Question

6104MECH and 6365ELE Industrial Management Question B.3 a) The following information is available in relation to two projects Year و نه يم لا Project A (5,000) 2.500 1.000 1,000 500 1,500 1,000 Project B (8.000) 1.500 2.000 2.500 1.000 1,000 2.500 ا م ا Calculate the payback period for the above-proposed projects and their Net Present Value (NPV) assuming that the organisation has proposed a discounting rate of 12%. Analyse the results and provide conclusions, Payback period and calculations [6 marks) Net present value and calculations [6 marks) Analysis of results and conclusions [3 marks] b) Find the Internal Rates of Return (IRR) of project A in part (a) above. Analyse the outcome if IRR is used, IRR calculations [7 marks] Analysis of the outcome [3 marks] January 2019 Page 7 of 9

Answer 1

Year uw NPO Project A Cash Cumulative Flows Cash Flows -$5,000 $5,000 $2,500 $2,500 (-$5000 + $ 2500] $1,000 -$1,500 (-$2500 + $1000] $1,000 -$500 (-$1500 + $1000] $500 $0 [-$500 + $500] $1,500 $1,500 ($0+ $1500] $1,000 $2,500 ($1500 + $1000] Project B Cash Cumulative Flows Cash Flows -$8,000 -$8,000 $1,500 $6,500 $2,000 -$4,500 $2,500 -$2,000 $1,000 $1,000 $1,000 $0 $2,500 $2,500 [-$8000 + $1500] [-$6500 + $2000] (-$4500 + $2500] (-$2000 + $1000] [-$1000 + $1000] [$0 + $2500] For Project-A, It is observed from above table that the cumulative cash flows becomes zero in year-4. It means that Project-A's payback period must be 4 years. For Project-B, It is observed from above table that the cumulative cash flows becomes zero in year-5. It means that Project-A's payback period must be 5 years.

3 PV Factor Year @ 12% 0.893 0.797 0.712 0.636 0.567 0.507 Present value of future cash flows Initial Investment Net Present Value (NPV) Project A Cash Present Flow Value $2,500 $2,232.50 [0.893 x $2500] $1,000 $797.00 (0.797 x $1000] $1,000 $712.00 (0.712 x $1000] $500 $318.00 (0.636 x $500] $1,500 $850.50 [0.567 x $1500] $1,000 $507.00 (0.507 x $1000] $5,417.00 $5,000.00 $417.00 ($5417 - $5000] Project B Cash Present Flow Value $1,500 $1,339.50 (0.893 x $1500] $2,000 $1,594.00 [0.797 x $2000] $2,500 $1,780.00 (0.712 x $2500) $1,000 $636.00 (0.636 x $1000] $1,000 $567.00 (0.567 x $1000] $2,500 $1,267.50 [0.507 x $2500) $7,184.00 -$8,000.00 -$816.00 [$7184 - $8000] Conclusion: In capital budgeting analysis, though there are many methods available for evaluating a project whether to accept or not. The methods include: Net Present Value (NPV), Profitability Index (PI), Internal Rate of Return (IRR), Accounting Rate of Return (ARR), Payback Period, Discounted Payback Period, Annual Worth (AW), Equal Annual Cash Flow (EUAC), etc. Out of all these methods available, NPV should be the best because it considers time value of money and delivers result in dollar value. So, for analyzing the given two alternatives, NPV should be the appropriate evaluation tool.

The Payback period (nothing but the traditional or conventional recovery period) is the period within which, cash outflows associated with the project can be recovered by the management but without considering time value of money. The answer is expressed in terms of number of periods (may be weeks or months or years, etc.). To calculate the payback period, cumulative cash flows year-by-year shall be calculated and then the year in which cumulative cash flows turns into positive is the payback period. However, in order to calculate exact payback period in decimal places, negative cumulative cash flows of previous year shall be divided by current year's cash flows and the decimal thus calculated shall be added to previous year to the year in which cumulative cash flows turned into positive. Based on Payback Period, Project-A shall be accepted because firm can recover all its cash otflows in 4 years itself whereas firm must wait for 5 years to recover its cash outflows if Project-B is selected. That is, Payback Period rule says that shorter the payback period, higher the acceptability of a project. Based on NPV, Project-A shall be accepted because its NPV is positive whereas Project-B's NPV is negative. NPV rule says that a project with positive NPV shall be accepted because firm can recover all cash outflows within project's economic life itself even after considering time value of money in case of positive NPV. b) For Project-A, NPV of $471 is higher than $0. Therefore, IRR must be higher than discount rate of 12%. On the other hand, Project-B's NPV of $816 is less than $0 which means that IRR must be lower than discount rate of 12%. Let the discount rate be 16% for Project-A and 8% for Project-B. Therefore, the NPV for two projects shall be:

Year Project A PV Factor Cash Present Year @ 16% Flow Value 0.862 $2,500 $2,155.00 (0.862 x $2500) 0.743 $1,000 $743.00 [0.743 x $1000] 0.641 $1,000 $641.00 (0.641 x $1000] 0.552 $500 $276.00 (0.552 x $500] 0.476 $1,500 $714.00 (0.476 x $1500] 0.410 $1,000 $410.00 (0.41 x $1000] Present value of future cash flows $4,939.00 Initial Investment $5,000.00 Net Present Value (NPV) $61.00 [$4939 - $5000] NM + in OWNE Project B PV Factor Cash Present @ 8% Flow Value 0.926 $1,500 $1,389.00 (0.926 x $1500] 0.857 $2,000 $1,714.00 [0.857 x $2000] 0.794 $2,500 $1,985.00 (0.794 x $2500] 0.735 $1,000 $735.00 [0.735 x $1000] 0.681 $1,000 $681.00 [0.681 x $1000] 0.630 $2,500 $1,575.00 (0.63 x $2500] $8,079.00 -$8,000.00 $79.00 [$8079 - $8000] (NPV1 (R2 – Rı)) IRR= R + (NPV1 - NPV) where: R1, R2 = randomly selected discount rates NPV1 = higher net present value $417 NPV2 = lower net present value -$61 Internal Rate of Return (IRR)-Project A 15.49% {12% + ($417 x (16%-12%) / ($417 - (-$61))] = 15.49%} (NPV(R2 – Rı)) IRR = R + (NPVI - NPV) where: R1, R2 = randomly selected discount rates NPV1 = higher net present value NPV2 = lower net present value Internal Rate of Return (IRR)-Project B {8% + [$79 x (12%-8%) / ($79 - $816)] = 8.43%} $79 -$816 8.43%

Conclusion: IRR stands for Internal Rate of Return which is nothing but the discount rate that makes NPV of the project equals to zero. In other words, it is the discount rate at which present value of future net savings is equal to initial investment made. IRR rule says that "Higher the IRR, Higher the acceptability of the project" because higher IRR implies that the project or equipment concerned has capability to generate sufficient cash inflows to absorb initial cash outflow made for it even after considering time value of money. Recommendation: For Project A, based on IRR, this project shall be accepted as its IRR of 15.49% is higher than firm's discount rate of 12%. For Project B, based on IRR, this project shall be rejected as its IRR of 8.43% is lower than firm's discount rate of 12%.