Answer:
14.2 years
Do not invest
yes
Explanation:
Discounted payback calculates the amount of time it takes to recover the amount invested in a project from it cumulative discounted cash flows
Cash flow each year = $12,000 - $2,000 = $10,000
Discounted cash flow in year 1 = 10,000 / 1.05 = 9.523.81
Discounted cash flow in year 2 = 10,000 / 1.05^2 = 9,070.29
Discounted cash flow in year 3 = 10,000 / 1.05^3 = 8,638.38
Discounted cash flow in year 4 = 10,000 / 1.05^4 = 8,227.02
Discounted cash flow in year 5 = 10,000 / 1.05^5 = 7,835.26
Discounted cash flow in year 6 = 10,000 / 1.05^6 = 7,462.15
Discounted cash flow in year 7 = 10,000 / 1.05^7 = 7,106.81
Discounted cash flow in year 8 = 10,000 / 1.05^8 = 6,768.39
Discounted cash flow in year 9 = 10,000 / 1.05^9 = 6,446.09
Discounted cash flow in year 10 = 10,000 / 1.05^10 = 6,139.13
Discounted cash flow in year 11 = 10,000 / 1.05^11 = 5846.79
Discounted cash flow in year 12 = 10,000 / 1.05^12 = 5568.37
Discounted cash flow in year 13 = 10,000 / 1.05^13 = 5303.21
Discounted cash flow in year 14 = 10,000 / 1.05^14 =5050.68
Discounted cash flow in year 15 = 10,000 / 1.05^15 = 4810.17
Discounted payback period = [-100,000 + ( discounted cash flows from year 1 to 14) ] + 1013.62/4810.17 = 14.2 years
The cash flows would turn positive between year 14 and 15
If the DPBP is 3 years, the project should not be accepted because the payback period is 14.2 years which is greater than 3 years
Bailey buy the gang punch based on DPBP because the amount invested is recouped with the useful life of the machine
