Answer:
The NPV is a negative which means leasing the machine is a better option. (THERE ARE 2 EXPLANATIONS) BUT BOTH ANSWERS ARE CORRECT!!!
Step-by-step explanation:
Explanation ONE :
To find the NPV of purchasing the new machine, we need to calculate the cash flows associated with this option:
Year 0: Initial cash outflow of $45,000
Years 1-5: Annual cash inflows of $4,100
Total cash inflows: $4,100 x 5 = $20,500
To calculate the present value of these cash flows, we need to discount them by the firm's cost of capital. Since the problem does not provide a cost of equity, we will assume that the firm's cost of capital is equal to the before tax cost of debt, which is 10%. Using a financial calculator or spreadsheet, we can calculate the present value of the cash inflows as:
PV = $4,100 x (1 - 1/1.1^5) / 0.1 = $16,228.24
The NPV of purchasing the new machine is:
NPV = PV of cash inflows - initial cash outflow
NPV = $16,228.24 - $45,000
NPV = -$28,771.76
This negative NPV means that purchasing the new machine is not a good investment for Ringo Manufacturing. It would cost the firm more in present value terms than it would save in operating costs.
Now let's calculate the net present value of leasing the machine:
Year 0: Initial cash outflow of $0 (since the first payment is due in 1 year)
Years 1-5: Annual cash outflows of $3,400
Total cash outflows: $3,400 x 5 = $17,000
To calculate the present value of these cash outflows, we again use the firm's cost of capital of 10%. Using a financial calculator or spreadsheet, we can calculate the present value of the cash outflows as:
PV = $3,400 x (1 - 1/1.1^5) / 0.1 = $13,568.24
The NPV of leasing the machine is:
NPV = -initial cash outflow + PV of cash outflows
NPV = -$0 + $13,568.24
NPV = $13,568.24
This positive NPV means that leasing the machine is a better option for Ringo Manufacturing than purchasing it. The firm would save money in present value terms by leasing instead of buying.
Explanation TWO:
To calculate the Net Present Value (NPV) of purchasing the new machine, we need to calculate the present value of all cash inflows and cash outflows associated with the purchase.
First, let's calculate the present value of the savings the machine is expected to generate:
PV of savings = $4,100 / (1 + r) + $4,100 / (1 + r)^2 + $4,100 / (1 + r)^3 + $4,100 / (1 + r)^4 + $4,100 / (1 + r)^5
where r is the discount rate.
Assuming a discount rate of 10%, we can calculate the present value of savings as:
PV of savings = $4,100 / (1 + 0.1) + $4,100 / (1 + 0.1)^2 + $4,100 / (1 + 0.1)^3 + $4,100 / (1 + 0.1)^4 + $4,100 / (1 + 0.1)^5 = $16,145.58
Next, let's calculate the present value of the cost of purchasing the machine:
PV of cost = -$45,000 / (1 + r) + 0 / (1 + r)^2 + 0 / (1 + r)^3 + 0 / (1 + r)^4 + 0 / (1 + r)^5
Since the machine can be depreciated on a straight-line basis to a zero salvage value over its life, the salvage value is zero. Therefore, we have zero salvage value at the end of the fifth year.
The present value of the cost of purchasing the machine can be calculated as:
PV of cost = -$45,000 / (1 + 0.1) + 0 / (1 + 0.1)^2 + 0 / (1 + 0.1)^3 + 0 / (1 + 0.1)^4 + 0 / (1 + 0.1)^5 = -$30,689.66
Lastly, we need to calculate the tax shield associated with depreciation. Since the machine is being depreciated on a straight-line basis, the annual depreciation expense is:
Annual depreciation expense = $45,000 / 5 = $9,000
The tax shield associated with depreciation can be calculated as:
Tax shield = Annual depreciation expense x Tax rate = $9,000 x 0.20 = $1,800
To calculate the present value of the tax shield, we need to determine the tax shield in each year, and discount it to the present value using the same discount rate.
Year 1 tax shield = $1,800 / (1 + 0.1) = $1,636.36
Year 2 tax shield = $1,800 / (1 + 0.1)^2 = $1,487.07
Year 3 tax shield = $1,800 / (1 + 0.1)^3 = $1,351.88
Year 4 tax shield = $1,800 / (1 + 0.1)^4 = $1,229.89
Year 5 tax shield = $1,800 / (1 + 0.1)^5 = $1,120.81
Total present value of tax shield = $1,636.36 + $1,487.07 + $1,351.88 + $1,229.89 + $1,120.81 = $7,826.01
Therefore, the net present value (NPV) of purchasing the new machine can be calculated as:
NPV = PV of savings + PV of tax shield + PV of cost = $16,145.58 + $7,826.01 - $30,689.66 = -$6,718.07
Since the NPV is negative, purchasing the new machine would not be a profitable investment. The company should consider leasing the machine instead.