Question

An investment project provides cash inflows of $735 per year for eight years.

  

What is the project payback period if the initial cost is $1,950? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Payback period

years

  

What is the project payback period if the initial cost is $3,800? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Payback period

years

  

What is the project payback period if the initial cost is $5,900? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

    

Payback period

years

Answer 1

Payback period is the number of years it takes to re-earn the initial cash investment.

Per year cash inflow = $735 for 8 years

Question 1:

Cash investment = $1,950

In year 1, cash flow = $735

In year 2, cash flow = $735. Cumulative cash flow = $735 * 2 = $1470. Amount required to complete payback = $1950 - $1470 = $480

Fraction of year 3 = $480/$735 = 0.65 year

Hence, payback = 2 + 0.65 years = 2.65 years

Question 2:

Cash investment = $3,800

In year 1, cash flow = $735

In year 2, cash flow = $735. Cumulative cash flow = $735 * 2 = $1470.

In year 3, cash flow = $735. Cumulative cash flow = $735 * 3 = $2205.

In year 4, cash flow = $735. Cumulative cash flow = $735 * 4 = $2940.

In year 5, cash flow = $735. Cumulative cash flow = $735 * 5 = $3675.

Amount required to complete payback = $3800 - $3675 = $125

Fraction of year 6 = $125/$735 = 0.17 year

Hence, payback = 5 + 0.17 years = 5.17 years

Question 3:

Cash investment = $5,900

In year 1, cash flow = $735

In year 2, cash flow = $735. Cumulative cash flow = $735 * 2 = $1470.

In year 3, cash flow = $735. Cumulative cash flow = $735 * 3 = $2205.

In year 4, cash flow = $735. Cumulative cash flow = $735 * 4 = $2940.

In year 5, cash flow = $735. Cumulative cash flow = $735 * 5 = $3675.

In year 6, cash flow = $735. Cumulative cash flow = $735 * 6 = $4410.

In year 7, cash flow = $735. Cumulative cash flow = $735 * 7 = $5145.

In year 8, cash flow = $735. Cumulative cash flow = $735 * 8 = $5880.

Given the cumulative cash flow never exceeds the initial investment, so payback would never complete.

Hence, payback = 0