Question

A project has the following total (or net) cash flows.

               ________________________________________

                Year         Total (or net) cash flow

               ________________________________________

1 $50,000
2 70,000
3 80,000
4 100,000
_______________________________________   

The required rate of return on the project is 13 percent. The initial investment (or initial cost or initial outlay) of the project is $100,000.
a) Find the (regular) payback period of the project.
b) Compute the discounted payback period of the project.

Answer 1

a.Payback period= full years until recovery + unrecovered cost at the start of the year/ cash flow during the year

= 1 year + ($100,000 - $50,000)/ $70,000

= 1 year + $50,000/ $70,000

= 1 year+ 0.71

= 0.71 years.

b.Discounted cash flow in year 1= $44,247.79.

Discounted cash flow in year 2= $54,820.27

Discounted cash flow in year 3= $55,443.90.

Cumulative cash flow in 2 years= $99,068.06

Discounted payback period= full years until recovery + unrecovered cost at the start of the year/ discounted cash flow during the year

= 2 years + ($100,000 - $99,068.06)/ $55,443.90

= 2 years + $931.94/ $55,443.90

= 2 years + 0.0168

= 2.02 years.

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