Bailey, Inc., is considering buying a new gang punch that would allow them to produce circuit boards more efficiently. The punch has a first cost of $100,000 and a useful life of 15 years. At the end of its useful life, the punch has no salvage value. Labor costs would increase $2,000 per year using the gang punch, but raw material costs would decrease $12,000 per year. MARR is 5 %/year. A. What is the discounted payback period for this investment? Image for Bailey, Inc., is considering buying a new gang punch that would allow them to produce circuit boards more effi years
B. If the maximum attractive DPBP is 3 years, what is the decision rule for judging the worth of this investment?
C. Should Bailey buy the gang punch based on DPBP?

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