Question

Project: replace existing equipment

There are three possible scenarios for the cost savings the company could capture with the new equipment:

Scenario 1: the company captures cost savings of $40,000/year (30% likelihood of occurring),

Scenario 2: cost savings of $35,000/year (10% likelihood), and

Scenario 3: cost savings of $30,000/year (60% likelihood).

Initial investment: ($200,000) for replacement equipment, plus a positive revenue of $20,000 selling the replaced equipment in the used equipment market (NOTE: treat as scrap value at beginning of project)

Project cost of capital: WACC of 7% + a project risk premium of +1%

Life of project: 10 years

1A. Calculate the project cash flows: NOTE: Use a weighted average of the three scenarios’ savings as the annuity cash flow for the project:

Cash flow for project = (CF scenario 1 x weight) + (CF scenario 2 x weight) + (CF scenario 3 x weight)

1B. Calculate NPV: Using the information provided and your cash flow estimate from #1 above, calculate the company’s NPV for the project. Show your steps!

1C. Calculate IRR: Given the information above, what is the IRR of the project? (show your steps)

NOTE: Remember that the IRR is the NPV for the project, where NPV = zero. You use the NPV equation, with NPV = zero, and solve for the PVIFA multiplier. Last, look up the PVIFA in the table for the project # of years.

Answer 1

1) Project cash flows in this question will be equal to weighted average of three scenario's savings.

CF scenario 1 = $40,000, Weight = 30% or 0.30

CF scenario 2 = $35,000, Weight = 10% or 0.10

CF scenario 3 = $30,000, Weight = 60% or 0.60

Annual Cash Flows =  (CF scenario 1 x weight) + (CF scenario 2 x weight) + (CF scenario 3 x weight)

= ($40,000*0.30)+($35,000*0.10)+($30,000*0.60)

= $12,000+$3,500+$18,000 = $33,500

2) Net Present value (NPV) = PV of annual cash flows - PV of cash outflows

Project cost of capital = 7%+1% = 8%

PV of cash Inflows = Annual cash flows*PVAF(8%,10 yrs)

= $33,500*6.7101 = $224,788

PV of cash outflows = Replacement cost - Sale of replaced equipment

= $200,000 - $20,000 = $180,000

NPV = $224,788 - $180,000 = $44,788

3) As IRR is the NPV for the project, where NPV = zero. The present value of cash outflow will be equal to present value of cash inflow at IRR. The IRR is calculated as follows:-

PV of cash Inflows = PV of cash Outflows

Annual Cash Flows*PVAF(10 yrs,IRR) = $180,000

$33,500*PVAF(10 yrs,IRR) = $180,000

PVAF(10 yrs,IRR) = $180,000/$33,500

PVAF(10 yrs,IRR) = 5.3731

From the annuity table the value of 5.3731 is between 13% and 14%. Therefore the IRR will be 13.25%(approx.)