Question

A project has an initial outlay of $1,000. The project will generate cash flows of $400 in Years 1-3 and cash flows of $200 in Years 4-6. What is the IRR of this project?

Answer 1

Year Cashflow DF@10% PV DF@25% PV

$ $ $

0 (1,000) 1 (1,000) 1 (1,000)

1-3 400 2.4869 995 1.952 781

4-6 200 1.8684 374 0.9994 200

NPV 369 NPV (19)

IRR = LR + NPV1/NPV1+NPV2 x (HR – LR)

IRR = 10 + 369/369 + 19 x (25 – 10)

IRR = 10 + 369/388 x 15

IRR =24.27%

Step-by-step explanation:

In this case, we need to obtain the positive NPV at 10%. The cashflow for year 1 to 3 is discounted at the present value of annuity factor for 3 years at 10% while the cashflow for year 4 to 6 is discounted at the present value of annuity factor for 6 years minus the present value of annuity factor for year 1 to 3. Then, we will determine the present value by multiplying the cashflows by the discount factors. We will obtain the net present value at 10% and 25% respectively. A higher discount rate of 25% is used in order to determine the negative NPV.

Finally, we will apply the interpolation formula stated above in order to determine the IRR.

Answer 2

IRR=24.33%

Step-by-step explanation:

The IRR for the project shall be calculated as follows:

Cash flow Year Present value@5% Present value@25%

(1000) 0 (1,000) (1,000)

400 1-3 1,089.23 780.80

200 4-6 470.49 199.88

$559.72 ($19.32)

IRR=A%+(a/a-b)*(B%-A%)

A%=5%,B%=25%,a=559.72 b=(19.32)

IRR=5%+(559.72/559.72+19.32)*(25%-5%)

IRR=24.33%