Question

Redesign Inc. is considering a project that has the following cash flow data. (a) What is the project's payback period? (b) What is the project's discounted payback period? Assume the cost of capital is 12%. Year 0 1 2 3 Cash flows -$500 $200 $200 $200

Answer 1

Cumulative cash flow for year 0 = -500

Cumulative cash flow for year 1 = -500 + 200 = -300

Cumulative cash flow for year 2 = -300 + 200 = -100

Cumualtive cash flow for year 3 = -100 + 200 = 100

100 / 200 = 0.5

Payback period = 2 + 0.5 = 2.5 years

When cash inflows are same, you can also find the payback period by simply dividing the cash flow amount from the initial investment, i.e, 500 / 200 = 2.5 years.

Present value of year 1 cash flow = 200 / ( 1 + 0.12)¹ = 178.57

Present value of year 2 cash flow = 200 / ( 1 + 0.12)² = 159.49

Present value of year 3 cash flow = 200 / ( 1 + 0.12)³ = 142.36

Cumulative cash flow for year 0 = -500

Cumulative cash flow for year 1 = -500 + 178.57 = -321.43

Cumulative cash flow for year 2 = -321.43 + 159.49 = -161.94

Cumulative cash flow for year 3 = -161.94 + 142.36 = -19.5

Since the project is unable to recover the initial investment of 500, discounted payback is 0.