Test Question:

  1. What do you understand by Capital Budgeting?
  2. Define Capital Budgeting
  3. List out the concept of Capital Expenditure
  4. Explain in brief that advantages of Capital Budgeting
  5. What is the need and importance of Capital Budgeting?
  6. List out the limitations of Capital Budgeting
  7. Explain the principle methods required for determining the profitability of any capital expenditure project.
  8. Compare the internal rate of return method and net present value method
  9. Explain- “Capital budgeting is the long-term planning to maintain the allocation of capital in different sectors of the ” What are its limitations?
  10. “For most of the investment decisions, either anorganization faces superior decision criterion for net present value or is at least good as a competing technique.” Explain the investment situation when the profitability index is better than net present value.
  11. Explain the circumstances for conflicting NPV and IRR methods recommendations. Tell us how these circumstances should overcome and why.
  12. How is the capital expenditure controlled in large scale organizations? Explain in steps.

 

Some Problems with their Solutions

Problem No. 1

For the below table, the cash outlay of $10,000 requires for each project. If the standard pay back period is 5 years, then which project should be accepted?

Year                             Project X ($)               Project Y ($)               Project Z ($)

1                                  2500                            4000                            1000

2                                  2500                            3000                            2000

3                                  2500                            2000                            3000

4                                  2500                            1000                            4000

 

Solution:

In the above table, all three projects have recovered their capital investment of $10,000 within the duration of 4 years. It has been found that Project X follows constant cash inflows whereas the project Y shows continuous decrease in their cash inflows. Considering the fact of Project Z, it shows gradual increase of cash flow every year.

Here, the project X shows the constant return point of view in every year. Thus, it is recommended.

Problem No. 2

A company has two projects with a tax rate of 50%. From the below table, the data will highlightits statistics.

Cash Inflows (Profit before Depreciation and Tax)

Year                             Project A                    Project B

$                                   $

0                                  15,000                         15,000

1                                  4,200                           4,200

2                                  4,800                           4,500

3                                  7,000                           4,000

4                                  8,000                           5,000

5                                  2,000                           10,000

Determine the depreciation rate on straight line basis using pay back period as criterion.

Solution:

  1. For Project A:

                        (–)                                                        Add                 Cash    Cumulative

Year     Profit  Depreciation  PAD     Tax      PAT     Depreciation  InflowsCash Inflows

$          $                      $          $          $          $                      $              $

1          4200    3000                1200    600      600      3000                3600        3600

2          4800    3000                1800    900      900      3000                3900        7500

3          7000    3000                4000    2000    2000    3000                5000        12500

4          8000    3000                4000    2000    2000    3000                5000         17500

5          2000    3000                –1000  –                      3000                2000          19500

Where,

PAD = Profit After Depreciation

PAT = Profit After Tax

Pay back period = 3 years and 6 months

Result:

Investment is $15,000

Capital Recovered in first three years is $12,500

During 4th year, balance of $2500 is recovered

1st Year            3,600

2nd Year           3,900

3rd Year           5,000

12,500

Balance           2,500

15,000

12 months/ 5,000 x 2,500 = How many months?

Thus, the time taken to recover the amount of $2,500 will be 6 months.

Hence, pay back period = 3 years 6 months

  1. Project B

Similarly,

(–)                                                        Add                 Cash    Cumulative

Year     Profit  Depreciation  PAD     Tax      PAT     Depreciation  InflowsCash Inflows

$          $                      $          $          $          $                      $              $

1          4200    3000                1200    600      600      3000                3600        3600

2          4500    3000                1500    750      750      3000                3700        7350

3          4000    3000                1000    500      500      3000                3500        10850

4          5000    3000                2000    2000    1000    3000                4000         14850

5          1000    3000                7000    7000    3500    3000                6500          21350

Note:

If necessary, then cumulative cash inflows should be prepared.

Here, Pay back period = 4 years and 8days

Result:

Investment is $15,000

Capital Recovered is $15,000

1st Year            3,600

2nd Year           3,750

3rd Year           3,500

4th Year            4,000

14,850

Balance           150

15,000

Time taken to recover the amount of $150 = 8days

For recovery of amount $6,500 in the 5th Year, time required = 365 days

For recovery of amount $15 in the 5th Year, time required = 8 days

Depreciation              Project A                    Project B

Cost/ Life                     15000/ 5                      15000/ 5

= $3,000                      = $3,000

Problem No. 3:

From the information given below, you have to determine the pay back period using:

  1. Traditional pay back method
  2. Discounted pay back method

Initial Outlay Estimated Life               5 Years            $80,000

Profit After Tax                                   Year 1              $6,000

End of the Years                                  2                      $14,000

3                      $24,000

4                      $16,000

5                      NIL

Take the cost of capital 20% per annum and PV of Re. 1 at this rate. Calculate depreciation under straight line method.

Year                 1          2          3          4          5

p/v factor       .83       .69       .58       .48       .40

Solution:

            Before             Add                 Profit Depreciation   p/v factor       present

Year     PAT                 Depreciation  but after tax               at 20%             value

$                      $                      $                                  $                      $

1          6,000               +16,000           = 22,000                      .83                   18,260

2          14,000             +16,000           = 30,000                      .69                   20,700

3          24,000             +16,000           = 40,000                      .58                   23,200

4          6,000               +16,000           = 22,000                      .48                   15,360

5          NIL                   +16,000           = 16,000                      .40                   6,400

 

Total present value                 = 83,920

Less : Initial Investment          = 80,000

Net Present Value                   = 3,920

  1. Traditional pay back method:

1st Year                                                $22,000

2nd Year                                               $30,000

Amount recovered for 2 years           $52,000

Balance                                               $28,000

$80,000

3rd Year profit is $40,000, but we require $28,000 to meet the original investment of $80,000

Hence, it can be written as,

12 months/ 40,000 x 28,000   = How many months?

= 2 years 8 months

  1. Discounted pay back method:

1st Year                                          $18,260

2nd Year                                         $20,700

3rd Year                                         $23,200

4th Year                                          $15,360

Balance                                         $77,520

Project Cost                                   $2,480

$80,000

In the 5th year, the cash inflow is $6,400, but for $2,480 to meet the original investment of $80,000

Hence, it can be written as,

12 months/ 6,400 x 2,480       = How many months?

= 4 years 4 months

Note:

Cost/ Life = 80,000/ 5

= 16,000

Problem No. 4:

Two competing proposals require an equal investment of $50,000. It is expected to produce net cash flows based on the following data:

Year     Project I                      Project II                     p/v at 10% per annum

$                                  $                                  $

1          25,000                         10,000                         .909

2          15,000                         12,000                         .826

3          10,000                         18,000                         .751

4          NIL                               25,000                         .683

5          12,000                         8,000                           .621

6          6,000                           4,000                           .564

Determine the project proposals using discounted cash flow methods. Tell us which one to choose and why.

Solution:

Year     Project I                      Project II                    

$                                  $

1          25,000                         10,000

2          15,000                         12,000

3          10,000                         18,000

4          NIL                               25,000

5          12,000                         8,000

6          6,000                           4,000

  1. a) Finding pay back period using traditional method:

Project I

1st Year                        $25,000

2nd Year                       $15,000

3rd Year                       $10,000

$50,000

Here, pay back period is 3 years.

Project II

1st Year                        $10,000

2nd Year                       $12,000

3rd Year                       $18,000

$40,000

Balance                       $10,000

$50,000

Here, pay back period can be obtained by,

2/ 25,000 x 10,000 = 4 years

Thus, as per the traditional method, Project I will be recommended because of its shorter pay back period.

  1. Discounted cash flow method:

For Project I:

Cash                Discount         Present                      

Year     Inflows            Factor             Value

at 10% p.a.    

$                      $                      $

1          25,000             .909                 22,725

2          15,000             .826                 12,390

3          10,000             .751                 7,510

4          NIL                   .683                    –

5          12,000             .621                 7,452

6          6,000               .564                 3,384

 

Total Present Value    =          $53,461

Less : Original Cost     =          $50,000

Net Present Value       =          $3,461

Criteria pay back period for Project I is 3years

For Project II:

Cash                Discount         Present                      

Year     Inflows            Factor             Value

at 10% p.a.    

$                      $                      $

1          10,000             .909                 9,090

2          12,000             .826                 9,912

3          18,000             .751                 13,518

4          25,000             .683                 17,075

5          8,000               .621                 4,968

6          4,000               .564                 2,256

 

Total Present Value    =          $56,819

Less : Original Cost     =          $50,000

Net Present Value       =          $6,819

Criteria pay back period for Project II is 3years 4 months

Note:

If considering the pay back period, then Project I is recommended. But, if considering the NPV, then Project II is recommended. This is because of surplus value in Project II i.e., $6,819.

Project 5:

Calculate the pay back period for a project whose cost is $5,00,000. It yields annual profit of $80,000 after its depreciation at 12% per annum before tax rate of 50%.

Solution:

Pay back period = Original Cost/ Annual Cash Inflows

Initial Investment = $5,00,000

Cash inflows = Profit after tax plus Depreciation

Profit Before Tax                                80,000

Less: Tax 50%                                      40,000

Profit After Tax                                   40,000

Add: Depreciation                               60,000

Annual Cash Inflows                            1,00,000

 

Hence, Pay back period          =          5,00,000/ 1,00,000

=          5 years

Note:

Depreciation   =          5,00,000 x 12/ 100

=          60,000

Problem No. 6

Calculate the net income before depreciation and tax of ABC Ltd. This company needs an initial investment of $40,000 for the project.

Year                                         $

1                                              10,000

2                                              12,000

3                                              14,000

4                                              16,000

5                                              20,000

Determine the project proposal considering Accounting Rate of Return Method.

Solution:

Year     Net Income                Less                 Profit              Less Tax           Profit After

            Before                         Depreciation  after                50%                 Tax and

            Depreciation                                      Depreciation                          Depreciation

and Tax ($)                 ($)                    ($)                    ($)                    ($)

1          10,000                         8,000               2,000               1,000               1,000

2          12,000                         8,000               4,000               2,000               2,000

3          14,000                         8,000               6,000               3,000               3,000

4          16,000                         8,000               8,000               4,000               4,000

5          20,000                         8,000               12,000             6,000               6,000

 

Accounting Rate of Return Method

  1. Return on Average Investment Method

Return = Average Profit

= Total Profit/ Number of years

= 16,000/ 5

= 3,200

Average Investment    = Original Investment/ 2

= 40,000/ 2

= 20,000

Return on Average Investment = 3,200 x 100/ 20,000

= 16%

Problem No. 7

Swamy Industries Ltd purchased a machine with aproposal to replace it with a new machine five years ago. This machine canbe sold at its original price where its life is estimated to have 10 years. Suppose you are a cost account. Submit your recommendations after going through the available data below.

Particulars                                          Existing Machine                   New Machine

                                                            $                                              $

Initial                                                   25,000                                     50,000

Machine hours p.a.                             2,000                                       2,000

Wages per running hour                     1.25                                         1.25

Power per hour                                   .50                                           2.00

Indirect material p.a.                          3,000                                       5,000

Other expenses p.a.                            12,000                                     15,000

Cost of materials per unit                   1                                              1

Number of units

produced per hour                              12                                            18

Selling price per unit                          2                                              2

On fresh capital invested, the interest rate will be of 10%.

Solutions:

Statement of Profit and Cost:

Particulars                                          Existing Machine                   New Machine

                                                            $                                              $

Production p.a. (units)                        24,000                                     36,000

Selling price per unit                          2.00                                         2.50

Sales Value                                          48,000                                     72,000

Expenses:       

Materials                                            24,000                                     36,000

Wages                                                 2,500                                       2,500

Power                                                  1,000                                       4,000

Indirect material                                 3,000                                       5,000

Other expenses p.a.                            12,000                                     15,000

Depreciation                                       2,500                                       5,000

Interest                                                 –                                             3,750

45,000                                     71,250

 

Sales                                                    48,000                                     72,000

Less : Total Cost                                  45,000                                     71,250

Total profit                                          3,000                                       750

Cost per unit                                       1.87                                         1.98

Profit per unit                                     0.13                                         0.02

 

Result:

Particulars                                          Existing Machine                   New Machine

Cost of material (24,000 x 1)              24,000                                     36,000 (36,000 x 1)

Wages (2,000 x 1.25)                          2,500                                       2,500 (2,500 x 1.25)

Power (2,000 x .50)                             1,000                                       4,000 (2,000 x .2)

Cost per unit =                                  

(Total Cost/ No. of Units)                 45,000/ 24,000 = 1.87                        71,250/ 36,000 = 1.98

 

Interest Calculation:

Investment in New Machine                                       50,000

Less : Sale Value of Old Machine                               12,500

Depreciation                                                               25,000

Fixed Installment System                                            12,500

Hence, 5,000/ 2500 x 5 = 10

Fresh Installment                                                        37,500

 

i.e., interest rate on fresh installment at 10% will be,

37,500 x 10/ 100 = 3,750

Note:

Depreciation              Old Machine                          New Machine

= Cost/ Life

  1. 25,000/ 10 = 2,500 50,000/ 10 = 5,000

 

Problem No. 8

Given below are the data of a project. Rank accordingly!

  1. Pay back
  2. Accounting rate of return method
  • Net present value

Particulars                  Year                 Project A                    Project B                     Project C

                                    $                      $                                  $                                  $

Investment                  0                      30,000                         30,000                         30,000

Annual Savings            1                      13,800                         36,150                         –        

2                      13,800                         –                                          

3                      13,800                         –                                  46,827

The discount factor for each year is 0.909, 0.826 and 0.751 respectively.

Solution:

  1. Pay back

Year                 Project A                    Cumulative                 Project B                     Project C

                        Cash Inflows               Cash Inflows               Cash Inflows               Cash Inflows

1                      13,800                         13,800                         36,150                         –        

2                      13,800                         27,600                                                        

3                      13,800                         41,000                                                           46,827

 

Now,

1st Year + 2nd Year       =          13,800 + 13,800

=          27,600

Balance                       =          2,400

30,000

12/ 13,800 x 2,400 = 2 months 8 days, this means 2 years 2 months 8 days

12/ 36,150 x 30,000 = 10 months

12/ 46,827 x 30,000 = 7 months 23 days

 

  1. Accounting Rate of Return Method:

Return/ Original Cost Investment x 100

Project A         =          13,800/ 30,000 x 100

=          46%

Project B         =          12,050/ 30,000 x 100

=          40.16%

Project C         =          15,609/ 30,000 x 100

=          52.03%

  • Net Present Value:

As the cost of capital is not provided, let us assume 10% cut off rate. Now, according to the formula,

Year     Project A        p.v.      Discounted     Project B         Discounted     Project CDiscounted             Cash                            Factor             Cash                Factor             Cash         Factor

Inflows            at 10%                         Inflows                                    Inflows

            $                                  $                      $                      $                      $               $

1          13,800             0.909   1,254.20          36,150             32,860             –                      –         

2          13,800             0.826   11,398.80        –                                                                           

3          13,800             0.751   10,363.80        –                                            46,827             35,167

 

Particulars                              Project A                    Project B                     Project C

Total present value                 34,306.80                    32,860                         35,167

Less : Initial Cost                     30,000.00                    30,000                         30,000

Net Present Value                   4,306.80                      2,860                           5,167

Now, Ranking will be

Project                        Pay Back                     Accounting Rate of Return               NPV

A                      III                                             II                                              I

B                      II                                              III                                             III

C                      I                                               I                                               I

Note:

From the above table, it has been found that Project C is preferable. This is because the rank of Project C has come first in all three techniques. Hence, it is recommended.

Problem No. 9

Lal Ltd will soon purchase new machine to carry out the operations performed by labour. A and B are its alternative models.The following table has been given to find out the profitability statement, work out pay back period of the machine.

Particulars                                                      Machine A                              Machine B

Estimated life of machine (yrs.)                     5                                              6

Cost of machine ($)                                        1,50,000                                  2,50,000

Cost of indirect materials ($)                         6,000                                       8,000

Estimated savings in scrap ($)                                    10,000                                     15,000

Additional cost of maintenance ($)                19,000                                     27,000

Estimated savings in direct wages

employees not required (numbers)                150                                          200

Wages per employees ($)                               600                                          600

Ignore depreciation for tax calculation. Take taxation at 50%. Recommend a model and state your reasons.

Solution:

Particulars                                          Machine A                  Machine B

$                                  $

Cost of the machine                            1,50,000                      2,50,000

Savings

Estimated saving in scraps                 10,000                         15,000

Estimated saving in

Direct Wages (150 x 600)                   90,000                         1,20,000

Total Savings                                       1,00,000                      1,35,000

Expenses                                             8,000                           6,000

Cost of Indirect materials                   27,000                         19,000

Additional cost of maintenance          35,000                         35,000

Total Expenses:                                 

Saving                                                  75,000                         1,00,000

Less : Tax 50%                                     37,500                         50,000

Net Saving (after tax)                         37,500                         50,000

 

Pay Back Period:

Original Cost/ Cash Inflow      =          1,50,000/ 37,500                     =          2,50,000/ 50,000

=          4 years for Machine A                        =          5 years for Machine B

As the pay back period for Machine A  is4 years, it is recommended because of its shorter pay back period.

Note:

Here, the depreciation is not considered.

Problem No. 10

A Ltd company is ready to invest money in a new project that requires an initial capital of $2,00,000. The following table has been with data:

Year                             $

1                                  1,00,000

2                                  1,00,000

3                                  80,000

4                                  80,000

5                                  40,000

Consider 20% depreciation on original cost and 50% taxation of net income. Determine the following according to the above statistics

  1. Pay back method
  2. Rate of return on original investment
  • Rate of return on average investment
  1. Discounted cash flow method with cost of capital at 10%
  2. Net present value index method
  3. Internal rate of return method

Solution:

Profitability Statement

Year     Profit after                 Less                 PAT                 Add                 Profit before

            Depreciation              Tax                                          Depreciation  Depreciation

            $                                  $                                              $                      but after tax ($)

1          1,00,000                      50,000             50,000             40,000             90,000

2          1,00,000                      50,000             50,000             40,000             90,000

3          80,000                         40,000             40,000             40,000             80,000

4          80,000                         40,000             40,000             40,000             80,000

5          40,000                         20,000             20,000             40,000             60,000

 

  1. Pay back period

1st Year                        90,000

2nd Year                       90,000

1,80,000

Balance                       20,000

2,00,000

The balance amount that will be recovered from 3rd year will be,

12 months/ 80,00 x 20,000 = 3 months

This means,

Pay back period = 2 years 3 months

 

  1. Rate of return on original investment method

Year                                         Net profit after tax and depreciation ($)

1                                                                      50,000

2                                                                      50,000

3                                                                      40,000

4                                                                      40,000

5                                                                      20,000

Total                                                               2,00,000

We know that,

Rate of Return on Original Investment = Return/ Original Investment

Return represents the Average Return, it should be calculated by;

Total Return/ Number of Years          =          2,00,000/ 5

=          $40,000

Thus,

Rate of Return on Original Investment = 40,000/ 2,00,000 x 100

= 20%

  • Rate of return on average investment method

Return = Average Investment x 100

Where,

Return = $40,000

Average Investment    = Original Investment/ 2

= 2,00,000/ 2

= 1,00,000

Hence, Rate of Return on Average Investment = 40,000/ 1,00,000x 100

= 40%

  1. Discounted cash flow method with cost of capital at 10%

Year                 Cash Inflows               Discount Factor         Present Value at 10% p.a.

1                      90,000                         0.909                                       81,810

2                      90,000                         0.826                                       74,340

3                      80,000                         0.751                                       60,080

4                      80,000                         0.683                                       54,670

5                      60,000                         0.621                                       37,260

Total Present Value    = $3,08,130

Initial Investment        = $2,00,000

Net Present Value       = 1,08,130

  1. Net present value index method

Total present value of cash inflows = Total present value of cash outflows

= 3,08,130/ 2,00,000

=1.541

Hence,

1.541 x 100 = 154.1%

  1. Internal rate of return method

As the annual cash inflows are not uniform, we will apply the formula,

Rate of Return, F = I/ C

Where,

F = Factor to be located

I = Initial Investment

C = Average Annual Cash Inflow

Hence,

F = 2,00,000/ 80,000

= 2.5

Showed in Table no. II, at this rate of return for 5 years is 28%

Now, discounted cash flow at 28% cost of capital

Year                 Cash Inflows               Discount Factor         Discounted Cash at 28% Inflows

1                      90,000                         0.781                                       70,290

2                      90,000                         0.610                                       54,900

3                      80,000                         0.477                                       38,160

4                      80,000                         0.373                                       29,840

5                      60,000                         0.291                                       17,460

 

Total Present Value    = $2,10,650

Less: Initial Investment= $2,00,000

Excess Present Value  = 10,650

Note:

As the present value if higher on $10,650, we will apply higher discount rate at 30% cost of capital.

Now, discounted cash flow at 30% cost of capital

Year                 Cash Inflows               Discount Factor         Discounted Cash at 30% Inflows

1                      90,000                         0.769                                       69,210

2                      90,000                         0.592                                       53,280

3                      80,000                         0.455                                       36,400

4                      80,000                         0.350                                       28,000

5                      60,000                         0.269                                       16,140

 

Total Present Value    = $2,03,030

Less: Initial Investment= $2,00,000

Excess Present Value  = 3,030

Note:

Thus, the excess present value comes $3,030 at 30% cost of capital. The internal rate of return will be then slightly greater than 30%. Moreover, small changes will not affect in huge level in the organization. Hence, for this case, the internal rate of return will be more or less than 30%.

Result and Decision:

With the investigation of project by applying all the techniques, it shows that new project seems to be attractive.

Problem No. 11

Madura Limited is expecting to replace their 5-year-old operational machine with a new machine. Neglect the interest while considering tax at 50%, suggest which of these two alternatives would be preferable.

Particulars                                          Old Machine                          New Machine

Purchase Price            ($)                               40,000                                     60,000

Estimated life of machine                  10 years                                  10 years

Machines running hours p.a.              2,000                                       2,000

Units per hour                                     24                                            36

Wages per running hour                     3                                              5.25

Power p.a.                                           2,000                                       4,500

Consumable stores per annum           6,000                                       7,500

Al other charges per annum               8,000                                       9,000

Materials cost per unit .50 .5fJ

Selling price per unit                          1.25                                         1.25

 

Assume that the information on cost of sales will remain throughout the economic life of both machines. As per the straight line method, the depreciation rate will be changed.

Solution:

Particulars                                          Old Machine                          New Machine

Cost of the machine ($)                      40,000                                     60,000

Life of the machine (years)                10                                            10

Output units 48,000 and 72,000

Sales Value                                          48,000 x 1.25 = 60,000           72,000 x 1.25 = 36,000

Less: Expenses

Material                                              48,000 x .50 = 24,000             72,000 x 0.50 = 36,000

Wages                                                 6,000                                       10,500

Power                                                  2,000                                       4,500

Consumable Stores                             6,000                                       7,500

Other Charges                                                8,000                                       9,000

Depreciation                                       4,000                                       6,000

50,000                                     73,500

Profit Before Tax                                10,000                                     16,500

Less: Tax 50%                                      5,000                                       8,250

Profit After Tax                                   5,000                                       8,250

Working:

Accounting Rate of Return:

  1. Return on original investment:

Average Net Earnings/ Original Investment

= 5,000/ 40,000 x 100                         and                  8,250/ 60,000

= 12.3%                                                                       13.75%

  1. Return on Average Investment Method:

Return/ Average Investment x 100

= 5,000/ 20,000 x 100                         and                  8,250/ 30,000

= 25%                                                                          27.5%

  1. Return on Incremental Investment:

Incremental Earnings/ Incremental Investment x 100

= 3,250/ 20,000 x 100                         and                  3,250/ 40,000 x 100

= 16.25%                                                                     8%

 

Note:

Incremental Earning               =          6250 – 5000                = $1,250

Incremental Investment         =          60,000 – 40,000          =  $20,000

Result:

It is thus recommended to replace the old machine by a new one.

Problem No. 12

Calculate the pay back period. For a project, the annual cash inflow is of $20,000 for 7 years for its initial cost of $1,00,000.

Solution:

Pay back period = Initial Investment/ Annual Cash Inflow

Here,

Initial Investment = $1,00,000

Annual Cash Inflow = $20,000

Pay back period = 1,00,000/ 20,000

= 5 years

Problem No. 13

Himalaya Construction Ltd. is looking for purchasing new machinery for its immediate expansion of the programme. Following data has been collected from the organization:

Particulars                              Machines 1                 Machines 2                 Machines 3

$                                  $                                  $

Capital Cost                             3,00,000                      3,00,000                      3,00,000

Sales at standard price           5,00,000                      4,00,000                      4,50,000

Net cost of production

of the machines:

Direct Material                       40,000                         50,000                         48,000

Direct Labour                          50,000                         30,000                         36,000

Factory Overheads                  60,000                         50,000                         58,000

Administration Costs               20,000                         10,000                         15,000

Selling and Distribution Costs 10,000                         10,000                         10,000

The scrap values of all the machines are $40,000, $25,000 and $30,000 respectively. The economic life of machine 1 is 2 years whereas other two have 3 years. The sales will be at the rates shown for each year during full economic life of expenditure that resultsfrom each machine.

Considering the tax paid at 50% net earnings per annum, it is assumed to settle down all its payables and receivables. The interest capital has set at 8% per annum. Calculate using pay back method which machine will be the most profitable one.

Solution:

Profitability Statement:

Particulars                                          Machines 1                 Machines 2                 Machines 3

$                                  $                                  $

Capital Cost                                         3,00,000                      3,00,000                      3,00,000

Sales at standard price                       5,00,000                      4,00,000                      4,50,000

Less: Expenses

Cost of Production                              1,50,000                      1,30,000                      1,42,000

Administration Cost                            20,000                         10,000                         15,000

Selling and Distribution Cost              10,000                         10,000                         10,000

Total Cost II                                         1,80,000                      1,50,000                      1,67,000

Profit before depreciation

and interest (S – RC) [i – ii] (iii)          3,20,000                      2,50,000                      2,83,000

 

Less: Depreciation                              1,30,000                      91,667                         90,000

Interest on borrowings                       24,000                         24,000                         24,000

Depreciation and

Interest (iv)                                         1,54,000                      1,15,667                      1,14,000

Profit before tax

(iii – iv = v)                                          1,66,000                      1,34,333                      1,69,000

Less: Tax 50%                                      83,000                         67,167                         84,500

Profit after tax                                                83,000                         67,167                         84,500

Add: Depreciation                               1,30,000                      91,667                         90,000

Net Cash Inflows                                 2,13,000                      1,58,834                      1,74,500

Hence,

Pay back period                                  1.41 years                   1.89 years                   1.72 years

 

Result:

Here, Machine 1 will be preferred because of shorter pay back period.

Working:

  1. Pay back period

Machine 1                              $2,13,000

1st Year                                    $87,000

Balance                                   $3,00,000

 

= 12 month/ 2,13,000 x 87,000

= 4 months

This means pay back period will be 1 year 4 months.

Machine 2                              $1,58,834

1st Year                                    $1,41,166

Balance                                   $3,00,000

= 12 month/ 1,58,834 x 1,41,166

= 10 months

This means pay back period will be 1 year 10 months.

Machine 3                              $1,74,500

1st Year                                    $1,25,000

Balance                                   $3,00,000

 

= 12 month/ 1,74,500 x 1,25,000

= 9 months

This means pay back period will be 1 year 9 months.

Result:

As per pay back period method, Machine 1 is preferred because of its shorter pay back.

  1. Depreciation:

Cost – Scrap/ Life

Machine 1                              Machine 2                              Machine 3

3,00,000 – 40,000/ 2               3,00,000 – 25,000/ 3               3,00,000 – 30,000/ 4

= 1,30,000                               91,667                                     90,000

Problem No. 14

The ABTS Co. Ltd. is expected to purchase a new machine. For this reason, two different machines are suggested. Each of these machines have initial cost of $4,00,000 along with the requirement of additional $20,000 at the end of 1st year. The following data shows the earnings after taxation:

Cash Inflows                           A                                  B

 (Year)                                     $                                  $

1                                              40,000                         1,20,000

2                                              1,20,000                      1,60,000

3                                              1,60,000                      2,00,000

4                                              2,40,000                      1,20,000

5                                              1,60,000                      80,000

It has target return on its capital of 10%. Compare the profitability of machines and suggest which machine to consider for financially preferable.

Note:

Following table represents the present value of Re. 1 due in ‘ n’ number of years:

Year                 1                      2                      3                      4                      5

PIV at 10%      0.91                 0.83                 0.75                 0.68                 0.62

Solution:

Present Value Statement

Machine A:

Year                 Cash Inflows                                       Discount                     Present Value

                        ($)                                                        Factor at 10%             ($)

1                      40,000                                                 .91                               36,400

2                      1,20,000                                              .83                               99,600

3                      1,60,000                                              .75                               1,20,000

4                      2,40,000                                              .68                               1,63,200

5                      1,60,000                                              .62                               99,200

Total Present Value of Cash Inflows                                                               5,18,400

Less: Total Present Value of Cash Outflows

(4,00,000 + 20,000 x 0.91)                                                                              4,18,200

Net Present Value                                                                                           1,00,200

Machine B:

Year                 Cash Inflows                                       Discount                     Present Value

                        ($)                                                        Factor at 10%             ($)

1                      1,20,000                                              .91                               1,09,200

2                      1,60,000                                              .83                               1,32,800

3                      2,00,000                                              .75                               1,50,000

4                      1,20,000                                              .68                               81,600

5                      80,000                                                 .62                               49,600

Total Present Value of Cash Inflows                                                               5,23,200

Less: Total Present Value of Cash Outflows

(4,00,000 + 20,000 x 0.91)                                                                              4,18,200

Net Present Value                                                                                           1,05,000

Result:

After finding the result, it has been found that Machine B will be preferable. This is because it has higher net present value as compared to Machine A. Hence, Machine B is recommended.

Problem No. 15

A company is expected to have two exclusive projects. With an initial cash outlay of $10,000, each has a life of 5 years.Its rate of return is 10% and taxation at 50%. If the project is depreciated on straight line basis, the before tax cash flows is expected to be:

Before Tax Cash Flows

Year                             1                      2                      3                      4                      5

Project A                    4,000               4,000               4,000               4,000               4,000

Project B                     5,000               5,000               5,000               5,000               5,000

Calculate:

  1. The pay back
  2. Accounting rate of return
  3. NPV
  4. PI

Also, suggest which project should be accepted and why?

Solution:

Profitability Statement

Project A:

Year     Cash Flows      Less:                TAX                 Less: PAT         Add: (PAT                   Cash

                                    Depreciation                                                  but before                  Inflow

                                    PBT                                                                  Depreciation

1          4000                2000                2000                1000                1000 + 2000                3000

2          4000                2000                2000                1000                1000 + 2000                3000

3          4000                2000                2000                1000                1000 + 2000                3000

4          4000                2000                2000                1000                1000 + 2000                3000

5          4000                2000                2000                1000                1000 + 2000                3000

Now,

  1. The pay back

Pay back period = 3 years 4 months

1st year                        3,000

2nd year           3,000

3rd year            3,000

9,000

Balance           1,000

To recover the balance amount of $1000 in how many months, this will be;

12/ 3,000 x 1,000

= 4 months

This means3 years 4 months

  1. Accounting rate of return

Return/ Original Investment x 100

Return = Average Profit (i.e., profit after tax)

ARR Total Profit = Average Profit

= Total Profit/ Number of Years

= 5,000/ 5

= 1,000

Hence,

ARR     = 1,000/ 10,000

= 10%

Project B:

Year     Cash Flows      Less:                TAX                 Less: PAT         Add: (PAT                   Cash

                                    Depreciation                                                  but before                  Inflow

                                    PBT                                                                  Depreciation

1          5000                2000                3000                1500                1500 + 2000                3500

2          5000                2000                3000                1500                1500 + 2000                3500

3          5000                2000                3000                1500                1500 + 2000                3500

4          5000                2000                3000                1500                1500 + 2000                3500

5          5000                2000                3000                1500                1500 + 2000                3500

Now,

  1. The pay back

Pay back period = 3 years 3 months

1st year                        3,500

2nd year           3,500

3rd year            2,000

9,000

Balance           1,000

To recover the balance amount of $ 1000 in how many months, this will be;

12/ 3,500 x 1,000

= 3 months

This means3 years 3 months

  1. Accounting rate of return

Return/ Original Investment x 100

Return = Average Profit (i.e., profit after tax)

ARR Total Profit = Average Profit

= Total Profit/ Number of Years

= 6,000/ 5

= 1,200

Hence,

ARR     = 1,200/ 10,000

= 12%

  1. NPV

Statement showing the Net Present Value

Project A:

Year                 Cash Inflows               p/v factor at 10%                  Discounted Cash Inflows

1                      3,000                                       0.909                                       2727

2                      3,000                                       0.826                                       2478

3                      3,000                                       0.751                                       2253

4                      3,000                                       0.683                                       2049

5                      3,000                                       0.621                                       1863

Total Present Value of Cash Inflows                                                               11,370

Less: Initial Cost                                                                                              10,000

Net Present Value                                                                                         1,370

 

Project B:

Year                 Cash Inflows               p/v factor at 10%                  Discounted Cash Inflows

1                      3,500                                       0.909                                       3181.50

2                      3,500                                       0.826                                       2891.00

3                      3,500                                       0.751                                       1502.00

4                      3,500                                       0.683                                       2390.00

5                      3,500                                       0.621                                       2173.50

Total Present Value of Cash Inflows                                                               12,138.00

Less: Initial Cost                                                                                              10,000.00

Net Present Value                                                                                         2,138

  1. PI

Probability Index         = Sum of Discounted Cash Inflows/ Cash Outflows x 100

= 11,370/ 10,000 x 100                                                                                                                       = 121,38%(Project A)

 

= 12,138/ 10,000 x 100

= 113.7% (Project B)

Note:

Project                                    Pay Back                     ARR                 NPV                 PI

A                                  II                                  II                      II                      II

B                                  I                                   II                      II                      II

Result:

After above calculation, it has been predicted that Project B is preferable. This is because of the four aspects of Project B and its Rank I in three techniques.

Problem No. 16

A small project with an initial investment of $20,000 has net cash flow of $6,000 for six years. Calculate the net present value. Assume the cost of funds to be at 8% per annum with no scrap value.

Solution:

The present value of an annuity of Re. 1 for 6 years at 8% per annum as per the annuity table is $4.623

Hence,

The present value of $6,000 will be;

6,000 x 4.623 = 27,738

Less: Original Cost      =          20,000

Net Present Value       =          7,738

Problem No. 17

The cash inflows of the equipmentis considered as $2,00,000 per year for the next 5 year. Its initial cost is $3,00,000 and the rate of return is 15%. Determine the excess present value index and net present value.

Solution:

Present value of Re. 1 received annually for 5 years at 15% as per annuity Table is 3.352

Present value of $2,00,000 received annually for 5 years will be;

$2,00,000 x 3×352 = 6,70,400

Less: Original Cost of the equipment = 3,00,000

Net Present Value = 3,70,400

Therefore,

Excess present value index will be;

Total present value of cash inflows/ Total present value of cash outflows

= 6,70,000/ 3,00,000 x 100

= 223.4

Problem No. 18

KVP Ltd. is expected to purchase a new machine with 4 years of estimated life for $1,20,000 and its scrap value is estimated to $20,000. This machine can generate extra revenue of $4,00,000 per annum with an additional operating cost of $3,20,000 per annum.The taxation is of 50% and cost of capital of the company is 20%. Suggest whether the machine should be purchased or not.

Solution:

Profitability Statement

Annual Revenue                                                          4,00,000

Less: Operational Costs                                              20,000

Net Income Before Depreciation and Tax                  80,000

Initial Investment                                                        1,20,000

Less: Scrap                                                                  20,000

Life of the Machinery                                                 4 years

Depreciation                                                               1,00,000/ 4,25,000

Tax Rate                                                                      50%

Net Income Before Depreciation and Tax                  80,000

Less: Depreciation                                                      25,000

Less: Tax                                                                      50%

Net Income After Tax and Depreciation                    27,500

Add: Depreciation                                                       25,500

Cash Inflows                                                                52,500

Present Value of Re. 1 for 4 years at 20%

52,500 x 2.588                                                                        1,29,400

Less: Initial Investment

(1,00,000 + 10,000 x 0.482)                                        1,09,640

Hence,

Net Present Value = $19,760

Result:

After the calculation, the NPV has positive value. This means that machine should be purchased.

Problem No. 19

Sumanth& Co. Ltd is expected to build a new assembly plant. After coming to a certain point, the company has decided two possibilities. Both these plants would have expected life of 10 years and none of them is expected to have salvage value after retirement. The company is looking for choosing the best plant with 10,000 gadgets production per month.

If the cost of capital is 10%, then suggest the desirable choice between these two.

Cost of monthly output/ production of 10,000 units

Particulars                              Large Plant                             Small Plant

$                                              $

Initial Cost                               30,00,000                                22,93,500

Direct Labours:

First Half (p.a.)                                    15,00,000                                7,80,000

Second Half-

Overheads (p.a.)                     2,40,000                                  2,10,000

The present value of ordinary annuity of Re.1 at 10% for 10 years is 6.1446.

Solution:

Profitability Statement:

The direct labour for small plant for both shifts will be

(7,80,000 + 9,00,000)                                                                          16,80,000

Now,

Direct labour for large plant                                                              15,00,000

The savings in indirect labourfor large plant                                     1,80,000

Hence,

Overhead costs for small plant operation                                          2,10,000

Less: Overhead costs for large plant operation                                 2,40,000 – 30,000

Therefore,

Net savings p.a. by using large plant = $50,000

 

 

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