(ignore income taxes in this problem)the following data pertain to an investment proposal:
cost of the investment $30,000
Annual cost saving 9,000
estimated salvage value 4,000
life of the project 5 years
discount rate 12%
Which is the net present value of the proposed investment closest to?
a. 4,713
b. 19.000
c. 2,445
d. 2.268
To find the net present value (NPV) of the proposed investment, you need to calculate the present value of all cash flows associated with the investment and then subtract the initial cost of the investment. Let's calculate the NPV step by step:
1. Calculate the present value of annual cash savings:
PV of annual cash savings = Annual Cash Savings / (1 + Discount Rate)^Year
For each year, calculate the present value of the annual cost savings:
Year 1: PV of annual cost savings = $9,000 / (1 + 0.12)^1 = $8,035.71
Year 2: PV of annual cost savings = $9,000 / (1 + 0.12)^2 = $7,174.11
Year 3: PV of annual cost savings = $9,000 / (1 + 0.12)^3 = $6,408.88
Year 4: PV of annual cost savings = $9,000 / (1 + 0.12)^4 = $5,727.40
Year 5: PV of annual cost savings = $9,000 / (1 + 0.12)^5 = $5,119.61
2. Calculate the present value of the salvage value at the end of the project:
PV of salvage value = Salvage Value / (1 + Discount Rate)^Year
PV of salvage value = $4,000 / (1 + 0.12)^5 = $2,267.97
3. Calculate the net present value:
NPV = PV of annual cash savings + PV of salvage value - Initial cost of the investment
NPV = $8,035.71 + $7,174.11 + $6,408.88 + $5,727.40 + $5,119.61 + $2,267.97 - $30,000
NPV = $34,734.68 - $30,000 = $4,734.68
Therefore, the net present value of the proposed investment is closest to option a. $4,713.