**Test Question:
**

- What do you understand by Capital Budgeting?
- Define Capital Budgeting
- List out the concept of Capital Expenditure
- Explain in brief that advantages of Capital Budgeting
- What is the need and importance of Capital Budgeting?
- List out the limitations of Capital Budgeting
- Explain the principle methods required for determining the profitability of any capital expenditure project.
- Compare the internal rate of return method and net present value method
- Explain- “Capital budgeting is the long-term planning to maintain the allocation of capital in different sectors of the ” What are its limitations?
- “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.
- Explain the circumstances for conflicting NPV and IRR methods recommendations. Tell us how these circumstances should overcome and why.
- 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:**

**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 4^{th} year, balance of $2500 is recovered

1^{st} Year 3,600

2^{nd} Year 3,900

3^{rd} 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

**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

1^{st} Year 3,600

2^{nd} Year 3,750

3^{rd} Year 3,500

4^{th} 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 5^{th} Year, time required = 365 days

For recovery of amount $15 in the 5^{th} 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:

- Traditional pay back method
- 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

**Traditional pay back method:**

1^{st} Year $22,000

2^{nd} Year $30,000

Amount recovered for 2 years $52,000

Balance $28,000

**$80,000**

3^{rd} 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

**Discounted pay back method:**

1^{st} Year $18,260

2^{nd} Year $20,700

3^{rd} Year $23,200

4^{th} Year $15,360

Balance $77,520

Project Cost $2,480

**$80,000**

In the 5^{th} 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

**a) Finding pay back period using traditional method:**

**Project I**

1^{st} Year $25,000

2^{nd} Year $15,000

3^{rd} Year $10,000

**$50,000**

Here, pay back period is 3 years.

**Project II**

1^{st} Year $10,000

2^{nd} Year $12,000

3^{rd} 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.

**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**

**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**

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

**Problem No. 8**

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

- Pay back
- 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:**

**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,

1^{st} Year + 2^{nd} 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

**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

- Pay back method
- Rate of return on original investment

- Rate of return on average investment

- Discounted cash flow method with cost of capital at 10%
- Net present value index method
- 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

**Pay back period**

1^{st} Year 90,000

2^{nd} Year 90,000

**1,80,000**

Balance 20,000

**2,00,000**

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

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

This means,

Pay back period = 2 years 3 months

**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%

**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

**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%

**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:

**Return on original investment:**

Average Net Earnings/ Original Investment

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

= 12.3% 13.75%

**Return on Average Investment Method:**

Return/ Average Investment x 100

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

= 25% 27.5%

**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:**

**Pay back period**

**Machine 1 **$2,13,000

1^{st} 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

1^{st} 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

1^{st} 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.

**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 1^{st} 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:

- The pay back
- Accounting rate of return
- NPV
- 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,**

**The pay back**

Pay back period = 3 years 4 months

1^{st} year 3,000

2^{nd} year 3,000

3^{rd} 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

**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,**

**The pay back**

Pay back period = 3 years 3 months

1^{st} year 3,500

2^{nd} year 3,500

3^{rd} 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

**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%

**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**

**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**

**Links of Previous Main Topic:-**

- Introduction to financial management
- Introduction and types of dividend
- Concept of cost of capital
- Capitalization meaning
- Concepts of working capital
- Concept of capital expenditure

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