Cirice Corp is considering opening a branch in another state

Cirice Corp. is considering opening a branch in another state. The operating cash flow will be $147,600 a year. The project will require new equipment costing $547,000 that would be depreciated on a straight-line basis to zero over the 6-year life of the project. The equipment will have a market value of $147,000 at the end of the project. The project requires an initial investment of $33,500 in net working capital, which will be recovered at the end of the project. The tax rate is 40 percent. What is the project\'s IRR?

14.53%

18.17%

18.13%

16.80%

15.97%

Solution

Cost of equipment = $547,000

Useful life of equipment = 6 years

Scrap value of equipment = $147,000

Annual depreciation = (Cost price - Scrap value)/Useful life

= (547,000 - 147,000)/6

= 400,000/6  

= $66,667

Increase in working capital = $33,500

Initial cash outflow = Cost of the equipment + Increase in working capital

= 547,000 + 33,500

= $5,80,500

Working capital of $33,500 will be released at the end of useful life of equipment.

To find out IRR, NPV is calculated at two different rates. Let us first discount cash flows at 18%.

Present value of cash inflows (at 18%) = Annual Cash inflows x PVAF(_{18%, 6}) + Release of working capital x PVF(_{18%, 6}) + Scrap value x PVF(_{18%, 6})

= 147,600 x 3.498+ 33,500 x 0.370 + 147,000 x 0.370

= 516,305 + 12,395 + 54,390

= $583,090

NPV( at 18%) = Present value of cash inflows - Present value of cash outflows

= 583,090 - 580,500

= $2,590

Since at 18% discount rate, NPV is positive, IRR must be slight above 18% . Let us discount cash inflows at 19%

Present value of cash inflows (at 19%) = Annual Cash inflows x PVAF(_{19%, 6}) + Release of working capital x PVF(_{19%, 6}) + Scrap value x PVF(_{19%, 6})

= 147,600 x 3.410 + 33,500 x 0.352 + 147,000 x 0.352

= 503,316 + 11,792 + 51,744

= $566,852

NPV( at 19%) = Present value of cash inflows - Present value of cash outflows

= 566,852 - 580,500

= -$13,648

Now, at 19% rate, NPV is negative. Hence, IRR must lie between 18% and 19%. IRR can be calculated as under:

IRR = Lower rate + [NPV at lower rate/(NPV at lower rate - NPV at higher rate)] x (Higher rate - Lower rate)

= 18% + (2,590/2,590 + 13,648) x (19 - 18)

= 18% + 2,590/16,238

= 18% + 0.17%

= 18.17%

Hence, correct option is (b)