Question

Grant deposited $9,000 in an investment account. He receives a monthly return of $350 for 3 years. After one year, he makes another investment of $3,000 at the same bank, with monthly returns of $250 for a year and a half. What is Grant’s IRR? (hint: first combine the cash flow streams)

Answer 1

Find the IRR using the rule NPV = 0

NPV = -9000 + 350(P/A, i%, 3*12) - 3000(P/F, i%, 1*12) + 250((P/A, i%, 2.5*12) - (P/A, i%, 1*12))

(P/A, i%, 2.5*12) - (P/A, i%, 1*12) gives the present worth factor for the cash flow under second series where 1st cash flow is received after 12 months from now and will be received for 18 months from 12 months from now or 30 months from now in total.

Now for i = 2%, NPV = 510.91 (computed as -9000+350*25.4888-3000*0.78849+250*(22.3965 - 10.5753))

For i = 3%, NPV = -1051.24

Find IRR = 2% + (3% - 2%)*(510.91/(510.91 + 1051.24)) = 2.3%

Hence IRR is 2.3%.