Question

Wendy's boss wants to use straight-line depreciation for the new expansion project because he said it will give higher net income in earlier years and give him a larger bonus. The project will last 4 years and requires $1,730,000 of equipment. The company could use either straight-line or the 3-year MACRS accelerated method. Under straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life. (Ignore the half-year convention for the straight-line method.) The applicable MACRS depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%. The project cost of capital is 10%, and its tax rate is 25%.

1. What would the depreciation expense be each year under each method? Enter your answers as positive values. Do not round intermediate calculations. Round your answers to the nearest dollar.

   Year	Scenario 1 (Straight Line)	Scenario 2 (MACRS)
   1	$	$
   2	$	$
   3	$	$
   4	$	$

2. Which depreciation method would produce the higher NPV, and how much higher would it be? Do not round intermediate calculations. Round your answer to the nearest cent.

   The NPV under -Select-Scenario 1Scenario 2Item 9 will be higher by $   .

Answer 1

a. The depreciation expense under both methods are computed below:

Year	Scenario 1 (Straight Line Computation)	Scenario 1 (Straight Line)	Scenario 2 (MACRS Computation)	Scenario 2 (MACRS)
1	= $ 1,730,000 / 4	$ 432,500	= $ 1,730,000 x 33.33%	$ 576,609
2	= $ 1,730,000 / 4	$ 432,500	= $ 1,730,000 x 44.45%	$ 768,985
3	= $ 1,730,000 / 4	$ 432,500	= $ 1,730,000 x 14.81%	$ 256,213
4	= $ 1,730,000 / 4	$ 432,500	= $ 1,730,000 x 7.41%	$ 128,193

b. In order to compute the NPV, we need to compute the tax savings on depreciation and then we shall compute the NPV by discounting

Tax Savings on depreciation using straight line

Year	Straight Line Depreciation	Tax Savings on depreciation
1	$ 432,500	= $ 432,500 x 25% = $ 108,125
2	$ 432,500	= $ 432,500 x 25% = $ 108,125
3	$ 432,500	= $ 432,500 x 25% = $ 108,125
4	$ 432,500	= $ 432,500 x 25% = $ 108,125

Now we shall compute the present value of tax savings on depreciation at cost of capital of 10% as follows:

= 108,125 / 1.10¹ + 108,125 / 1.10² + 108,125 / 1.10³ + 108,125 / 1.10⁴

= $ 342,741.70 Approximately

Tax Savings on depreciation using MACRS

Year	MACRS Depreciation	Tax Savings on depreciation
1	$ 576,609	= $ 576,609 x 25% = $ 144,152.25
2	$ 768,985	= $ 768,985 x 25% = $ 192,246.25
3	$ 256,213	= $ 256,213 x 25% = $ 64,053.25
4	$ 128,193	= $ 128,193 x 25% = $ 32,048.25

Now we shall compute the present value of tax savings on depreciation at cost of capital of 10% as follows:

= 144,152.25 / 1.10¹ + 192,246.25 / 1.10² + 64,053.25 / 1.10³ + 32,048.25 / 1.10⁴

= $ 359,942.24 Approximately

So the NPV by using the MACRS method is greater as compared to the NPV computed by using straight line by

= $ 359,942.24 - $ 342,741.70

= $ 17,200.54

Feel free to ask in case of any query relating to this question