Question

Your company is considering a new project that will require $10,000 of new equipment at the start of the project. The equipment will have a depreciable life of five years and will be depreciated to a book value of $3,000 using straight-line depreciation. The cost of capital is 9 percent, and the firm's tax rate is 34 percent. Estimate the present value of the tax benefits from depreciation.

A. $476
B. $924
C. $1,400
D. $1,851

Answer 1

The present value of the tax benefits from depreciation is approximately B. $924.

Step-by-step explanation:

The present value of the tax benefits from depreciation can be calculated using the formula:

Present Value = Tax Benefit × (1 - Tax Rate) × PV Factor

Where:

• Tax Benefit is the depreciation amount
• Tax Rate is the firm's tax rate
• PV Factor is the present value factor determined by the cost of capital

In this case, the tax benefit is the difference between the initial cost of the equipment ($10,000) and the book value at the end of the depreciation period ($3,000), which is $7,000.

Using the formula and given that the cost of capital is 9 percent, we can calculate the present value of the tax benefits:

Present Value = $7,000 × (1 - 0.34) × (1/(1 + 0.09)^5)

Calculating this, we get:

Present Value ≈ $924

Answer 2

Estimate the present value of the tax benefits from depreciation:

D. $1,851

Step-by-step explanation:

Step 1: Determine annual depreciation

A.D=(A.C-S.V)/N

where;

A.D=annual depreciation

A.C=acquisition cost

S.V=salvage value

N=useful life

In our case;

A.D=unknown, to be determined

A.C=$10,000

S.V=$3,000

N=5 years

replacing;

A.D={(10,000-3,000)/5}=7,000/5=$1,400

Annual depreciation=$1,400

Step 2: Determine annual tax benefits

Annual tax benefits=tax rate×annual depreciation

where;

tax rate=34%=34/100=0.34

annual depreciation=$1,400

replacing;

Annual tax benefits=0.34×1,400=$476

Step 3: Determine present value of the annual tax benefits

Year Future value Present value

1 476 476/{(1+0.09)^1}=436.70

2 476 476/{(1+0.09)^2}=400.64

3 476 476/{(1+0.09)^3}=367.56

4 476 476/{(1+0.09)^4}=337.21

5 476 476/{(1+0.09)^5}=309.37

Total present value of the tax benefits=436.70+400.64+367.56+337.21+309.37=$1,851.48

Estimate the present value of the tax benefits from depreciation=$1,851