Question

A granary has two options for a conveyor used in the manufacture of grain for transporting, filling, or emptying. One conveyor can be purchased and installed for $70,000 with $3,000 salvage value after 16 years. The other can be purchased and installed for $110,000 with $4,000 salvage value after 16 years. Operation and maintenance for each is expected to be $18,000 and $14,000 per year, respectively. The granary uses MACRS-GDS depreciation, has a marginal tax rate of 25%, and has a MARR of 9% after taxes.

a. Determine which alternative is less costly, based upon comparison of after-tax annual worth. Show the AW values used to make your decision.

b. What must the cost of the second (more expensive) conveyor be for there to be no economic advantage between the two?

Answer 1

1. Alternative 1 : The cost of the project is $70,000. The life of the project is 16 years. The salvage value is $3,000 after 16 years. Since the cost of the project is for installation of a conveyor the MACRS-GDS 5-year property class is applicable here. The rates are 20%, 32%, 19.20%, 11.52%, 11.52%, and 5.76%. See after tax cash flow below.

Table 1.1 shows about the Statement of after tax cash flow as follows:

Comment

1. Step 2 of 10

   Before tax cash flowis the excess amount of sales after deducting operating expenses in each year. The ATCF is the excess amount of taxable incomeover taxafter adding DWO. You calculate depreciationon $70,000 based on above rates. Taxable income is the difference between BTCF and DWO.

   You calculate tax @40% on TI in each year. In this way you get ATCF in each year. You add the salvage value with BTCF at the end of the project, which is year 16.

   Comment

2. Step 3 of 10

   Calculate present worth as follows:

   If you convert free cash flow into its present value using opportunity cost then the amount so appeared is known as PW. See below the formula of PW.

   

   Where,

   “r” means the rate of opportunity cost and

   “n” is the number of year.

   Comment

3. Step 4 of 10

   Since ATCF of different years can now calculate the PW as under:

   

   Thus, PW after tax is. PW is negative here because this is the present value of expenditure for the project.

   Comment

4. Step 5 of 10

   Formula and calculation of annual worth has shown below:

   

   Where,

   “r” means after tax MARR and

   “n” means life of the project.

   AW is useful to compare between alternative projects.

   

   Comment

5. Step 6 of 10

   Alternative 2 : The cost of the project is $110,000. The life of the project is 16 years. The salvage value is $4,000 after 16 years. Since the cost of the project is for installation of a conveyor the MACRS-GDS 5-year property class is applicable here. The rates are 20%, 32%, 19.20%, 11.52%, 11.52%, and 5.76%. See after tax cash flow below.

   Table 1.2 shows about the Statement of after tax cash flow as follows:

   

   Comment

6. Step 7 of 10

   Before tax cash flowis the excess amount of sales after deducting operating expenses in each year. The ATCF is the excess amount of taxable incomeover taxafter adding DWO. You calculate depreciationon $110,000 based on above rates.

   Comment

7. Step 8 of 10

   Since ATCF of different years can now calculate the PW as under.

   

   PW after tax is . PW is negative here because this is the present value of expenditure for the project.

   Comment

8. Step 9 of 10

   Formula and calculation of annual worth has shown below:

   

   Where,

   “r” means after tax MARR and

   “n” means life of the project.

   AW is useful to compare between alternative projects.

   

   Comment

9. Step 10 of 10

   After tax annual worth in case of alternative 1 is -$16,741 and in case of alternative 2 is -$17,367.

   Alternative 1 has less negative value than alternative 2. Therefore alternative 1 is less costly. It is advisable to implement alternative 1 and reject alternative 2..

   b)

   Find out the cost of the second conveyor so that there is no economic advantage between two alternatives. It means, at what cost of second conveyor their PWs are equal?

   Since alternative 1 is getting the economic advantage its PW must equal to PW of alternative 2. See below

   

   Therefore, the cost of the second alternative is .