Question

A firm is considering an expansion project that will last three years. The project requires an immediate purchase of a new equipment that costs $900,000. The equipment will be fully depreciated using straight-line method over the next three years. The resale price of the equipment at the end of year three is estimated to be $200,000. The project will generate annual sales of $750,000 and incur annual costs (all costs except depreciation expense) of $200,000 for each of the next three years. The project requires an immediate investment of $50,000 in NWC, which will be fully recovered in year 3. The corporate tax rate is 30%.

calculate the payback period, the discounted payback period, the net present value, and the internal rate of return. Assume that the required rate of return is 15%.

Answer 1

Solution: 0 | Sales Less : costs Less : Depreciation Taxable income Less : tax at 30% Net income Add: Depreciation OCF Cost of equipment After tax sale value of equiment=200000*(1-0.3) Change in NWC Project cash flows 1 750000 -200000 -300000 250000 -75000 175000 300000 475000 2 750000 -200000 -300000 250000 -75000 175000 300000 475000 3 750000 -200000 -300000 250000 -75000 175000 300000 475000 -900000 -50000 -950000 140000 50000 665000 475000 475000 Payback period: Year cash flow cumulative cash flow 0 -950000 -950000 1 475000 475000 2 475000 3 665000 665000 Payback period 2 years Discounted Payback period: Year cumulative PV cash flow PV factor at 15% PV a b c=a*b 0 -950000 1.00000 -950000.00 1 475000 0.86957 413043.48 2 475000 0.75614 359168.24 3 665000 0.65752 437248.29 -950000.00 -536956.52 -177788.28 259460.01 2.41 Years Discounted Payback period: 2+177788.28/437248.29)

NPV Year cash flow PV factor at 15% PV la b c=a*b 0 -950000 1.00000 -950000.00 1 475000 0.86957 413043.4783 2 475000 0.75614 359168.242 3 665000 0.65752 437248.2946 NPV 259460.01 IRR by trial and error method Year 0 1 2 3 cash flow PV factor at 30% PV P V factor at 29% PV c=a* b d e=a*d -950000 1.00000 -950000.00 1.00000-950000.00 475000 0.76923365384.62 0.77519 368217.05 475000 0.59172 281065.09 0.60093 285439.58 665000 0.45517| 302685.48 0.46583 309779.39 NPV -864.82 NPV 13436.02 By interpolation: IRR= 30-864.82/864.82 +13436.02) 29.94%