Answer:
The correct option is A. $3,833
Explanation:
Note: This question is not complete has the options are omitted. The complete question is therefore provided before answering the question as follows:
Mcclam, Inc., is considering the purchase of a machine that would cost $100,000 and would last for 9 years. At the end of 9 years, the machine would have a salvage value of $23,000. The machine would reduce labor and other costs by $19,000 per year. Additional working capital of $2,000 would be needed immediately. All of this working capital would be recovered at the end of the life of the machine. The company requires a minimum pretax return of 13% on all investment projects. The net present value of the proposed project is closest to:
A. $3,833
B. $5,167
C. -$2,492
D. $11,514
The explanation of the answer is now given as follows:
Given:
Machine cost = $100,000
Additional working capital = $2,000
Salvage value = $23,000
A = Annual cost saving = $19,000
r = minimum pretax return = 13%, or 0.13
n = number of useful years of the machine = 9
The net present value of the proposed project is now calculated using the following steps:
Step 1: Calculation of the total cost
TC = Total cost = Machine cost + Additional working capital = $100,000 + $2,000 = $102,000
Step 2: Calculation of the present value of the annual cost saving
The present value of the annual cost saving can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PVACS = A * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PVACS = Present value of annual cost saving = ?
A = Annual cost saving = $19,000
r = Minimum pretax return = 13%, or 0.13
n = number of useful years of the machine = 9
Substituting the values into equation (1), we have:
PVACS = $19,000 * ((1 - (1 / (1 + 0.13))^9) / 0.13)
PVACS = $19,000 * 5.13165512782676
PVACS = $97,501.45
Step 3: Calculation of the present value of the salvage value and the recovered working capital
This can be calculated using the present value formula as follows:
PVSW = SW / (1 + r)^n ……………………….. (2)
Where;
PVSW = present value of the salvage value and the recovered working capital = ?
SW = salvage value and the recovered working capital = $23,000 + $2,000 = $25,000
r = Minimum pretax return = 13%, or 0.13
n = number of useful years of the machine = 9
Substituting the values into equation (2), we have:
PVSW = $25,000 / (1 + 0.13)^9
PVSW = $25,000 / 3.00404193798427
PVSW = $8,322.12
Step 4: Calculation of the net present value of the proposed project
This can be calculated as follows:
NPV = PVACS + PVSV - TC ……………………………. (3)
Where;
NPV = net present value of the proposed project = ?
PVACS = Present value of annual cost saving = $97,501.45
PVSW = present value of the salvage value and the recovered working capital = $8,322.12
TC = Total cost = Machine cost + Additional working capital = $100,000 + $2,000 = $102,000
Substituting the values into equation (3), we have:
NPV = $97,501.45 + $8,322.12 - $102,000
NPV = $3,824
From the options in the question, the calculated NPV of $3,823.57 is close to option A. $3,833. Therefore, the net present value of the proposed project is closest to $3,833.
