NPV

CFA Level II Corporate Finance
#1

Hi,

Please help me understand this question and explain its solution also. What does the last line in the solution mean that the tax deferral due to the accelerated depreciation adds to the NPV.

Domez Company is considering an investment of 500,000 in a new project. The company currently uses straight-line depreciation but wants to evaluate the effect of a switch from straight-line to accelerated depreciation on the project’s NPV. The following table gives the depreciation and tax savings from both the depreciation methods. The project life is 5 years. Year Straight-line Depreciation Tax savings Accelerated Depreciation Tax Savings ($) (Corporate Tax Rate 40%) MACRS 3-Year Property

1 100,000 40,000 166,650 66,660 2 100,000 40,000 222,250 88,900 3 100,000 40,000 74,050 29,620 4 100,000 40,000 37,050 14,820 5 100,000 40,000 0 0 PV at 10% $151,632 PV at 10%

The change from straight-line to accelerated depreciation would A. have no effect on the NPV. B. subtract $14,815 from the NPV. C. add $14,815 to the NPV.

C is correct. The present value of tax savings from straight-line depreciation is given as $151,632. The present value of tax savings from accelerated depreciation is calculated by using FC: CF0 = 0, CF1 = 66,660, CF2 = 88,900, CF3= 29,620, CF4 = 14,820; I = 10, NPV CPT = 166,447. The tax savings from accelerated depreciation increased by ($166,447- $151,632) $14,815 from straight-line depreciation. The tax deferral due to accelerated depreciation adds to the NPV of the project. Section 6. LO.a.

#2

In either case you are depreciating the whole $500,000 over a five year period and thus save $200,000 in tax payments during this period. If you use an accelerated depreciation method those tax savings are shifted toward the earlier years and thus their NPV is higher.

For example in year 1 with the accelerated depreciation method you save $26,660 in taxes more than with the linear depreciation method. Those $26,660 will be saved in a later year with the linear depreciation method (remember overall dollar amount of savings is $200,000 for both methods) and thus will have to be discounted more (e.g. divided by 1.1^x instead of 1.1^1 with x > 1) than using the accelerated depreciation method.