IRR and NPV calculation The cash flows for three independent

(IRR and NPV calculation) The cash flows for three independent projects are found below:

a. Calculate the IRR for each of the projects.
b. If the discount rate for all three projects is 9%, which project or projects would you
want to undertake?
c. What is the net present value of each of the projects where the appropriate discount
rate is 9%

Solution

a. IRR is the rate which make the NPV equal to 0 i.e. present value of inflows - present value of of outflows is 0.

Let the IRR be x%. So, PV of any inflow = amount of inflow/(1+IRR)^time

So, for project A, sum of all inflows = 12,000/(1+x)+18,000/(1+x)^2+21000/(1+x)^3+28000/(1+x)^4+29000/(1+x)^5

So x should make the above sum equal to the outflow amount of 45,000.

Project wise IRR calculation for all projects (using the same logic as shown for project A)in excel using trial and error method:

This was achieved in excel using a rate of 32.099%

Project B

This was achieved in excel using a rate of 7.57%

Project C:

IRR = 36.31%

b. If discount rate is 9%, then project A and C should be undertaken as their IRR is more than the discount rate.

c. NPV of Project A using a rate of 9% (using the formula 12,000/(1+x)+18,000/(1+x)^2+21000/(1+x)^3+28000/(1+x)^4+29000/(1+x)^5 - 45,000: where x = 9%

PV of inflows = $81,0519.18. PV of outflows = 45,000. NPV = PV of inflows - PV of outflows = $36,059.18

NPV of project B (using the same formula as for project A, but using project B\'s cash flows)

PV of inflows = 101130.9 PV of outflow = 105000. NPV = - ($3,869.07)

NPV of project C (using the same formula as for project A, but using project C\'s cash flows)

PV of inflows = 607510.7 PV of outflow = 400000. NPV = $207,510.7