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Test Question of Capital Budgeting

  1. What is meant by Capital Budgeting.

 

  1. Explain the concept of Capital Expenditure.

 

  1. Define Capital Budgeting.

 

  1. Explain the need and importance of C:apital Budgeting.

 

  1. What are the advantages of Capital Budgeting ?

 

  1. Explain the limitations of Capital Budgeting.

 

  1. What are the principle methods employed for ascertaining the profitability of a capital      expenditure project ?’

 

  1. Give a comparative description of net present value method and internal rate of return method.

 

  1. “Capital budgeting is long-term planning for making and financing proposed capital outlays Explain. What are the limitation of capital budgeting ?

 

  1. “For most investment decisions that a firm faces net present value is either a superior       decision criterion or is at least as good as the competing technique”. In what investment situation  is the profitability index better than the net present value ?

 

  1. Under what circumstances may NPV and IRR give conflicting recommendatwns ? Which criteria should be followed in such circumstances and why ?

 

  1. Briefly explain the steps involved in the control of capital expenditure in a large scale organizations.

 

PROBLEMS AND SOLUTIONS

 

Problem 1. Each of the following projects requires a cash outlay of $ 10,000. You are required to suggest which project should be accepted if the standard pay back period is 5 years.

 

Year               Project X                    Project Y                     Project Z

$                      $                                   $                                  $

1                  2500                           4000                           1000

2                  2500                            3000                            2000

3                  2500                            2000                           3000

4                  2500                            1000                           4000

 

 

Solution:

 

All the three projects recovered their original capital $ 10,000 within the period of 4 years. Here project X has constant cash inflow. Project Y initially has higher cash inflows but gradually decreased.

 

Project Z initially has low cash inflows but it has gradually incrl’ased.

As per the constant return point of view, project X is recommended.

 

Problem 2. A Company has to choose one of the following two mutually exclusive  projects. Both the projects have to be depreciated on straight line basis. The tax rate is 50%.

 

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

 

You have to use pay-back period as the criterion.

 

                                       (-)  profitAfter

Year  Profit   Depreciation   Depreciation   Tax

$             $                    $                 $

1.       4200         3000            1200         600

2.       4800         3000             1800         900

3.      7000          3000            4000         2000

4.       8000         3000            4000         2000

5.       2000         3000            -1000            -

 

 

PAT           Add

$        Depreciation

600              3000

900              3000

2000              3000

2000               3000

1000             3000

                  cumulativeCash             Cash

Inflows         Inflows

$                  $.

3600                 3600

3900                   7500

5000              12500

5000            17500

2000               19500

[PAT = Profit After Tax]

 

Pay back period = 3 years and 6 months

 

Working :

 

Investment is $15,000

Upto three years i.e., first three years

Capital recovered is $ 12,500

Balance of $. 2500 recovered during the 4th year

I year                           3,600

II year                                     3,900

III year                        5,000

12,500

Balance                       2,500

15,000

 

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

 

Time taken for recovery of this amount of $ 2,500 = 6 months. Pay back period = 3 years 6 months.

 

Project-B

 

                                       (-)  profitAfter

Year  Profit   Depreciation   Depreciation   Tax

$             $                    $                 $

1.       4200         3000            1200         600

2.       4500         3000             1500         750

3.      4000          3000            1000         500

4.       5000         3000            2000         2000

5.       1000         3000            7000         7000

 

 

PAT           Add

$        Depreciation

600              3000

750              3000

500              3000

1000               3000

3500             3000

                  cumulativeCash             Cash

Inflows         Inflows

$                  $.

3600                 3600

3700                   7350

3500                 10850

4000            14850

6500              21350

 

(pat =profit after tax)

 

NOTE : If necessary only prepare cumulative cash inflows, otherwise there is no need.  Pay back period = 4 years and 8 days

 

Result and decision : Project A is preferable, because it has a shorter pay back period as compared to project A

 

Workings                     Initial investment is $ 15,000

Its recovered :

I year                           3,600

II year                         3,750

III year                                    3,500

IV year                        4,000

14,850

Balance 150

15,000

 

Time taken for recovery of this amount $. 150/- = 8 days.

For recovery of $ 6,500 in the 5th year.

Time required = 365 days.

For recovery of $. 150 in the 5th year.

Time required = /6,500 x 150 8 days

 

 

Depreciation :Project A

Cost /life =  15,000 / 5 years = $ 3,000

Project B

15,000 /5 years = $ 3,000

 

 

Problem 3. Using the information given below, compute the pay-back period under (a)

Traditional pay-back method and (b) Discounted pay-back method

        Initial outlayEstimated life

Profit after tax

End of the years

5 years

year 1

2

3

4

5

$ 80,000 

$ 6,000

$ 14,000

$ 24,000

$ 16,000

Nil

 

Depreciation has been calculated under straight line method. The cost of capital may be taken 20% p.a. and the PV of Re. 1 at 20% p.a. is given below.

 

Year                  1          2          3          4          5

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

 

                                                      Profit beforePAT           Add            Depreciation

Year        (A)          Depreciation    but after Tax

$                     $                       $

1            6,000         + 16,000             = 22,000

2           14,000       + 16,000             = 30,000

3           24,000      + 16,000              = 40,000

4           6,000        + 16,000                = 22,000

5           Nil             + 16,000               = 16,000

 

 

 

 

(a) Traditional payback method

I year $

II year $

Amount recovered for 2 years

Balance $

          P/ V factor at20%

 

.83

.69

.58

.48

.40

Total present value

Less : Initial investment

Net Present Value

 

 

22,000

30,000

52,000

28,000

80,000

PresentValue

 

 

18,260

20,700

23,200

15,360

6,400

83,920

80,000

3,920

 

 

 

III year profit is $. 40,000. But we require only $ 28,000 to meet the original investment

of $ 80,000

 

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

 

i.e., 2 years 8 months(b) Discounted pay back method

I year

II year

III year

IV year

Balance $

Project cost

 

18,260

20,700

23,200

15,360

77,520

2,480

80,000

 

In the V year cash inflow is $ 6400. But actually we require only $ 2480 to meet the

original investment of $ 80,000

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

 

i.e., 4 years 4 months

Pay back period = 4 year· 4 months

 

NOTE : Depreciation :

Cost/Life=80,000/5= 16,000

 

Problem 4. A choice is to be made between two competing proposals which require an equal investment of $ 50,000 and are expected to generate net cash flows as under.

 

Year                Project              Project II                    P/V at 10% P.a.

$                          $

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

 

Which project proposal should be chosen and why ? Evaluate the project proposals under

discounted cash flow methods

 

        Year                         Project I$

1                        25,000

2                         15,000

3                         10,000

4                                 Nil

5                         12,000

6                            6,000

Project II$

10,000

12,000

18,000

25,000

8,000

4,000

 

Pay back period under Traditional method

 

Project I

I year               25,000

II year             15,000

III year                        10,000

50,000

 

Pay back period is 3 years.

Project II

I year               10,000

II year             12,000

III year                        18,000

40,000

Balance           10,000

50,000

2/25,000 x 10,000 =4.8 i.e; 4

As per Traditional pay back period Project I is recommended because it has shorter pay

back period.

 

Discounted cash flow method

 

                 Project IYear        Cash Inflows        Discount

$                      Factor at

10% p.a

1              25,000                      .909

2              15,000                    .826

3              10,000                     .751

4                 Nil                       .683

5               12,000                   .621

6             6,000                      .564

 

 

 

Total present value

Less : Original Cost

Net Present Value

Present

Value

$

22,725

12,390

7,510

-

7,452

3,384

 

 

 

53,461

50,000

3,461

      Cash Inflows     Discount$            Factor at

year                     10% p.a

 

1          10,000          .909

2          12,000          .826

3         18,000           .751

4          25,000          .683

5          8,000            .621

6          4,000            .564

 

 

 

Total present value

Less : Original Cost

Net Present Value

PresentValue

$

9,090

9,912

13,518

17,075

4,968

2,256

 

 

 

 

56,819

50,000

6,819

 

      CriteriaPay back period

NPV

Project X3 years

$ 3,491

      Project Y3 years 4 months

$ 6,819

 

As per the pay back period point of view, Project X is recommended. But by NPV point

of view, Project Y is recommended because it has surplus of $ 6,819.

 

Problem 5 . .A project costs $ 5,00,000 and yields annually a profit of $ 80,000 after

depreciation at 12% p.a. but before tax of 50%. Calculate pay back period.

 

Solution:

 

Pay back period =Original Cost/Annual Cash Inflows

Initial investment = $ 5,00,000

Cash inflows = Profit after tax plus Depreciation

Profit before Tax =

Less : Tax 50% =

profit after Tax =

Add : Depreciation =

Annual cash inflows =

Pay back period  =

$

80,000

40,000

40,000

60,000

1,00,000

5,00,000 /1 00 000  5 years

 

NOTE : Depreciation = 5,00,000 x12/100 = 60,000

 

Problem 6. ABC Ltd is proposing to take up a project which will need an investment of $ 40,000. The net income before depreciation and tax is estimated as follows.

 

Year                                        $

1                                              10,000

2                                              12,000

3                                              14,000

4                                              16,000

5                                              20,000

 

Evaluate the project proposal under accounting Rate of Return Method.

 

Solution:

 

Year          Net Income             Less                  Profit after

before Depreciation    Depreciation      Depreciation

and Tax                     $                       before Tax

$                                                        $

1           10,000                        8,000                     2,000

2            12,000                       8,000                     4,000

3            14,000                      8,000                      6,000

4           16,000                       8,000                       8,000

5           20,000                        8,000                      12,000

Less tax

50%

$

 

1,000

2,000

3,000

4,000

6,000

Profit after

Tax and

Depreciation

$

1,000

2,000

3,000

4,000

6,000

 

Accounting Rate of Return

 

(i) Return on Average Investment Method

Return = Average profit

= i.e., Total Profit/ No . 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 7. Swamy Industries Ltd purchased a machine five years ago. A proposal is under consideration to replace it by a new machine. The life of the machine is estimated to be 10 years. The existing machine can be sold at its written down value. As the cost accountant of the company you are required to submit your recommendations based on the following information.

 

 

Particulars                            Existing Machine

Initial cost                     ($)                                          25,000

Machine hours P.a.                              2,000

Wages per running hour  $                                                1.25

Power per hour                $                                                .50

Indirect material P.a.       $                                             3,000

Other expenses P.a.         $                                             12,000

Cost of materials per unit                                                    1

Number of units produced

Per hour                                               12

Selling price per unit                                                     2

New Machine

50,000

2,000

1.25

2.00

5,000

15,000

1

18

2

 

Interest to be paid at 10% on fresh capital invested.

 

Solution :                      Statement of profit and cost

 

 

 

Production p.a. (units)

Selling price per unit $

Sales value $

Expenses :

(i) Materials

(ii) Wages

(iii) Power

(iv) Indirect material

(v) Other expenses p.a.

(vi) Depreciation

(vii) Interest

 

 

Sales

Less : Total cost

Total profit

(viii) Cost per unit

Profit per unit

 

Workings:

Existing

Machine $

24,000

2.00

48,000

 

24,000

2,500

1,000

3,000

12,000

2,500

-

45,000

 

48,000

45,000

3,000

1.87

0.13

New machine

$

36,000

2.50

72,000

 

36,000

2,500

4,000

5,000

15,000

5,000

3,750

71,250

 

72,000

71,250

750

1.98

0.02

 

 

 

 
 

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

(ii) Wages (2,000 x 1.25)

(iii) Power (2,000 x .50)

(iv) Cost per unit =

 

Total Cost / Number of Units

 

(v) Interest calculation

 

 

Existing Machine

24,000

2,500

1,000

45,000/24 000 = 1·87 ‘

 

 

 

Investment in new machine

Less : Sale value of the old machine

($ 25,000 – Depreciation

$. 12,500 on fixed instalment

system)

i. e;5,000 =2 500×5=12 500) i.e., 10

 

fresh Investment

New Machine

36,000 (36,000 X 1)

2,500 (2,000 X 1.25)

4,000 (2,000 X .2)

71,250 /36,000 = 1.98

 

 

 

50,000

12,500

 

 

 

 

 

37,500

 

. . Interest @ 10% on fresh investment is as follows.

 

37500 x 10/ 100 = 3,750

 

(vi) Depreciation =cost  / = Life          Old machine                                      New machine

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

 

Problem 8. Rank the following projects on the basis of

(a) Pay back

(b) Accounting rate of return method

(c) Net present value

 

Particulars                     Year                         Project A

$                                  $

Investment                     0                                 30,000

Annual savings             I                                  13,800

II                                  13,800

III                                  13,800

         Project B                     Project C

$                                 $

30,000                       30,000

36,150                           -

-                                -

-                            46,827

 

Discount factor for the year I, II, III, are 0.909, 0.826, 0. 751 respectively.

 

Solution:

(a) Pay Back

 

   Year                       Project A

Cash Inflows

1                          13,800

2                            13,800

3                              13,800

             Cumulative

Cash Inflows

13,800

27,600

41,400

   Project B                        Project C

Cash Inflows              Cash Inflows

36,150                               -

-                                        -

-                                     46,827

 

 

A.    I year 13,800 + II year 13,800 = 27,600

Balance = 2,400

30,000

 

12/13,800  x 2,400 = 2 months 8 days i.e., 2 years 2 months 8 days.

 

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

 

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

 

(b) 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%

 

(c) Net Present value

 

If cost of capital detail is not given in the problem, we have to assume 10% as cut off rate.

 

 

Project A         P.V.     Discounted      Project B      Discounted     Project C      Discounted

Year    Cash              Factor      Cash                Cash             Cash              Cash                   Cash

Inflows            at 10%     Inflows         inflows          Inflows            Inflows             Inflows

$                        $             $                     $                  $                        $                      $.

1       13,800               0.909       12,54 .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

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

 

Project             Pay back          Accounting Rate of                           NPV.

Return

A                     III                                II                                             II

B                     II                                 III                                           III

C                     I                                  I

I

 

As per the above Ranking table project C is preferable. It gets· I rank in the application of all the three techniques. So it is recommended.

 

Problem 9. Lal Ltd is considering the purchase of a new machine which will carry out operations performed by labour. A and B are alternative models. Prepare profitability statement and work out pay back period in respect of each machine based upon the following information.

 

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 employee ($)                                              600                                         600

 

Taxation is to be regarded as 50% of profit(ignore depreciation for calculation of tax).

Which model would you recommend ? State your reasons. [M.Com May 2000 PU]

 

Solution :                       Profitability Statement

 

                                                                 Machine

A

 

Cost of the machine                                 1,50,000

Savings

Estimated saving in scrap                          10,000

Estimated saving in Direct wages

[150 X 600]                                                 90,000

Total Savings                          1,00,000

 

Expenses

Cost of indirect materials                             6,000

Additional cost of maintenance                 19,000

Total Expenses                    25,000

Savings [Sayings -- Expenses]                     75,000

Less . Tax 58%                                               37,500

Net saving [after tax)                                     37,500

Machine

B

$

2,50,000

 

15,000

 

1,20,000

1,35,000

8,000

 

27,000

35,000

 

1,00,000

50,000

50,000

 

 

Pay  back period

 

 

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

= 4 years                 = 5 years

 

 

Pay back period in case of machine A is 4 years; machine B is 5 years. A has the shorter pay back period so it should be recommended.

 

 

NOTE : Here Depreciation is not taken into account.

 

 

Problem 10. A Ltd company is considering to invest in a project requiring a capital outlay of $  2,00,000. Forecast for annual income after depreciation but before tax is as follows

 

 

Year                            $

1                                  1,00,000

2                                  1,00,000

3                                  80,000

4                                  80,000

5                                  40,000

 

Depreciation may be taken as 20% on original cost and taxation at 50% of net income.

 

 

you are required to evaluate the project according to each of the following methods.

(a) Pay-back method

(b) Rate of return on original investment method

(c) Rate of return on average investment method

(d) Discounted cash flow method taking cost of capital as 10%

(e) Net present value index method

(f) Internal rate of return method [M.Com Madurai] [MCA Madras]z

Solution :                      Profitability Statement

 

Year       Profit after

Depreciation

$

1             1,00,000

2            1,00,000

3               80,000

4              80,000

5               40,000

        Less

Tax

$

50,000

50,000

40,000

40,000

20,000

      PAT

$

 

50,000

50,000

40,000

40,000

20,000

      Add                    Profit before

Depreciation          Depreciation

$.                    but after tax $

40,000                           90,000

40,000                            90,000

40,000                            80,000

40,000                            80,000

40,000                               60,000

(a) Pay Back Period

I    year                        90,000

II   year                       90,000

1,80,000

Balance                       20,000

2,00,000

 

Balance amount recovered from III rd year

 

i.e.,       12 months / 80,000  x 20,000 = 3 months

 

Pay back period = 2 years 3 months.

 

(b) Rate of Return 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 Return                              2,00,000

 

Rate of Return on original investment = Return / Original investment

 

Return represents the Average Return

 

Average Return should calculate in the following

 

Total return / Number of years

2,00,000 / = 5

Average Return=$. 40,000

 

Rate of  return on original investment =  40,000 /2,00,000 x 100

= 20%

 

(c) Rate of Return on Average investment method

 

Return = Average Investment x 100

Return = $ 40,000

 

Average Investment = Original investment/ 2

 

2,00,000/ 2 = 1,00,000

 

Rate of  Return on average investment =40,000 /1,00,000  x 100 = 40%

 

(d) Discounted cash flow method [Cost of capital @ 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

 

(e) Net present value index

 

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

 

=3,08,130 /2,00,000 = 1.541

 

1.541 X 100 = 154.1%

 

(f) Internal Rate of Return method. The annual cash inflows are not uniform. We have to apply the following formula to determine the approximate rate of return.

 

F          = I/C

F          = Factor to be located

I           = Initial investment

C         = Average annual Cash inflow

F          = 2,00,000 /80,000

= 2.5

 

Showed Table No II at this factor rate of return in the column for 5 years is 28%.

 

Discounted cash flow [cost of capital @ 28%]

 

Year                       Cash Inflows               Discount Factor                      Discounted Cash

$                      At 28% Inflows                                  $

1                                  90,000                                    .781                                        70,290

2                                  90,000                                     .610                                        54,900

3                                  80,000                                     .477                                        38,160

4                                  80,000                                    .373                                         29,840

5                                  60,000                                     .291                                        17,460

 

Total Present values                            2,10,650

Less : Initial investment                      2,00,000

Excess Present Value                          10,650

 

NOTE : The present value is higher on the level of $ 10,650. Now we apply higher discount rate i.e., taking 30% as cost of capital.

 

Discounted cash flow at cost of capital is 30% 

 

Year                Cash Inflows               Discount Facto                       Discounted Cash

$.                     At 28%                                   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

 

The excess present value at 30% is $ 3,030. So the internal rate of return be slightly higher than 30%. Small amount will not affect huge level in the organisation. Hence, internal rate of return is more or less 30%.

 

Results and Decision :

 

Investigation of project with the help of all the techniques show that the new project seems to be fairly attractive.

 

Problem 11. The directors of Madura limited are contemplating the purchase of new machine to replace a machine which has been in operation in the factory for the last 5 years.

 

Ignoring interest but considering tax at 50% of net earnings, suggest which of the two alternatives should be preferred. The following are the details

 

Particulars                               Old Machine                           New Machine

Purchase price ($)                                40,000                                                 60,000

Estimated life of machine                   10 years                                               10 years

Machine 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 p.a.                       6,000                                                  7,500

All other charges p.a.                          8,000                                                  9,000

Material cost per unit .50 .5fJ

Selling price per unit                           1.25                                                     1.25

 

You may assume that the above information regarding sales and cost of sales will be held throughout the economic life of each machine. Depreciation has to be charged according to straight line method.

        Particulars                                     Old Machine                                      New Machine

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

Life of the machine (yrs)                             10                                                                10

Output units. 48,000 72,000

Sales value (48,000 x 1.25)                      60,000                    (72,000xl.25)                   90,000

Less : Expenses

Material 48,000 x .50              24,000                               (72,000 x .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            50,000                      6,000                        73,500

Profit before tax                                               10,000                                                     16,500

Less : Tax 50%                                                 5,000                                                        8,250

Profit after tax                                                   5,000                                                         8,250

 

 

Workings:

 

Accounting Rate of Return Old Machine

 

(i) Return on original investment

Average net earnings /Original investment

5,000 /40,000 x 100 = 12.3%              8,250/60,000 x 100 =13.75%

 

(ii) Return on Average Investment Method

 

Return / Average investment x 100

5,000 /20,000 x 100 =25%      8,250 / 30,000 x 100 =27.5%

 

(iii) Return on incremental investment

Incremental earnings /   Incremental investment x 100

 

= 3,250 /20,000 x 100 =16.25 %     or            3,250 /40,000 x 100 =8%

 

NOTE  :

 

Incremental earning    = 6250 –  5000            =  1250

Incremental investment = 60,000 – 40,000    = 20,000

 

Result  : Recommended to replace an old machinery.

 

Problem  12. A project costs $ 1,00,000 and yields an annual cash inflow of $ 20,000 for 7 years. Calculate pay back period.

 

 

Solution :

                  

Pay back period =Initial investment /Annual cash inflow

Initial investment is = $ .1,00,000

 

Annual cash inflow $ = 20,000

 

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

= 5 years

 

Problem 13. Himalaya Construction Ltd is considering the purchase of a new machine for its immediate expansion programme. There are three possible machines suitable for the purpose. Their details are as follows :

 

Machines

1                      2                                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 :

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 economic life of machine No.1 is 2 years while it is 3 years for the other two. The scrap values are $ 40,000, $ 25,000 and $ 30,000 respectively.

 

Sales are expected to be at the rates shown for each year during the full economic life of expenditure resulting from each machine.

 

Tax to be paid is expected at 50% of the net earnings of each year. It may be assumed that all payables and receivables will be settled promptly, strictly on cash basis with no outstanding from one accounting year to another. Interest on capital has to be paid at 8% p.a.

 

You are requested to show which machine would be the most profitable investment on the principle of “Pay-back method”.

 

Solution :                      Profitability Statement

 

Particulars                   Machine I                   Machine II                  Machine III

$                                   $                                        $.

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

 

Sales (i)                                               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 - TC) [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

(a) Pay back period                             1.41 years                   1.89 years                   1.72 years

 

Result : Machine I is preferable because it has shorter payback period as compared to the other machine.

 

Working:

(a) Pay back Period

 

(a) Pay back Period

 

Machine I

I year

Balance

 

 

 

 

Machine II

I year

Balance

(a) Pay back Period

 

Pay back period 1 year 10 months

Machine III

I year

Balance

 

$

2,13,000

87,000

3,00,000

= 12 month/2,13,000= x  87,000

= How many months ? = 4 months

= 1 year 4 month

 

1,58,834

1,41,166

3,00,000

= 12 month/1,58,834 x 1,41,166 = 10 months

 

 

 

1,74,500

1,25,500

3,00,000

12/1,74,500 x 1,25,500 = 8.62 i.e., 9 months

= 1 year 9 months

 

 

Machine I                    Machine II                  Machine III

Payback period           1 year 4 months           1 year 10 months        1 year 9 months

 

Result : As per the pay back period point of view, machine I is preferable because it has a shorter pay back.

 

(b) Depreciation

 

Machine I                    Machine II                  Machine III

 

Cost – Scrap / Life     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 14. The ABTS Co Ltd is considering the purchase of a new machine. Two

alternative machines (A and B) have been suggested each having an initi.al cost of $. 4,00,000 and requiring $ 20,000 as additional working capital at the end of the 1st year Earnings after taxation are expected to be as follows.

 

Cash Inflows

 

year                                        A                                 B

$                                   $.

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

 

The company has target return on capital of 10% and on this basis, you are required to

compare the profitability of the machines and state which alternatives you consider financially

preferable.

 

Note : The following table gives the present value of Re. 1 due in ‘n’ number of years.

 

Year    1         2          3          4         5

PIV at 10%     .91       .83      .75      .68      .62

 

 

 

Solution:              Present Value Statement

Machine A

 

Year                      Cash Inflows                           Discount Factor

$.                                             At 10%

1                                40,000                                              . 91

2                               1,20,000                                            .83

3                                1,60,000                                           .75

4                                 2,40,000                                          .68

5                                1,60,000                                            .62

 

Total Present value of cash inflows

Less : Total Present value of cash outflows

(4,00,000 + 20,000 X .91)

Net present value

 

Present Value

Rs .

36,400

99,600

1,20,000

1,63,200

99,200

5,18,400

4,18,200

1,00,200

       Year                      Cash Inflows                 Discount Factor                     Present Value

$                                   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 .91) 4,18,200

Net present value                                1,05,000

 

 

Result : Machine B is preferable because it has a higher net present value as compared to Machine A. So machine B is recommended for purchase.

 

Problem 15. A Company is considering two mutually exclusive projects. Both require an initial cash outlay of $ 10,000 each and have a life of 5 years. The company’s required rate of return is 10% and pays tax at 50%. The project will be depreciated on a straight line  basis. The before tax cash flows expected to be generated by the project are as follows

 

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 for each project :

(i) The payback                                    (iii) NPV

(ii) The accounting rate of return        (iv) PI

 

Which project should be accepted and why ?

Solution :                      Profitability Statement

Project A

 

Year          Cash                 Less                        Less

Flows          Depreciation    PBT      tax        PAT

$                          $             $           $             $

 

1                  4000              2000          2000       1000      1000

2                  4000               2000         2000        1000     1000

3                  4000               2000         2000        1000      1000

4                 4000                2000         2000        1000       1000

5                  4000              2000            2000       1000    1000

Add                       cash  Inflow

(profit after tax

Depreciation           but before                              $                          depreciation)

+ 2000                         3000

+ 2000                         3000

+ 2000                         3000

+ 2000                          3000

+ 2000                         3000

 

(i)                     Pay back period = 3 years 4 months

I year   3,000

II year              3,000

III year  3,000

9 ,000

Balance 1,000                         To recover balance amount of Rs. 1000

for how many months

10,000 ; 12/ 3,000 x 1,000 =4

= 3 years 4 months

 

(ii) 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

 

ARR =1,000 /10,000 = 10%

 

 

Year          Cash                 Less                        Less

Flows          Depreciation    PBT      tax        PAT

$                          $             $           $             $

 

1                  5000              2000          3000       1500      1500

2                  5000               2000         3000        1500     1500

3                  5000               2000              0               0      1500

4                 5000                2000         3000        1500       1500

5                  5000              2000            3000       1500    1500

Add                       cash  Inflow

(profit after tax

Depreciation           but before                              $                          depreciation)

2000                         3500

2000                         3500

2000                         2000

2000                          3500

2000                         3500

 

 

(i)                     Pay back period = 3 years 3 months

I year   3,500

II year              3,500

III year  2,000

9 ,000

Balance 1,000

10,000

To recover balance amount of $. 1000 in  how many months

 

12/3,500 x 1,000 =3 months

 

(ii) ARP: Return / Original cost x 100, i.e., Return = Average Profit (profit after tax)

 

Average  profit= Total Profit / No. of Years = 16,000 /5 = 1,200 /10,000 x  100 = 12%

 

Statement showing net present value

Profitability index = Sum of discounted cash inflows / Cash outflow x 100

 

Project A

Profitability  index – 11,370 / 10,000 x 100 = 113. 7%

Project B

Profitability index = 12,138 / 10,000   x  100 = 121.38%

Result:

Project             Pay back          ARR                NPV               PI

A                     II                      II                    II                      II

B                     I                       II                      II                      II

 

Result :

 

Based upon the above calculation project B is preferable. Because in all the four aspects

project B would get I Rank in three technique.

Problem 16. Calculate the net present value for a small sized project requiring an initial investment of $. 20,000 and which provides a net cash inflow of $ 6000 each year for six years. Assume the cost of funds to be 8% p.a. and that there is no scrap value.

 

Solution:

 

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

 

Hence, the present value of $ 6,000 is

6,000 X 4.623 = 27,738

Less : original cost = 20,000

Net present value = 7,738

 

Problem 17. The initial cost of an equipment is $ 3,00,000. Cash inflows for 5 years are estimated to be $ 2,00,000 per year. Desired rate of return is 15%. Calculate the net present value and excess present value index.

 

Solution : Present value of Re. 1 received annually for 5 years at 15% as per annuity Table = 3.352. Present value of $. 2,00,000 received annually for 5 years

 

$

2,00,000  x 3.352 = 6,70,400

Less : original cost of the equipment = 3,00,000

Net present value = 3,70,400

 

Excess present value index = Total present value of cash inflows / Total present value of cash outflows

 

6,70,000 /3,00,000 x  100 = 223.4

 

Problem 18. KVP Ltd is considering the purchase of a new machine for $ 1,20,000. It has a life of 4 years and an estimated scrap value of $ 20,000. The machine will generate an extra revenue of $. 4,00,000 p.a. and has an additional operating cost of $ 3,20,000 p.a. The company’s cost of capital is 20% and tax rate 50%. Should the machine 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 is                $ 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 .482) = 1,09,640

Net present value =                 19,760

 

Result : As per the calculation there could be a positive NPV, so the machine may be

purchased.

 

Problem 19. Sumanth & Co Ltd is considering building an assembly plant. The decision has been narrowed down to two possibilities. The company desires to choose the best plant at a level of operations of 10,000 gadgets a month. Both plants have expected life of 10 years and are expected not to have any salvage value at the time of their retirement. The cost of capital is 10%. Suggest what should be the desirable choice.

 

Cost of monthly output of 10,000 units.

 

Large Plant                              Small Plant

$                                              $.

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

Direct labours : First half        15,00,000                                7,80,000

(p.a.)                                        (p.a.)

Second half –                                                                           9,00,000 (p.a.)

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

 

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

 

Solution :                      Profitability Statement

 

$

Direct labour for small plant for both shifts

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

Direct labour for large plant                                         15 ,00,000

Savings in indirect labour (using large plant)                                      1,80,000

Overhead costs for small plant = 2,10,000

Less : overhead costs for large plant =    2,40,000                  -30,000

Net savings p.a. by using large plant1,                                       50,000