What is the present value at a 10% discount rate of the depreciation tax shield

Question

What is the present value at a 10% discount rate of the depreciation tax shield for a firm in the 35% tax bracket that purchases a $50,000 asset being depreciated straight-line over a 5-year life to a zero salvage value?

A. $10,866
B. $13,268
C. $17,500
D. $37,908

Which of the following costs probably should not be allocated to the investment needed for a new project?
A. Increase in accounts receivable
B. New warehouse, built for this project
C. 25% of the Vice President's salary
D. Labor expense for employees in new warehouse

What should be the current price of a stock if the expected dividend is $5, the stock has a required return of 20%, and a constant dividend growth rate of 6%?
A. $19.23
B. $25.00
C. $35.71
D. $37.86

Explanation / Answer

Hi,

Please find the answers as follows:

Part 1:

Annual Depreciation = Initial Cost/Life of the Asset = 50000/5 = 10000

Annual Tax Benefit on account of Depreciation = Depreciation*Tax Rate = 10000*35% = 3500

Present Value of Tax Shield = 3500/(1+0.1)^1 + 3500/(1+0.1)^2+ 3500/(1+0.1)^3+ 3500/(1+0.1)^4+ 3500/(1+0.1)^5= 13267.75 or 13268

Option B (13268) is the correct answer.

Part 2:

Option C (25% of the Vice President's salary) is the correct answer.

Part 3:

Current Value of the Stock = D1/(ke-g)

D1 = 5

ke = 20% (indicates required rate of return)

g = 6% (indicates growth rate)

Current Value of the Stock = 5/(.20 - .06) = 35.71

Option C (35.71) is the correct answer.

Thanks.

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