Question

Managers at Even Flow Instruments Inc. are considering three projects that will each cost $4,000. Project A will return $2,000 each year for 3 years, Project B will return $1,000 each year for 5 years, and Project C will return $5,000 in 1 year. If available capital is $8,000 and the cost of capital is 10%, which projects should be selected using the NPV maximization method?

Answer 1

To choose the project on the basis of capital constraint, we will calcuate profitability index for each project. Project having Highest PI satisfy NPV maximization rule. So project shall be selected on the basis of highest ranking to lowest. Project below PI of 1 will not be selected and rejected.

Project A,

Cash outlfow = $4000

it is also in terms of Present value, So present value of cash outflow = $4000

Discount rate (r)= 10%

Number of years (n)= 3

Year 1 to 3 have uniform cash inflows of $2000. So Present Value of Annuity formula will be used

Present value of Cash inflows = Annual amount * (1-(1/(1+r)^n) / r

=2000*(1-(1/(1+10%)^3))/10%

=4973.703982

Profitability index = Present value of cash inflow/Present value of cash outflow

=4973.703982/4000

=1.243425996

Project B

Cash outlfow = $4000

it is also in terms of Present value, So present value of cash outflow = $4000

Discount rate (r)= 10%

Number of years (n)= 5

Year 1 to 5 have uniform cash inflows of $1000. So Present Value of Annuity formula will be used

Present value of Cash inflows = Annual amount * (1-(1/(1+r)^n) / r

=1000*(1-(1/(1+10%)^5))/10%

=3790.786769

Profitability index = Present value of cash inflow/Present value of cash outflow

=3790.786769/4000

=0.9476966923

Project C

Cash outlfow = $4000

it is also in terms of Present value, So present value of cash outflow = $4000

Discount rate (r)= 10%

Number of years (n)= 1

Year 1 have single cash inflows of $5000. So Present Value of future formula will be used

Present value of future value = Future value/(1+i)^n

=5000/(1+10%)^1

=4545.454545

Profitability index = Present value of cash inflow/Present value of cash outflow

=4545.454545/4000

=1.136363636

Profitability Index of A is highest, so A will be selected

Then PI of C is highest. So C will be selected.

B will be rejected as PI is less than 1

So $8000 will be allocated to project A and C