Luke Sky walker invests in a new X-Wing. The purchase price of this new X-wing i

Question

Luke Sky walker invests in a new X-Wing. The purchase price of this new X-wing is $ 100,000. He believes that the X-Wing will be worth $5,000 in salvage value at the end of the 6^th year. By purchasing this new X-wing, it will result in net savings (gross revenues minus all other business expenses) of $20,000 annually. If Luke Skywalker falls under the 15% tax bracket for the Rebel Alliance and his minimum attractive rate of return (MARR) is 10%, please answer the following questions. What is the after-tax internal rate of return if Luke Skywalker uses straight-line depreciation? What is the after-tax internal rate of return if Luke Skywalker uses the 5-year property class MACRS depreciation schedule? Why will there be a difference in the after-tax rate of returns? A graph may suffice. Which depreciation schedule will Luke Skywalker choose? Why?

Explanation / Answer

a) IRR using SL depreciation: Initial investment: cost of X wing 100000 Operational cash inflows: yearly savings 20000 depreciation (100000-5000)/6 15833 incremental savings before tax 4167 tax @ 15% 625 net savings after tax 3542 add: depreciation 15833 after tax annual operational cash flows 19375 Terminal cash flows: salvage value 5000 IRR is that rate which will equate the PV of the yearly operational cash flows and the PV of the terminal cash flows with the Initial investment. 100000 = 19375*pvifa(irr,6) + 5000*Pvif(irr,6) The value of irr should be found by trial and error so the PV of the inflows = $100000. Starting with 5% PV = 19375*5.0757 + 5000*0.7462 = 102072.69 discounting with 6% PV = 19375*4.9173 + 5000*0.7050 = 98797.69 exact rate = 5 + 2072.69/3275 = 5.63% IRR = 5.63% b) IRR using MACRS Depreciation: Operational cash inflows: 1 2 3 4 5 6 yearly savings 20000 20000 20000 20000 20000 20000 depreciation 20000 32000 19200 11520 11520 5760 incremental savings before tax 0 -12000 800 8480 8480 14240 tax @ 15% 0 -1800 120 1272 1272 2136 net savings after tax 0 -10200 680 7208 7208 12104 add: depreciation 20000 32000 19200 11520 11520 5760 after tax annual operational cash inflows 20000 21800 19880 18728 18728 17864 after tax terminal cash inflow (5000*0.85) 4250 Net yearly cash inflows 20000 21800 19880 18728 18728 22114 pvif @ 5% 0.952381 0.90703 0.8638 0.823 0.7835 0.7462 pv 19048 19773 17173 15408 14674 16502 102577 pvif @ 6% 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 pv 18868 19402 16692 14834 13995 15589 99380 IRR = 5 + 2577/3197 = 5.81% IRR = 5.81% depreciation rate-% 20.00 32.00 19.20 11.52 11.52 5.76 (200%, half year convention) c) After tax rate of return differs as the Tax shield due to depreciation differs with the use of different methods. While for the SL method the tax shield on account of depreciation is the same every year at 15,833*0.15 = 2375, under the MARCS, the tax shield is more in the initial years due to higher depreciatio in the initial years. Difference in tax shield produces difference in cash flows. Hence, the IRR is different for the two methods. d) Luke Skywalker will choose the MACRS, as it gives higher IRR of 5.81%.

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