# Problem-1 (Net present value method with income tax)

Posted in: Capital budgeting techniques (problems)

A mining company is considering to open a new coal mine. The company has collected the following information about the cash flows associated with this project:

- Equipment needed for new mine: $900,000
- Working capital required for new mine: $210,000
- Expected annual cash inflow from the sale of coal: $750,000
- Expected annual cash expenses associated with the new mine: $500,000
- Road repairs required after 5 years: $110,000

The coal in the mine would be exhausted after 15 years. The equipment would be sold for its salvage value of $250,000 at the end of 15-year period. The company uses straight line method of depreciation and does not take into account the salvage value for computing depreciation for tax purpose. The tax rate of the company is 30%.

**Required: **

- Compute net present value (NPV) of the new coal mine assuming a 15% after-tax cost of capital.
- On the basis of your computations in requirement 1, conclude whether the coal mine should be opened or not.

## Solution:

### (1) Computation of net present value:

*Value from “present value of an annuity of $1 in arrears table“.

**Value from “present value of $1 table”.

### (2) Conclusion:

Yes, the coal mine should be opened because its net present value (NPV) is positive.

16 Comments on Problem-1 (Net present value method with income tax)I agree with your calculation for determing NPV. However, I don’t understand why you have computed tax savings on road repiar expenses. If you are computing tax savings on it, does it imply that road repair expense is capital expenditure? My assumption is that capital expenditure qualifies for tax savings. If the answer is yes, shouldn’t road repair expense ( capital expenditure) be depreciated and used to arrive at adjusted basis to determine capital gain/loss at the time of sale ?

Because it is a revenue expenses and tax on income get reduced by tax rate so net out flow of road expenses is = Road expenses less .tax shavings

i.e. Road expenses…………………………..1,10,000 (A)

Tax Shaving @30%…………………….. 33,000 on A (B)

Hence net outflow for road exp ……………. 77,000 9A-B)

can somebody help me in understanding ,

1) depreciation tax shield?

2)tax effect calculation?

Tax Shield is the impact of tax benefit;

Understand as follows:

Income ……………………………………………..1,00,000 (A)

Depreciation …………………………………………… 20,000 (B)

Net Taxable (Differential Figure A-B) …………….. 80,000 (C) = (A-B)

Tax (@Rate 30 %) ……………………………………… 24000 (D)

Net Income ………………………………………………………76000 (C-D)

Without deduction of Depreciation Tax on Income @ 30% 30,000 (30% of A) (F)

But after Depreciation Tax is ………………………………………. 24,000 (G)

Tax shaving due to depreciation……………………………….. 6000 (F-G) This is tax shied on Dep

Simply it is calculated by multiplying tax rate to depreciation Depreciation 20,000

and 30 % on depreciation is 20000*30/100 =6000

Thank you for the examples and explanations. They were very helpful. Continue your good work.

Once again and big THANK YOU.

how did you get the 60,000 for depreciation?

Straight line depreciation on equipment: $900000/15 years = $60,000 per year

Why didnt they subtract the salvage value when calculating depreciation?

What is the differences between npv after tax and before tax

As it is given in question that for tax purpose full value of mine is depreciated without considering the salvage value.

In case question is silent one should reduce the salvage value from the equipment cost for calculating depreciation.

I have to clear regarding depreciation value please help me I did not get how come $60000 depreciation

It is cost $ 9,00,000 depreciated in 15 years

Dividing 9,00,000 by number of useful life i.e. 15 years you get 60,000

Magagula Lovemore’s Farms Ltd. is considering investing in a new project. The project will need an initial investment of E1, 500,000 and will generate E800, 000 (after-tax) cash flows for three years. Calculate the NPV for the project if the cost of capital is 20%. Please help

how did you compute dep tax shield? thank you

Tax Shield = Depreciation Expense * Tax Rate

Depreciation Exp = Overall Cost of Equipment / useful life of the asset

Depreciation Expense = 9000000/15 = 60000 annually

Tax shield = 60,000 * 0.30 =18,000

Tax Shield = Depreciation Expense * Tax Rate

Depreciation Exp = Overall Cost of Equipment / useful life of the asset

Depreciation Expense = 900,000/15 = 60,000 annually

Tax shield = 60,000 * 0.30 =18,000