Question

An investment is expected to produce the following annual year-end cash flows: year 1: $5,000 year 4: $5,000 year 2: $1,000 year 5: $6,000 year 3: $0 year 6: $863.65 The investment will cost $13,000 today. I got that IRR is 10%

Prove your answer for IRR by showing how much of each year’s cash flow is recovery of the $13,000 investment and how much of the cash flow is return on investment. (Hint: See Exhibit 3–13 and Concept Box 3.2.)

Answer 1

For the given series of Cash Flows, IRR = 10%

So this means every year we get 10% return on the investment compounded yearly.

So, at the end of 1st year we should get $13000*10% = $1300

But we get $5000

So $1300 is return on investment and remaining $5000-$1300 = $3700 is the recovery of investment.

So remaining Investment Balance = $13000-$3700 = $9300

At the end of 2nd year we should get $9300*10% = $930

But we get $1000

So $930 is return on investment and remaining $1000-$930 = $70 is the recovery of investment.

So remaining Investment Balance = $9300-$70 = $9230

At the end of 3rd year we should get $9230*10% = $923

But we get only 0

So 0 is return on investment and remaining $923 is the added to investment.

So remaining Investment Balance = $9230+$923 = $10153

At the end of 4th year we should get $10153*10% = $1015.3

But we get $5000

So $1015.3 is return on investment and remaining $5000-$1015.3 = $3984.7 is the recovery of investment.

So remaining Investment Balance = $10153-$3984.7 =  $6168.3

At the end of 5th year we should get $6168.3*10% = $616.83

But we get $6000

So $616.83 is return on investment and remaining $6000-$616.38 = $5383.17 is the recovery of investment.

So remaining Investment Balance = $6168.3-$5383.17 = $785.13

At the end of 6th year we should get $785.13*10% = $78.51

But we get $863.65

So $78.51 is return on investment and remaining $863.65-$78.51 = $785.14 is the recovery of investment.

So remaining Investment Balance = $785.13-$785.14 = $0

Hence at the end of 6 years the return on investment is 10% annually compounded and the initial investment is also completely recovered.