## Tax and Depreciation

1. A depreciable asset costs \$8,000 and has an estimated salvage value of \$1,000 at the end of its four year depreciable life. The asset is to be depreciated by the sum-of-years-digits method.
a. Compute the amount of depreciation that will be allowed for this asset in the first two years of its life.
b. With the sum-of-years-digits method how will the book value relate to the estimated salvage value at the end of four years.

2. A depreciable asset costs \$10,000 and has an estimated salvage value of \$1,000 at the end of its six-year depreciable life.
a. The asset is to be depreciated by the double rate declining balance method. Compute the amount of depreciation that will be allowed for this asset in the first two years of its life.
b. With the double rate declining balance method how will the book value relate to the estimated salvage value at the end of six years?
c. What role does depreciation play in a before tax economic analysis?

3a. YABC Corp. purchased a machine costing \$10,000 for its manufacturing plant at Austin. The machine has a useful life of 5 years. The revenue generated by the machine and maintenance costs for the 5 years are as given below.

 Years 1-3 Years 4-5 Revenue \$6,000 5,000 Maintenance costs \$1,000 \$3,000

The company uses the straight line method for depreciation and assumes zero salvage when computing the depreciation charges for this machine. In fact, due to shortage of this equipment in the market, the actual salvage for the machine will be \$1000 at the end of 5 years.

The tax rate is 50% for all incomes (including the capital gain on the salvage value).
a. Compute the before and after tax cash flows for this company associated with this project.
b. Show the equations that must be solved to determine the before and after tax rate of returns.

3b. The company described in problem 3 uses the SOYD depreciation method for depreciation and assumes zero salvage when computing the depreciation charges for this machine. In fact, due to shortage of this equipment in the market, the actual salvage for the machine will be \$1000 at the end of 5 years.

The tax rate is 50% for all incomes (including the capital gain on the salvage value).
a. Compute the before and after tax cash flows for this company associated with this project.
b. Show the equations that must be solved to determine the before and after tax rate of returns.

3c. The company described in problem 3 uses the double rate declining balance depreciation for depreciation and assumes zero salvage when computing the depreciation charges for this machine. In fact, due to shortage of this equipment in the market, the actual salvage for the machine will be \$1000 at the end of 5 years.

The tax rate is 50% for all incomes (including the capital gain on the salvage value).
a. Compute the before and after tax cash flows for this company associated with this project.
b. Show the equations that must be solved to determine the before and after tax rate of returns.

4. A machine initially costs \$4500. Projections concerning the machine are shown in the table below. Both operating expenses and income are assumed to occur at the end of each year. The depreciation schedule is determined using the sum-of-the-years-digits method with a life of 5 years and a salvage value of 0. The actual estimated salvage at the end of year 5 is \$1000. We will keep the machine for 5 years. The tax rate is 20% for both net income and capital gains.
a. Fill in the depreciation schedule in the space provided in the table.
b. Show the cash flows we should use for an after tax analysis.
c. Find the after tax rate of return for this investment.

5a. For the following, tell which you prefer and why? You may respond that the options are equal.
A. Depreciate an asset with the straight line method assuming zero salvage.
B. Depreciate an asset with the double declining balance method with a switch to straight line at the optimum time. The final book value is zero.

5b. For the following, tell which you prefer and why? You may respond that the options are equal.
A. A depreciation schedule that allows an asset to be depreciated to a book value of zero, even though the salvage value of the asset will be larger than zero.

B. A depreciation schedule that allows an asset to be depreciated to a book value exactly equal to the salvage value.

5c. For the following, tell which you prefer and why? You may respond that the options are equal.
A. A machine that costs \$1000 has zero salvage and provides an income of \$200 per year for five years. No tax is charged on the income and no depreciation is allowed on the investment.

B. A machine that costs \$1000 has zero salvage and provides an income of \$240 per year for five years. The tax rate is 20% and the asset is depreciated with the straight-line method.
6. At the beginning of the year a truck has a book value of \$3,000. It is being depreciated with the double rate declining balance method of depreciation assuming a life of 5 years. During the year the truck earns a net income of \$2000. At the end of the year the truck is sold for \$600. What is the after tax cash flow generated by this truck for the year? Assume a tax rate of 30% for both ordinary income and capital gains.

7. We bought a truck three years ago. Now, it has a book value of \$3,000. There are two years left to go on its tax life. For depreciation purposes, we assume the tax salvage after the two years is zero. We are using the Sum of Years Digits method for depreciation. What was the initial cost of the truck?