)^7 = 1.7189247
Now divide the future value by this number:
PV = $68,000 / 1.7189247
Using a calculator or a spreadsheet, we can determine:
PV ≈ $39,615.46
Therefore, the present value of the savings is approximately $39,615.46.