# mock exam drives me crazy

in the case of Seth Hornsby, the solution says the change from accelearted to straight-line depreciation will decrease NPV. suppose I have a 3-yr project, each year cash flow is 10, the initial cash flow outlay is 12, assuming tax rate is 50%, discount back at 10% using accelerated deprecitaion, yr one depreciates 6, yr 2 depreciates 4, yr 3 depreciates 2 yr 1 is (10-6)*0.5 = 1.5 yr 2 is (10-4)*0.5 = 3 yr 3 is (10-2)*0.5 =4 NPV = 6.848 using straight line depreciation yr 1,2,3, are all (10-4)*0.5=3 NPV = 7.4 the straight line depreciation increased NPV because it moved the cost to future time. Please help me here.

The sooner in the life of a project you get inflows, the greater the NPV would be. Accelerating depreciation in the early years lowers the tax basis (by deducting more as depreciation), you get the earnings after taxes but before interest, and then add back depreciation (because depreciation is a non-cash charge) and you have an after tax cash flow higher than a straight line depreciation would. With accelerated depreciation, early inflows in the NPV would be bigger, hence NPV larger. Also, check the numbers on y1 with accelerated depreciation, (10-6)*0.5=2, not 1.5. Add back the depreciation, and you get the after tax operating cash flow.

Sorry a typo here, using accelerated deprecitaion, yr one depreciates 6, yr 2 depreciates 4, yr 3 depreciates 2 yr 1 is (10-6)*0.5 = 2 yr 2 is (10-4)*0.5 = 3 yr 3 is (10-2)*0.5 =4 NPV = 7.3028 using straight line depreciation yr 1,2,3, are all (10-4)*0.5=3 NPV = 7.4 the straight line depreciation increased NPV because it moved the cost to future time. Please help me here.

Thank you very much map1, you helped me with Level I, now you’re helping me with Level 2. thanks so much map1 Wrote: ------------------------------------------------------- > The sooner in the life of a project you get > inflows, the greater the NPV would be. > Accelerating depreciation in the early years > lowers the tax basis (by deducting more as > depreciation), you get the earnings after taxes > but before interest, and then add back > depreciation (because depreciation is a non-cash > charge) and you have an after tax cash flow higher > than a straight line depreciation would. > > With accelerated depreciation, early inflows in > the NPV would be bigger, hence NPV larger. > > Also, check the numbers on y1 with accelerated > depreciation, (10-6)*0.5=2, not 1.5. Add back the > depreciation, and you get the after tax operating > cash flow.

The above works perfect with the double declining method of depreciation, but then remember there is the MACRS, a special case of accelerating depreciation, that (unlike DD) allows depreciation below the salvage value. If you dispose on the asset producing the inflow at the end of the project, you will have a lower book value under MACRS than under the straight line, and if you sell it at the same price under both straight line and MACRS, your gain from the asset selling under MACRS would be larger, you’ll pay more taxes on the capital gain (because capital gain is larger). This will influence the last year’s inflows, and I am not sure of the effect on the final NPV, you’ll have to go with numbers, but I tend to believe NPV would still be larger under MACRS because of the back loading of taxes expense in the last year.