Questions: If the interest rate is 10 percent and cash flows are 1,000 at the end of year one and 2,000 at the end of year two, then the present value of these cash flows is Multiple Choice 2,562. 3,200. 439. 3,000.

Solution Steps

To find the present value of future cash flows, we need to discount each cash flow back to the present value using the given interest rate. The formula for the present value of a future cash flow is \( PV = \frac{CF}{(1 + r)^n} \), where \( CF \) is the cash flow, \( r \) is the interest rate, and \( n \) is the year. We will calculate the present value for each cash flow and sum them up to get the total present value.

We are given cash flows of \$1,000 at the end of year one and \$2,000 at the end of year two. The interest rate is 10%, or \( r = 0.10 \).

To find the present value of each cash flow, we use the formula: \[ PV = \frac{CF}{(1 + r)^n} \]

• For the cash flow at the end of year one (\$1,000): \[ PV_1 = \frac{1000}{(1 + 0.10)^1} = \frac{1000}{1.10} \approx 909.0909 \]

• For the cash flow at the end of year two (\$2,000): \[ PV_2 = \frac{2000}{(1 + 0.10)^2} = \frac{2000}{1.21} \approx 1652.8926 \]

Add the present values of the cash flows to get the total present value: \[ PV_{\text{total}} = PV_1 + PV_2 = 909.0909 + 1652.8926 \approx 2561.9835 \]

Final Answer