INTERNAL RATE OF RETURN AND NET PRESENT VALUE

The formula for calculation NPV is
NPV=∑_(k=1)^n▒〖 ck/((1+r)^k )〗 -I
Where ck is cash flows
              R is discount rate
              K is the number of years
              I is the initial investment
Question
Consider the two projects A and B whose cash flows are shown in the table below:
Project A Project B
        Initial investment
        10 000 15 000
Year Cash inflows
1 3 000 4 200
2 3 000 4 200
3 3 000 4 200
4 3 000 4 200
5 3 000 4200

Determine the internal rate of return (IRRs) for the two projects and the net present values (NPVs) at a discount rate of 5% per annum. Show that the IRR and NPV figures yield different recommendations. (Hint use a financial calculator to calculate IRR). (6 MARKS)

Solution
Tip: The first part is to read and understand the question then highlight important terms.
NPV
NPV=∑_(k=1)^n▒〖 ck/((1+r)^k )〗 –I
NPV_A = (3 000)/((1+0.05)) + (3 000)/((1+0.05)^2 ) + (3 000)/((1+0.05)^3 ) + (3 000)/((1+0.05)^4 ) + (3 000)/((1+0.05)^5 ) – 10 000
           =2 988.43
NPV_B=(4 200)/((1+0.05)) + (4 200)/((1+0.05)^2 ) + (4 200)/((1+0.05)^3 ) + (4 200)/((1+0.05)^4 ) + (4 200)/((1+0.05)^5 )  -15 000
          = 3 183.80
IRR
I〖RR〗_A=15.2%
I〖RR〗_B=12.4%
This is how you enter IRR in your financial calculator:
Reset your calculator and memory first.
〖IRR〗_A= Key operation 3 000(x,y) 5(data)
         =display –data set:cf 1:00
         =press (on) then (2nd) (cash) (2nd) (CA) (Comp)
         =  answer 15.24= 15.2%
Recommendations: the net present values shows that project B will be a good investment whereas the internal rate of return shows that project A is good. Therefore the two financial indicators yield different recommendations.