Question

Determine the discounted payback period of a new manufacturing process that costs $15,000,000 with an annual savings of $3,800,000 going up by 3% per year at a MARR of 10%

Please show all work and steps. Any help will be appreciated and thank you for your time!

Answer 1

P = F/(1+i)^t

Present value of annual savings of yr 1 = 3800000 / (1+0.1) = 3454545.45

Cumulative cash flow after including presnt value of yr 1 = -15000000 + 3454545.45 = -11545454.55

Present value of annual savings of yr 2 = 3800000 * (1+0.03) / (1+0.1)^2

= 3800000 * (1.03) / (1.1)^2

= 3234710.74

Cumulative cash flow after including presnt value of yr 2 =-11545454.55 + 3234710.74 = -8310743.81

Present value of annual savings of yr 3 = 3800000 * (1+0.03)^2 / (1+0.1)^3

= 3800000 * (1.03)^2 / (1.1)^3

= 3028865.515

Cumulative cash flow after including presnt value of yr 3 =-8310743.81 + 3028865.515 = -5281878.295

Present value of annual savings of yr 4 = 3800000 * (1+0.03)^3 / (1+0.1)^4

= 3800000 * (1.03)^3 / (1.1)^4

= 2836119.527

Cumulative cash flow after including presnt value of yr 4 =-5281878.295 + 2836119.527 = - 2445758.768

Present value of annual savings of yr 5 = 3800000 * (1+0.03)^4 / (1+0.1)^5

= 3800000 * (1.03)^4 / (1.1)^5

= 2655639.194

Cumulative cash flow after including presnt value of yr 5 = - 2445758.768 + 2655639.194 = 209880.43

Discounted payback period = 4 + (2445758.768 / 2655639.194)

= 4 + 0.92 = 4.92 yrs