To calculate the present value (PV) of the money machine using a financial calculator, you need to enter the appropriate values for N (number of periods), I/Y (interest rate per year), PMT (payment per period), FV (future value), and PV (present value).
Here’s how you can break it down based on the given information:
- Future Payments: The money machine will pay $4,497.00 annually for 29 years, starting 8 years from today.
- Interest Rate (I/Y): This is given as 11.00%.
- Payment (PMT): This is the annual payment amount, which is $4,497.00.
- Number of Payments (N): Since the first payment starts 8 years from today, you will first need to calculate the present value of the annuity as of year 8, and then discount it back to today.
Step 1: Calculate the PV of the annuity at year 8
- N: 29 (the number of payments to be received)
- I/Y: 11.00% (the interest rate)
- PMT: $4,497.00 (the payment amount)
- FV: $0 (no future value in this scenario)
Now, calculate the present value (PV) of these payments at year 8.
Step 2: Discount this PV back to today
Once you find the PV at year 8, it becomes a lump sum amount that needs to be discounted back to today.
- N: 8 (because you need to discount it back for the 8 years before the first payment)
- I/Y: 11.00% (the same interest rate)
- PV: [The result from Step 1] (present value of the annuity calculated in step 1)
- PMT: $0 (since you are now considering a single sum you will discount)
- FV: [The result from Step 1] (This will compute back to present value)
Summary of Steps:
-
Calculate the PV of the annuity at year 8:
- N = 29
- I/Y = 11%
- PMT = 4,497
- FV = 0
- (Calculate and note this result, let's call it PV1)
-
Discount PV1 back to today:
- N = 8
- I/Y = 11%
- PMT = 0
- FV = PV1
- Calculate PV (this will give you the present value today of the entire cash flow).
Follow these steps with your financial calculator, and you'll find the present value today of the cash flows from the money machine.