A 30 year project is estimated to cost $35 million and provide annual cash ﬂows of $5 million per year in years 1-5; $4 million per year in years 6-20 and $2 million per year in years 21-30. If the
Company's required rate of return is 10%, determine the payback of the project.
A) 6.50 years
B) 7.00 years
C) 7.50 years
D) 8.00 years
E) 8.50 years

Question

Quizplus · Accepted Answer

To calculate the payback of the project, we need to find the time taken to recover the initial investment of $35 million.

In years 1-5, the total cash inflow is $5 million x 5 = $25 million. 
In years 6-20, the total cash inflow is $4 million x 15 = $60 million. 
In years 21-30, the total cash inflow is $2 million x 10 = $20 million.

So the total cash inflow over the entire 30-year period is $25 million + $60 million + $20 million = $105 million.

To calculate the payback period, we need to find the year in which the cumulative cash inflow equals the initial investment of $35 million.

Year 1: Cumulative cash inflow = $5 million 
Year 2: Cumulative cash inflow = $10 million 
Year 3: Cumulative cash inflow = $15 million 
Year 4: Cumulative cash inflow = $20 million 
Year 5: Cumulative cash inflow = $25 million 
Year 6: Cumulative cash inflow = $29 million 
Year 7: Cumulative cash inflow = $33 million 
Year 8: Cumulative cash inflow = $37 million 
Year 9: Cumulative cash inflow = $41 million 
Year 10: Cumulative cash inflow = $45 million 
Year 11: Cumulative cash inflow = $49 million 
Year 12: Cumulative cash inflow = $53 million 
Year 13: Cumulative cash inflow = $57 million 
Year 14: Cumulative cash inflow = $61 million 
Year 15: Cumulative cash inflow = $65 million 
Year 16: Cumulative cash inflow = $69 million 
Year 17: Cumulative cash inflow = $73 million 
Year 18: Cumulative cash inflow = $77 million 
Year 19: Cumulative cash inflow = $81 million 
Year 20: Cumulative cash inflow = $85 million 
Year 21: Cumulative cash inflow = $87 million 
Year 22: Cumulative cash inflow = $89 million 
Year 23: Cumulative cash inflow = $91 million 
Year 24: Cumulative cash inflow = $93 million 
Year 25: Cumulative cash inflow = $95 million 
Year 26: Cumulative cash inflow = $97 million 
Year 27: Cumulative cash inflow = $99 million 
Year 28: Cumulative cash inflow = $101 million 
Year 29: Cumulative cash inflow = $103 million 
Year 30: Cumulative cash inflow = $105 million

So the payback period is in the range of 7-8 years. Since the cumulative cash inflow exceeds the initial investment between years 7 and 8, the payback period can be estimated to be 7.5 years. Therefore, the best choice is C.

A 30 Year Project Is Estimated to Cost $35 Million