Question

an investment costs $163,000 today and promises a series of $52,000 annual cash inflows in each of the next 4 years. the first cash inflow occurs one year from today. what is the net present value of this investment if the discount rate is 9%? round your answer to the nearest dollar. be sure to enter a negative sign (-) if your answer is a negative number.

Answer 1

The net present value (NPV) of the investment is $4,172.75.

To calculate the net present value (NPV) of the investment, we need to discount each cash inflow to its present value and then subtract the initial cost of the investment.

Using a discount rate of 9%, we can calculate the present value of each $52,000 cash inflow using the formula PV = CF/(1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

Here are the calculations for each year:

• Year 1: PV = $52,000/(1 + 0.09)^1 = $47,706.42
• Year 2: PV = $52,000/(1 + 0.09)^2 = $43,742.12
• Year 3: PV = $52,000/(1 + 0.09)^3 = $40,065.49
• Year 4: PV = $52,000/(1 + 0.09)^4 = $36,657.72

To calculate the NPV, we sum up all the present values and subtract the initial cost of the investment:

NPV = -$163,000 + $47,706.42 + $43,742.12 + $40,065.49 + $36,657.72 = $4,172.75

Since the NPV is positive, the investment is expected to generate a positive return at a 9% discount rate.