Question

determine the net present value for a project that costs $117,000 and would yield after-tax cash flows of $18,000 the first year, $20,000 the second year, $23,000 the third year, $25,000 the fourth year, $29,000 the fifth year, and $35,000 the sixth year. your firm's cost of capital is 10.00%.

Answer 1

The net present value (NPV) of the project is -$7,350.51.

Step-by-step explanation:

To determine the net present value (NPV) of the project, we need to discount the after-tax cash flows to their present values using the firm's cost of capital. Using a discount rate of 10.00%, we can calculate the present value of each cash flow and then sum them up to get the NPV.

The present values for each cash flow are:

• Year 1: $18,000 / (1 + 0.10)^1 = $16,363.64
• Year 2: $20,000 / (1 + 0.10)^2 = $16,528.93
• Year 3: $23,000 / (1 + 0.10)^3 = $18,318.18
• Year 4: $25,000 / (1 + 0.10)^4 = $18,140.50
• Year 5: $29,000 / (1 + 0.10)^5 = $19,289.26
• Year 6: $35,000 / (1 + 0.10)^6 = $21,008.98

Now, we sum up the present values:

Total PV = $16,363.64 + $16,528.93 + $18,318.18 + $18,140.50 + $19,289.26 + $21,008.98 = $109,649.49

The net present value (NPV) is calculated by subtracting the initial investment from the total present value:

NPV = Total PV - Initial Investment

NPV = $109,649.49 - $117,000 = -$7,350.51