Question

The answer is already given, I just don't understand how. Can you please show how each value is caculated and label please!

2. Depreciation, taxes and source of finance. Compute the present value of a project with the following characteristics: Initial investment required 1 million dollars, 40% of it will be financed with a loan at 10% interest rate payable yearly in five years. Yearly savings for the first year of the project is $300,000, increasing by 50,000 year after year. Depreciation is computed using MACRS GDS for 5 years. Tax rate is 35% and MARR = 15%. Life for the project is 7 years. Solution End Loan Cash flow MACRS Factor Deprec Loan Balance Loan Payment Loan Interest principal Taxable Tax Cash flow PW Income Year reduction - 1000000 400,000 (5600,000) 150,853 300,000 0.2 200,000 105,519.0 40,000 65,519.0 105,519.0 33,448 $ (600,000.0) 173,481 245,687 230,865 72,070.9 60,000 (3,448.1) 181,759 185,775 334,481 262,410 183,132 95,926 0 21,000.0 (1,206) 63,615 110,770 79,278.0 0.32 0.192 0.1152 0.1152 0.0576 151,797 320,000.0 192,000.0 115,200.0 115,200. 0 57,600.0 350,000 400,000 450,000 500,000 550,000 600,000 105,519.0 105,519.0 105,519.0 26,241 18,313 9,592 87,205.8 316,486 233,710 133,624 95,926.4 375,207 131,322 263,158 130,836 377,660 163,272 492, 400 600,000 172,34 210,000 390,000 146,615 Total PW 462,775

Answer 1

Price of machine is $ 1,000,000

Depreciation is calculated by multiplying the price with MACRS factor.

1st year, Depreciation = $ 1,000,000 × 0.2 = $ 200,000

2nd year, Depreciation = $ 1,000,000×0.32 = $ 320,000

Like wise it is Calculated for each year.

Loan of $ 400,000 at a rate of 10% for 5 years.

Annual payment = $400,000(A/P,10%,5) = $ 400,000 × 0.263797

Annual or Loan payment = $ 105,518.99

= $ 105,519(Approximately)

Loan interest

1st year interest = 10% of $ 400,000 = $ 40,000

Principal paid in first year = $ 105,519 - 40,000 = $ 65,519

Loan remaining after 1st year = 400,000 - 65,519 = $ 334,481

2nd year interest = 0.1×334,481 = $ 33,448

Remaining principal = 334,481 - 33,448 = $ 301,033

Like this we can calculate the loan payment, loan balance, loan interest.

Taxable income = Income - Depreciation - Interest paid

1st year taxable income = 300,000 - 200,000 - 40,000 = $ 60,000

2nd year TI = 350,000 - 320,000 - 33,448 = -$3,448

3rd year, TI = 400,000 - 192,000- 26,241 = $ 181,759

Like this you can calculate Taxable income.

Tax is charged at a rate of 35%

1st year, Tax = $ 60000 × 0.35 = $ 21,000

2nd year, Tax = 0.45 ×(-3,448) = - $ 1,206

,Like this you can calculate the Tax amount.

Then cash flow can be calculated using the following formula

Cash flow = Income (1st column) -Loan payment - Tax

1st year, Cash flow = 300,000 - 105,519 - 21,000 = $ 173,481

2nd year, CF = 350,000 - 105,519 -(-1206) = $ 245,687

3rd year, CF = 400,000 - 105,519 - 63,615 = $ 230,865

Like this you can calculate the remaining year values.

Last column is just the discounted value of cash flow

1st year, 173,481/1.15 = $ 150,853

2nd year, 245,687/1.15² = $ 185,775

3rd year, 230,865/1.15³ = $ 151,797

Like this you can calculate for the remaining years as well.

Present worth is the sum of all the values of the last column.

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