Question

Managers of a firm are planning to invest $180,000.00 in a new four-year long project to implement automation in the packaging department. Considering associated risk of the project, the managers are requiring 11% return from this investment. This project is expected to generate future cash flow of $65,000.00 in each year. Find

1. Net present Value
2. Internal Rate of Return
3. Present Value Index
4. Payback period
5. Discounted Payback Period

please show the steps Clear without using financial calculator.

Thanks

Answer 1

Initial Investment =180000
Number of years =4
Rate =11%
a. NPV =PV of cash flows -Initial Investment =65000*((1-(1+11%)^-4)/11%)-180000=21658.97

b. IRR is the rate at which NPV is 0
0 =65000/(1+IRR)+65000/(1+IRR)^2+65000/(1+IRR)^3+65000/(1+IRR)^4-180000
By using hit and trial method we get IRR =16.52%

c.Present Value Index =1+NPV/Investment =1+21658.97/180000 =1.12

d. . Payback period formula = Years before recovery + Cost not covered in that year/ Cash flow for that year
=2+(180000-65000-65000)/65000 =2.77 years

e. Discounted Cash flow in year 1 =65000/(1+11%) =58558.5586
Discounted Cash flow in year 2 =65000/(1+11%)^2=52755.4582
Discounted Cash flow in year 3 =65000/(1+11%)^3=47527.4398
Discounted Cash flow in year 4 =65000/(1+11%)^4=42817.5133
Discounted Payback period formula = Years before recovery + Cost not covered in that year/ Cash flow for that year
=3+(180000-58558.5586-52755.4582-47527.4398)/42817.5133 =3.49 years