Johnson Ltd a manufacturer of office equipment is considering purchasing a new machine for $2,000,000. The company is expecting an annual cash inflow of $1,220,000 from the sale of the products and an annual cash outflow of $350,000 for each of the six years of the machine's useful life. The annual cash outflow do not include annual depreciation charges for the machine. The machine is depreciated using the straight line method. The machine is expected to last for six years, with a residual value estimated to be $500,000 at the end of the sixth year. The cost of capital for Johnson Ltd is 10%. Calculate the necessary investment appraisal techniques
To calculate the necessary investment appraisal techniques for Johnson Ltd, we can use three commonly used methods: Net Present Value (NPV), Payback Period, and Internal Rate of Return (IRR). Let's calculate each of them step by step:
1. Net Present Value (NPV):
NPV is the difference between the present value of cash inflows and the present value of cash outflows. The formula for NPV is:
NPV = Present Value of Cash Inflows - Present Value of Cash Outflows
To calculate NPV, we need to discount the cash inflows and outflows to their present values. Since the cost of capital for Johnson Ltd is given as 10%, we will use a discount rate of 10% for all cash flows.
Cash inflows: $1,220,000 per year for 6 years
Discounted cash inflows: $1,220,000 / (1+0.1)^1 + $1,220,000 / (1+0.1)^2 + ... + $1,220,000 / (1+0.1)^6
Cash outflows: $350,000 per year for 6 years
Discounted cash outflows: $350,000 / (1+0.1)^1 + $350,000 / (1+0.1)^2 + ... + $350,000 / (1+0.1)^6
Residual value at the end of the sixth year: $500,000
Discounted residual value: $500,000 / (1+0.1)^6
NPV = Discounted cash inflows - Discounted cash outflows - Discounted residual value
2. Payback Period:
The payback period is the time required to recover the initial investment. We need to sum the cash inflows until they equal or exceed the initial investment of $2,000,000.
Payback Period = Number of years it takes to recover the initial investment
3. Internal Rate of Return (IRR):
IRR is the discount rate that makes the present value of cash inflows equal to the present value of cash outflows.
To calculate IRR, we can use the NPV formula and set it equal to zero:
0 = Present Value of Cash Inflows - Present Value of Cash Outflows
We can then solve for the discount rate that makes the NPV zero.
Now, let's calculate each of the investment appraisal techniques for Johnson Ltd using the provided information.