Answer:
The net present value of the proposed project is close to $19,544.65.
Explanation:
The net present value of the proposed project can be calculated as follows:
Step 1: Calculation of the proposed project's present value of saving of labor and other costs
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PVC = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PVC = Present value of the proposed project of saving of labor and other costs = ?
P = Proposed project's saving of labor and other costs = $96,000
r = required pretax return = 19%, or 0.19
n = number of years of the project = 8
Substitute the values into equation (1), we have:
PVC = $96,000 * ((1 - (1 / (1 + 0.19))^8) / 0.19)
PVC = $379,619.10
Step 2: Calculation of the proposed project's present value of working capital investment recovered at the end of the life of the machine
This can be calculated using the formula for calculating the present value as follows:
PVW = W / (1 + r)^n .......................... (2)
PVW = Present value of proposed project's working capital investment recovered at the end of the life of the machine = ?
W = Proposed project's working capital investment recovered at the end of the life of the machine = $4,000
r = required pretax return = 19%, or 0.19
n = number of years of the project = 8
Substitute the values into equation (2), we have:
PVW = $4,000 / (1 + 0.19)^8
PVW = $994.68
Step 3: Calculation of present value of the machine salvage value
This can be calculated using the formula for calculating the present value as follows:
PVS = W / (1 + r)^n .......................... (3)
PVS = present value of the machine salvage value = ?
W = machine salvage value = $52,000
r = required pretax return = 19%, or 0.19
n = number of years of the project = 8
Substitute the values into equation (3), we have:
PVS = $52,000 / (1 + 0.19)^8
PVS = $12,930.87
Step 4: Calculation of the net present value of the proposed project
Net present value = PVC - Cost of machine - Initial working capital investment + PVW + PVS
Net present value = $379,619.10 - $370,000 - $4,000 + $994.68 + $12,930.87
Net present value = $19,544.65
