Question

Division D is considering two possible expansion plans. Plan A would expand a current product line at a cost of $8,440,000. Expected annual net cash inflows are $1,500,000​, with zero residual value at the end of 10 years. Under Plan​ B, Division D would begin producing a new product at a cost of $8,300,000. This plan is expected to generate net cash inflows of $1,080,000 per year for 10 ​years, the estimated useful life of the product line. Estimated residual value for Plan B is $1,200,000. Division D uses​ straight-line depreciation and requires an annual return of 10​%.

The IRR rate of Plan A & B

Answer 1

Solution :

Plan A :

Initial investment = $8,440,000

Expected annual cash inflows = $1,500,000

Period = 10 years

Let IRR = i

Now

$1,500,000 * Cumulative PV Factor at i for 10 periods = $8,440,000

Cumulative PV Factor at i for 10 periods = 5.6266666

This PV Factors falls between 12% and 13%

Cumulative PV Factor at 12% = 5.65022

Cumulative PV factor at 13% = 5.42624

IRR= 12% + (5.65022 - 5.62667) - (5.65022 - 5.42624)

= 12.10%

Plan B:

Initial investment = $8,300,000

Expected annual cash inflows = $1,080,000

Residual value = $1,200,000

Period = 10 years

Let IRR = i

Lets compute present value of cash inflows at 6% and 7%

Present value of cash inflows at 6% = $1,080,000 *Cumulative PV factor at 6% for 10 periods + $1,200,000 * PV Factor at 6% for 10th period

= $1,080,000 * 7.36009 + $1,200,000 * 0.55839

= $8,618,968

Present value of cash inflows at 7% = $1,080,000 *Cumulative PV factor at 7% for 10 periods + $1,200,000 * PV Factor at 7% for 10th period

= $1,080,000 * 7.02358 + $1,200,000 * 0.50835

= $8,195,487

IRR = 6% + ($8,618,968 - $8,300,000) / ($8,618,968 - $8,195,487)

= 6.75%