The manager of Malan Pty Ltd wants to buy a new machine to replace the one currently being used. The new machine will cost $100 000 with no disposal value at the end of a five-year useful life. The manager estimates that the machine will reduce annual operating costs by $30 000. Depreciation will be $20 000 per year for five years. The tax rate for each year is expected to be 20 per cent and the company has an after-tax hurdle rate of 12 per cent. What is the after-tax payback period of the machine?

Question

Quizplus · Accepted Answer

To find the after-tax payback period, we need to calculate the net cash inflows and outflows for each year and add them up until the initial investment is fully recovered.

Year 1: 
Net cash flow = Operating cost savings - Depreciation - Taxes 
Net cash flow = $30,000 - $20,000 - ($30,000 - $20,000) x 20% 
Net cash flow = $8,000

Year 2: 
Net cash flow = Operating cost savings - Depreciation - Taxes 
Net cash flow = $30,000 - $20,000 - ($30,000 - $20,000) x 20% 
Net cash flow = $8,000

Year 3: 
Net cash flow = Operating cost savings - Depreciation - Taxes 
Net cash flow = $30,000 - $20,000 - ($30,000 - $20,000) x 20% 
Net cash flow = $8,000

Year 4: 
Net cash flow = Operating cost savings - Depreciation - Taxes 
Net cash flow = $30,000 - $20,000 - ($30,000 - $20,000) x 20% 
Net cash flow = $8,000

Year 5: 
Net cash flow = Operating cost savings - Depreciation - Taxes 
Net cash flow = $30,000 - $20,000 - ($30,000 - $20,000) x 20% 
Net cash flow = $8,000

To calculate the payback period, we add up the net cash flows until we reach the initial investment:

Year 1: $8,000 
Year 2: $16,000 
Year 3: $24,000 
Year 4: $32,000 
Year 5: $40,000

The initial investment of $100,000 will be recovered at the end of year 3, since the cumulative net cash flows will be $96,000. However, we need to take into account the taxes paid in year 3, which reduce the net cash flow by another $2,000. Therefore, the after-tax payback period is:

Year 1: $8,000 
Year 2: $16,000 
Year 3: $22,000 
Payback period: 3 + ($2,000 ÷ $8,000) 
Payback period: 3.25 years

Since the after-tax payback period of the machine is 3.25 years, the best choice is B.

The Manager of Malan Pty Ltd Wants to Buy a New