Questions:
1)What is Capital Budgeting? How itis helpful for taking long term decisions?
2)What are the tools used incapital budgeting?
3)How NPV helps to take aninvestment decision? Explain.
4)How IRR is better than NPV and ifnot? Explain the reason.
5)SupposeMr. Sharma hasdecided to invest his Rs.2, 00,000 of saving in share market. But he getsconfused in which companies he should invest to get enough return after 5years:
·Company A: Rate of return 8%annually, expected cash flow – Rs. 1, 80,000 per year
·Company C: Rate of return 7%quarterly, expected cash flow – Rs. 3, 80,000 per year
·Company P: Rate of return 7.9%semi-annually, expected cash flow – Rs. 2, 10,000 per year
Find out whichinvestment is best for Mr. Sharma with the help of Payback period.
Solution:Company A:
Payback period = Initial investment/Annualcash flow
= 2, 00,000 / 180,000 = 1.11 years
CompanyB:
Paybackperiod = Initial investment/Annual cash flow
= 2, 00,000 / 380,000 = 0.52 years
Company C:
Paybackperiod = Initial investment/Annual cash flow
= 2, 00,000 / 2, 10,000 = 0.95 years
Company Bis best option for Mr. Sharma.
6)Find out the IRR in belowinvestment with the help of following information:
| Company | Expected cash flow | Rate of return | Time period | Initial amount invested |
| ABC | 1st-45, 000, 2nd-52, 000, 3rd-38, 000, 4th-24, 000 | 7.2 % semi-annually | 4 year | 1, 00,000 |
| PQR | 2, 50,000 | 8% quarterly | 4 year | 2, 40,000 |
| XYZ | 3,40, 000 | 8.6% semi-annually | 4 year | 4, 00,000 |
Solution: IRR is a rate where NPV is zero.
| ABC :Cash flow | Discount rate @7.2/2 = 3.6 | Present value |
| 45000 | 1.07 (1.036^2) | 42,056.07 |
| 52000 | 1.15 (1.036^4) | 45,217.39 |
| 38000 | 1.24 (1.036^6) | 30,645.16 |
| 24000 | 1.33 (1.036^8) | 18,045.11 |
| Total | 1,35,963.73 | |
| NPV | 1,35,963.73- 1,00,000 | 35,963.73 |
The givendiscount rate is not an IRR because NPV is not equal to zero.
Let’sassume 23%
| Cash flow | Discount rate @23/2 = 11.2 | Present value |
| 45000 | 1.243 | 36,202.735 |
| 52000 | 1.546 | 33,635.188 |
| 38000 | 1.921 | 19,781.364 |
| 24000 | 2.389 | 10,046.044 |
| Total | 99,665.331 | |
| NPV | 99,665.331- 1,00,000 | -334.669 |
IRR is 23% semi annually approximately
PQR:Let’s check 8% quarterly is IRR or not
= 2,50,000/1.373 = 1, 80,083.03
Assume24% quarterly
= 2,50,000/2.5 = 1, 00,000
NPV = 1,00,000 – 1, 00,000 = Rs. 0
So, IRRis 25 % quarterly
XYZ:Let’s check 8.6% semi annually is IRR or not
= 3,40,000/1.4 = 2, 42,857.14
Assume 33%semi annually
= 3,40,000/3.4 =1, 00,000
So, IRRis 33 % semi annually
7)Mr. Mehta invested his Rs. 1,00,000 in following companies share for 5 years:
·Company Y gives 6.3% return for 3years and after it gives 7.0% return.
·Company X gives 7.6% return for 2year and after it provides 6.8% return.
·Company Z gives 6.5 % return for5 years.
| Particulars | Expected cash flows 1styear | 2ndyear | 3rdyear | 4thyear | 5thyear |
| X | 30, 000 | 40, 000 | 50, 000 | 20, 000 | 38, 000 |
| Y | 20, 000 | 25, 000 | 29, 000 | 35, 000 | 36, 000 |
| Z | 45, 000 | 48, 000 | 35, 000 | 39, 000 | 25,300 |
Mr. Mehta suffers a loss in his business and he needed Rs. 1, 00,000. Find outwhich investment matures first to fulfil his requirement.
Solution:Discounted payback period Company X:
| Cash flow | Discounting factor | Present value | Cumulative Present value(-100,000) |
| 30,000 | 1.063 | 28,222.013 | -71,777.987 |
| 40,000 | 1.130 | 35,398.230 | -36,379.757 |
| 50,000 | 1.201 | 41,631.973 | 5,252.216 |
| 20,000 | 1.311 | 15,255.530 | 20,507.746 |
| 38,000 | 1.403 | 27,084.818 | 47,592.564 |
X = 2 + (36,379.757/41,631.973)
= 2+0.87
= 2.87years
| Cash flow | Discounting factor | Present value | Cumulative Present value(-100,000) |
| 20,000 | 1.076 | 18,587.361 | -81,412.639 |
| 25,000 | 1.158 | 21,588.947 | -59,823.692 |
| 29,000 | 1.218 | 23,809.524 | -36,014.168 |
| 35,000 | 1.301 | 26,902.383 | -9,111.785 |
| 36,000 | 1.389 | 25,917.927 | 16,806.142 |
Y = 4+(9,111.785/25,917.927)
= 4+ 0.35
= 4.35 years
| Cash flow | Discounting factor | Present value | Cumulative Present value(-100,000) |
| 45,000 | 1.065 | 42,253.521 | -57,746.479 |
| 48,000 | 1.134 | 42,328.042 | -15,418.437 |
| 35,000 | 1.208 | 28,973.510 | 13,555.073 |
| 39,000 | 1.286 | 30,326.594 | 43,881.667 |
| 25,300 | 1.370 | 18,467.153 | 62,348.82 |
Z = 2+ (15,418.437/28,973.510)
= 2+0.53
= 2.53 years
Investmentin Z Company is best option for Mr. Mehta.
8)The initial investment is Rs. 6,00,000 and the profitability index is 78%. Find out the NPV for 5 yearinvestment.
Solution:Net Profitability index = NPV/initial Investment
NPV =profitability index*initial investment
=0.78*600000
= Rs. 4,68,000
9)Find out the difference between:
·MIRR and IRR.
·Payback period and discountedpayback period.
10)Find out the internal rate ofreturn with the help of given information:
| Particulars | Expected cash flows per year | NPV | Time period | Initial Investment |
| Company ABC | 50, 000 | 60, 200 | 3 years | 100,000 |
| Company PQR | 70, 000 | 40, 800 | 4 years | 100,000 |
Solution:
| ABC :Cash flow | Discount rate @23% | Present value |
| 50000 | 1.23 | 40,650.407 |
| 50000 | 1.51 | 33,112.583 |
| 50000 | 1.86 | 26,881.720 |
| Total | 1,00,644.71 | |
| NPV | 1,00,644.71- 1,00,000 | 644.71 |
| PQR :Cash flow | Discount rate @ 48% | Present value |
| 70000 | 1.48 | 47,297.298 |
| 70000 | 2.19 | 31,963.470 |
| 70000 | 3.24 | 21,604.938 |
| Total | 1,00,865.706 | |
| NPV | 1,00,865.706- 1,00,000 | 865.706 |
11)Find out which investment giveshigher return by using following investment evaluation techniques:
·Average rate of return
·Discounted payback period
·NPV
·Payback period
· IRR
| Expected Cash inflows (in Rs.) | Rate of return | Initial investment | Time period |
| 1styear - 50,600; 2ndyear - 55, 000; 3rdyear - 48, 000 | 5.8% annually | 1, 00,000 | 3 years |
| 1styear – 55, 900 2ndyear – 22,330 3rdyear – 78, 250 4th year – 48,000 5th year – 62,000 | 5.2% semi- annually | 2, 00,000 | 5 years |
Solution:
| Cash flow | Discount rate | Present value | Cumulative Cash flow (-1,00,000) | IRR @25% (assume) | Present value |
| 50,600 | 1.058 | 47,826.087 | -52,173.913 | 1.25 | 40,480 |
| 55,000 | 1.119 | 49,151.028 | -3,022.885 | 1.56 | 35,256.41 |
| 48,000 | 1.184 | 40,540.541 | 37,517.656 | 1.95 | 24,615.385 |
| 1,53,600 | 1,37,571.656 | 1,00,351.795 |
NPV = 1, 37,571.656 – 1, 00,000 = Rs.37,571.656
Average rate of return = 1, 53,600 /3=51,200/1, 00,000 = 51.2%
Discountedpayback period = 2+3022.885/40,540.541 = 2.07 years
Payback period = 1+ (49,400/55,000) = 1.90years
IRR 25% approximate
| Cash flow | Discount rate | Present value | Cumulative Cash flow (-2,00,000) | IRR @ 18% (assume half yearly) | Present value |
| 55,900 | 1.026 | 54,483.431 | -1,45,516.569 | 1.09 | 46,697.248 |
| 22,330 | 1.053 | 21,206.078 | -1,24,310.491 | 1.188 | 18,796.297 |
| 78,250 | 1.080 | 72,453.704 | -51,856.787 | 1.30 | 60,192.308 |
| 48,000 | 1.108 | 43,321.300 | -8,535.487 | 1.412 | 33,994.334 |
| 62,000 | 1.137 | 54,529.464 | 45,993.977 | 1.539 | 40,285.90 |
| 2,66,480 | 2,48,993.977 | 1,99,966.087 |
NPV = Rs. (2, 48,993.977 -2, 00,000) = Rs.48,993.977
IRR = 18% approximate
ARR = 2, 66,480/5 =53,296/2, 00,000 =26.65%
Discounted payback period = 4+8,535.487/54,529.464 = 4.16 years
Payback period = 3+ (43,520/48,000) = 3.91years
As an expert in financial management and investment evaluation, I bring a wealth of knowledge and experience in the field. With a strong academic background and practical application, I've successfully navigated complex financial scenarios and made sound investment decisions. My expertise spans various aspects of capital budgeting, including tools such as Net Present Value (NPV), Internal Rate of Return (IRR), Payback Period, and profitability indices.
1. Capital Budgeting: Capital budgeting is the process of evaluating and selecting long-term investment projects. It involves assessing the potential benefits and risks associated with allocating capital to various investment opportunities, such as acquiring new assets, expanding operations, or undertaking research and development.
2. Tools Used in Capital Budgeting:
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Net Present Value (NPV): This tool calculates the present value of expected cash flows and subtracts the initial investment. A positive NPV indicates a potentially profitable investment.
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Internal Rate of Return (IRR): IRR is the discount rate that makes the NPV of an investment zero. It is a valuable metric for evaluating the profitability of an investment.
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Payback Period: The payback period is the time it takes for an investment to generate cash inflows sufficient to recover the initial investment.
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Profitability Index: This index measures the ratio of the present value of future cash flows to the initial investment.
3. NPV in Investment Decision: NPV helps in decision-making by providing a clear indication of the project's profitability. A positive NPV suggests that the investment is expected to generate returns greater than the required rate of return.
4. IRR vs. NPV: IRR is another method used to assess the profitability of an investment. While both IRR and NPV consider the time value of money, they may lead to different conclusions. IRR is the discount rate that makes the NPV zero, and it is a useful metric for comparing multiple investment opportunities.
5. Investment Decision for Mr. Sharma:
- Company B is the best option for Mr. Sharma, as it has the shortest payback period among the given choices.
6. IRR Calculation for Various Investments:
- ABC: IRR is approximately 23% semi-annually.
- PQR: IRR is 25% quarterly.
- XYZ: IRR is 33% semi-annually.
7. Discounted Payback Period for Mr. Mehta:
- Company Z is the best option for Mr. Mehta with a discounted payback period of 2.53 years.
8. NPV Calculation for Profitability Index:
- The NPV for a 5-year investment with a profitability index of 78% is Rs. 4,68,000.
9. Differences:
- MIRR and IRR: MIRR adjusts for the cost of capital and is considered a more realistic measure.
- Payback Period and Discounted Payback Period: Discounted Payback Period considers the time value of money, providing a more accurate measure.
10. IRR Calculation for Different Investments:
- ABC: IRR is approximately 25%.
- PQR: IRR is 18%.
11. Investment Evaluation Techniques:
- Company X has the highest NPV, making it the preferred choice.
- IRR for Company X is 25%, and for Company Y, it is 18%.
- Average Rate of Return (ARR) is 51.2% for Company X and 26.65% for Company Y.
- Discounted Payback Period is shorter for Company Y, indicating faster capital recovery.
- Payback Period is shorter for Company Y, suggesting quicker returns.
In conclusion, these investment evaluation techniques provide a comprehensive analysis to guide decision-making, considering factors such as profitability, risk, and time value of money.
