BH Holding Inc. is considering undertaking a capital project, costing $8 million today. in addition, the project will be installed over the next 2 years, costing $1.0 million at the end of the first year and $0.5 million at the end of the second year. thereafter, the project is expected to generate $1.5 million per annum from year 3 to year 12. at the end of year 12 from today, the project is expected to have the resale value of $3 million. assume that the project's cost of capital is 8% per annum. calculate the NPV of the project.
To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows using the project's cost of capital.
Step 1: Calculate the present value of the cash inflows during year 3 to 12:
We have 10 years of cash inflows, generating $1.5 million per year. Using the formula for the present value of an annuity:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
C = Cash inflow per year
r = discount rate (cost of capital)
n = number of years
PV = $1.5 million * (1 - (1 + 0.08)^(-10)) / 0.08
PV = $1.5 million * (1 - 0.4665) / 0.08
PV = $1.5 million * 0.5335 / 0.08
PV = $9 million / 0.08
PV = $112.5 million
Step 2: Calculate the present value of the resale value at the end of year 12:
To calculate the present value of the $3 million resale value at the end of year 12, we use the formula for the present value of a single future cash flow:
PV = FV / (1 + r)^n
Where:
FV = Future Value
PV = Present Value
r = discount rate (cost of capital)
n = number of years
PV = $3 million / (1 + 0.08)^12
PV = $3 million / (1.08)^12
PV = $3 million / 1.9797
PV = $1.514 million
Step 3: Calculate the present value of the initial investment and cash inflows during year 1 and year 2:
We have the initial investment of $8 million today and cash outflows of $1.0 million at the end of year 1, and $0.5 million at the end of year 2. We need to discount these cash flows to their present value.
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = discount rate (cost of capital)
n = number of years
PV of initial investment = $8 million / (1 + 0.08)^0
PV of initial investment = $8 million
PV of cash outflow at the end of year 1 = -$1.0 million / (1 + 0.08)^1
PV of cash outflow at the end of year 1 = -$1.0 million / 1.08
PV of cash outflow at the end of year 1 = -$0.925 million (negative since it's a cash outflow)
PV of cash outflow at the end of year 2 = -$0.5 million / (1 + 0.08)^2
PV of cash outflow at the end of year 2 = -$0.5 million / 1.1664
PV of cash outflow at the end of year 2 = -$0.429 million (negative since it's a cash outflow)
Step 4: Calculate the NPV by summing up all the present values:
NPV = PV of initial investment + PV of cash outflows + PV of cash inflows + PV of resale value
NPV = $8 million + (-$0.925 million) + (-$0.429 million) + $112.5 million + $1.514 million
NPV = $8 million - $0.925 million - $0.429 million + $112.5 million + $1.514 million
NPV = $8 million + $112.5 million + $1.514 million - $0.925 million - $0.429 million
NPV = $120.66 million
Therefore, the NPV of the project is $120.66 million.
To calculate the Net Present Value (NPV) of the project, we need to discount all the cash flows to their present value and then subtract the initial investment.
Step 1: Calculate the present value of the cash inflows:
The cash inflows consist of the annual cash flows from year 3 to year 12 ($1.5 million per year) and the resale value at the end of year 12 ($3 million).
Using the formula for calculating the present value of a future cash flow:
PV = CF / (1 + r)^n
CF = Cash flow
r = Discount rate (cost of capital)
n = Number of periods
PV of cash inflows = [(Cash flow in year 3 to year 12) + Resale value in year 12] / (1 + r)^n
PV of cash inflows = [(1.5 million * 10) + 3 million] / (1 + 0.08)^12
PV of cash inflows = [15 million + 3 million] / (1.08)^12
PV of cash inflows = 18 million / 1.996709
PV of cash inflows ≈ 9.015 million
Step 2: Calculate the present value of the cash outflows:
The cash outflows consist of the initial investment ($8 million), the cost at the end of the first year ($1 million), and the cost at the end of the second year ($0.5 million).
PV of cash outflows = [Initial investment + Cost at end of the first year + Cost at end of the second year] / (1 + r)^n
PV of cash outflows = (8 million + 1 million + 0.5 million) / (1 + 0.08)^2
PV of cash outflows = 9.5 million / (1.08)^2
PV of cash outflows = 9.5 million / 1.1664
PV of cash outflows ≈ 8.148 million
Step 3: Calculate the NPV:
NPV = PV of cash inflows - PV of cash outflows
NPV = 9.015 million - 8.148 million
NPV ≈ 0.867 million
Therefore, the NPV of the project is approximately $0.867 million.