Question

Landry Corporation is considering the purchase of a new ocean-going vessel that could potentially reduce labor costs of its operation by a considerable margin. The new ship would cost $500,000 and would be fully depreciated by the straight-line method over 10 years. At the end of 10 years, the ship will have no value and will be scuttled. Landry's cost of capital is 12 percent, and its marginal tax rate is 40 percent. Refer to Landry Corporation. What is the present value of the depreciation tax benefit of the new ship? (Round to the nearest dollar.) Present value tables or a financial calculator are required. Select one: a. $113,004 b. $282,510 c. $169,506 d. $200,000

Answer 1

the present value of the depreciation tax benefit of the new ship is approximately $169,506, which is closest to option (c).

To calculate the present value of the depreciation tax benefit of the new ship, you can follow these steps:

Step 1: Calculate the annual depreciation expense:

Annual Depreciation Expense = Initial Cost / Useful Life

Annual Depreciation Expense = $500,000 / 10 years

Annual Depreciation Expense = $50,000 per year

Step 2: Calculate the tax savings due to depreciation each year:

Tax Savings per Year = Annual Depreciation Expense * Tax Rate

Tax Savings per Year = $50,000 * 0.40 (40% tax rate)

Tax Savings per Year = $20,000 per year

Step 3: Determine the present value of these tax savings over the 10-year period, considering the cost of capital (12%):

Using the formula for the present value of an annuity:

`\[PV = PMT * \left(1 - (1)/((1 + r)^n)\right) / r\]`

Where:

PMT = Annual tax savings ($20,000)

r = Discount rate (12% or 0.12)

n = Number of years (10)

`\[PV = $20,000 * \left(1 - (1)/((1 + 0.12)^(10))\right) / 0.12\]`

`\[PV ≈ $169,506\]`

So, the present value of the depreciation tax benefit of the new ship is approximately $169,506, which is closest to option (c).