Question

(Present value) The state lottery's million-dollar payout provides for $3 million(s) to be paid over 24 years in 25 payments of $120,000. The first $120,000 payment is made immediately. and the 24 remaining $120,000 payments occur at the end of each of the next 24 years. If 9 percent is the appropriate discount rate, what is the present value of this stream of cash flows? If 18 percent is the appropriate discount rate, what is the present value of the cash flows?

a. If 9 percent is the appropriate discount rate, what is the present value of this stream of cash flows? (Round to the nearest cent.)

Answer 1

The present value of the cash flows at a 9% discount rate is approximately $1,502,748.97. At an 18% discount rate, the present value is approximately $915,745.98.

Step-by-step explanation:

To calculate the present value of a stream of cash flows, we use the formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n

Where PV is the present value, CF is the cash flow in each period, r is the discount rate, and n is the number of periods.

For the given question:

1. At a 9% discount rate:

• The present value of the immediate $120,000 payment is $120,000 / (1 + 0.09)^0 = $120,000.
• The present value of the remaining 24 payments of $120,000 is $120,000 / (1 + 0.09)^1 + $120,000 / (1 + 0.09)^2 + ... + $120,000 / (1 + 0.09)^24 ≈ $1,502,748.97.
• Therefore, the present value of the cash flows at a 9% discount rate is approximately $1,502,748.97.

At an 18% discount rate:

• Using the same formula, the present value of the cash flows at an 18% discount rate is approximately $915,745.98.