(Inflation) A project’s initial investment is $40,000, and it has a five-year life. At the end of the fifth year, the equipment is expected to be sold for $12,000, at which time its net book value will be $5,000. The CFATs (including inflation, depreciation, and net salvage value) for the next five years are expected to be $20,000, $25,000, $10,000, $10,000, and $10,000. In real terms, the project’s cost of capital is 10%, and the riskless return is 7%. The tax rate is 46%, and the inflation rate is 3%. What is the project’s NPV?
To calculate the project's net present value (NPV), we need to discount the cash flows to their present value and then subtract the initial investment cost.
Step 1: Calculate the inflation-adjusted cash flows:
To adjust for inflation, we need to find the real cash flows by dividing the expected cash flows by (1 + inflation rate). In this case, the inflation rate is 3%.
Year 1: $20,000 / (1 + 0.03) = $19,417.48
Year 2: $25,000 / (1 + 0.03)² = $23,722.47
Year 3: $10,000 / (1 + 0.03)³ = $9,174.31
Year 4: $10,000 / (1 + 0.03)⁴ = $8,899.68
Year 5: $10,000 / (1 + 0.03)⁵ = $8,640.40
Step 2: Calculate the tax-adjusted cash flows:
To calculate the after-tax cash flows, we need to multiply the cash flows by (1 - tax rate). In this case, the tax rate is 46%.
Year 1: $19,417.48 * (1 - 0.46) = $10,483.33
Year 2: $23,722.47 * (1 - 0.46) = $12,808.72
Year 3: $9,174.31 * (1 - 0.46) = $4,956.47
Year 4: $8,899.68 * (1 - 0.46) = $4,799.80
Year 5: $8,640.40 * (1 - 0.46) = $4,674.42
Step 3: Calculate the present value of cash flows:
To calculate the present value of each cash flow, we need to discount it using the project's cost of capital. In this case, the cost of capital is 10%.
Year 1: $10,483.33 / (1 + 0.1) = $9,530.30
Year 2: $12,808.72 / (1 + 0.1)² = $10,786.83
Year 3: $4,956.47 / (1 + 0.1)³ = $3,690.18
Year 4: $4,799.80 / (1 + 0.1)⁴ = $3,295.55
Year 5: $4,674.42 / (1 + 0.1)⁵ = $2,964.78
Step 4: Calculate the present value of the salvage value:
To calculate the present value of the salvage value, we need to discount it using the riskless return rate. In this case, the riskless return rate is 7%.
Salvage Value: $12,000 / (1 + 0.07)⁵ = $9,997.29
Step 5: Calculate the project's NPV:
To calculate the NPV, we sum up the present value of the cash flows and subtract the initial investment cost. In this case, the initial investment cost is $40,000.
NPV = -$40,000 + $9,530.30 + $10,786.83 + $3,690.18 + $3,295.55 + $2,964.78 + $9,997.29
NPV = -$40,000 + $30,264.63
NPV = $264.63
Therefore, the project's NPV is $264.63.
To calculate the project's NPV (Net Present Value), we need to find the present value of each cash flow, which includes the initial investment, CFATs (including inflation), and the net salvage value. Then we subtract the initial investment from the sum of the present values.
Step 1: Calculate the inflation-adjusted CFATs:
To calculate the CFATs considering inflation, we need to adjust the cash flows using the inflation rate of 3%.
Inflation-adjusted CFATs:
Year 1: $20,000 / (1 + 0.03) = $19,417.48
Year 2: $25,000 / (1 + 0.03)^2 = $24,271.84
Year 3: $10,000 / (1 + 0.03)^3 = $9,708.74
Year 4: $10,000 / (1 + 0.03)^4 = $9,417.48
Year 5: $10,000 / (1 + 0.03)^5 = $9,139.17
Step 2: Calculate the present value of each cash flow:
We need to find the present value of each cash flow using the real cost of capital of 10%. The formula to calculate the present value of a cash flow is:
PV = CF / (1 + r)^n
Where PV is the Present Value, CF is the cash flow, r is the discount rate, and n is the number of years.
Present Value of Initial Investment:
PV of $40,000 = $40,000 / (1 + 0.10)^0 = $40,000
Present Value of Inflation-Adjusted CFATs:
PV of Year 1 = $19,417.48 / (1 + 0.10)^1 = $17,652.25
PV of Year 2 = $24,271.84 / (1 + 0.10)^2 = $20,059.14
PV of Year 3 = $9,708.74 / (1 + 0.10)^3 = $7,487.70
PV of Year 4 = $9,417.48 / (1 + 0.10)^4 = $6,594.13
PV of Year 5 = $9,139.17 / (1 + 0.10)^5 = $6,070.82
Present Value of Salvage Value:
PV of $12,000 = $12,000 / (1 + 0.10)^5 = $6,191.74
Step 3: Calculate the NPV:
The NPV is the sum of the present values of all cash flows minus the initial investment.
NPV = PV of Initial Investment + PV of CFATs + PV of Salvage Value
NPV = $40,000 + $17,652.25 + $20,059.14 + $7,487.70 + $6,594.13 + $6,070.82 - $12,000
NPV = $86,864.04 - $12,000
NPV = $74,864.04
Therefore, the project's NPV is $74,864.04.