QUESTION
a) Calculate the effective annual rate for the required rate of return in the example above.
b) Evaluate the new project using the NPV method. Note – you should use the effective annual interest rate as your required rate of return.
c) Perform sensitivity analysis and calculate the NPV differential given the following optimistic and pessimistic estimations of the required rate of return:
Optimistic 8% p.a.
Pessimistic 15% p.a.
d) In 300 words or less, critically analyse the advantages and disadvantages of three different techniques of project evaluation other than net present value
SOLUTION
| Project evaluation in Practice | ||||||||
| Answers | ||||||||
| a) | Effective annual rate of return | = | (1+i/n)^n-1 | |||||
| where i= stated rate of return = 12% | ||||||||
| n=compounding frequency = 12 | ||||||||
| EAR | = | (1+0.12/12)^12-1 | ||||||
| = | 0.12682503 | |||||||
| = | 12.68% | |||||||
| Although the rate of return for the project is 12% but the firm compounds it monthly so the effective rate of return is actually a little higher at 12.68%. | ||||||||
| b) | Initial cash outflows | |||||||
| factory and machine | -145000000 | |||||||
| purchase of raw material(cash blocked) | -15000000 | |||||||
| Total initial outflow (PV of cash outflows) | -160000000 | |||||||
| Annual cash flows | Amounts in $ | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | ||
| Inflows | ||||||||
| Annual revenue | 60,000,000 | 60,000,000 | 60,000,000 | 60,000,000 | 60,000,000 | |||
| Less reduction in existing sales | 24,000,000 | 24,000,000 | 24,000,000 | 24,000,000 | 24,000,000 | |||
| Incremental revenue | 36,000,000 | 36,000,000 | 36,000,000 | 36,000,000 | 36,000,000 | |||
| Outflows | ||||||||
| Cost of goods sold and other operating expenses | (18,000,000) | (18,000,000) | (18,000,000) | (18,000,000) | (18,000,000) | |||
| Less Reduction in existing variable expenses | (11,000,000) | (11,000,000) | (11,000,000) | (11,000,000) | (11,000,000) | |||
| Incremental operating expenses | (7,000,000) | (7,000,000) | (7,000,000) | (7,000,000) | (7,000,000) | |||
| Maintenance expenses | (2,000,000) | (2,200,000) | (2,400,000) | (2,600,000) | ||||
| Depreciation | (29,000,000) | (29,000,000) | (29,000,000) | (29,000,000) | (29,000,000) | |||
| Total operating expenses | (38,000,000) | (38,200,000) | (38,400,000) | (38,600,000) | (36,000,000) | |||
| EBIT | (2,000,000) | (2,200,000) | (2,400,000) | (2,600,000) | – | |||
| Tax @30% | – | – | – | – | – | |||
| PAT | (2,000,000) | (2,200,000) | (2,400,000) | (2,600,000) | – | |||
| Add back depreciation | 29,000,000 | 29,000,000 | 29,000,000 | 29,000,000 | 29,000,000 | |||
| Cash inflows | 27,000,000 | 26,800,000 | 26,600,000 | 26,400,000 | 29,000,000 | |||
| PVF for 12.68% | 0.8875 | 0.7876 | 0.6990 | 0.6203 | 0.5505 | |||
| PV of cash inflows @ 12.68% | 23962500 | 21107680 | 18592655.2 | 16376342.4 | 15964819 | 96,003,996.60 | ||
| PV of total annual cash flows | ||||||||
| Terminal Cash Inflows | ||||||||
| scrap value of machine | 10,000,000 | |||||||
| depreciated value of machine | – | |||||||
| Long term capital gain | 10,000,000 | |||||||
| Tax on LTCG @ 30% | 3,000,000 | |||||||
| Net cash inflow on sale of factory and machine | 7,000,000.00 | |||||||
| PV of terminal cash inflow @12.68% | 3,853,577 | |||||||
| NPV of project @ 12.68% effective rate of return | = | PV of Initial cash flows+PV of annual cash flows+ PV of terminal cash flows | ||||||
| = | (60,142,426) | |||||||
| Since the NPV of this project is negative at effective rate of return of 12.68%, hence this project should be discarded. | ||||||||
| c) | Sensitivity analysis | |||||||
| Variable | Optimistic | Effective annual rate of return | Pessimistic | |||||
| Rate of Return | 8% | 12.68% | 15% | |||||
| NPV | (47,003,588) | (60,142,426) | (65,778,380) | |||||
| Assuming Optimistic rate of return 8% | ||||||||
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | ||||
| Annual Cash inflows | 27,000,000 | 26,800,000 | 26,600,000 | 26,400,000 | 29,000,000 | |||
| PVF for 8% | 0.9259 | 0.8573 | 0.7938 | 0.7350 | 0.6806 | |||
| PV of cash inflows @ 8% | 24,999,300 | 22,975,640 | 21,115,080 | 19,404,792 | 19,737,400 | 108,232,212 | ||
| PV of total annual cash flows @ 8% | ||||||||
| Net cash inflow on sale of factory and machine | 7,000,000.00 | |||||||
| PV of terminal cash flow @8% | 4764200 | |||||||
| NPV @ 8% | = | PV of Initial cash flows+PV of annual cash flows+ PV of terminal cash flows | ||||||
| = | (47,003,588) | |||||||
| Assuming Pessimistic rate of return 15% | ||||||||
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | ||||
| Annual Cash inflows | 27,000,000 | 26,800,000 | 26,600,000 | 26,400,000 | 29,000,000 | |||
| PVF for 15% | 0.8696 | 0.7561 | 0.6575 | 0.5716 | 0.4972 | |||
| PV of cash inflows @ 15% | 23,479,200 | 20,263,480 | 17,489,500 | 15,090,240 | 14,418,800 | 90741220 | ||
| PV of total annual cash flows @ 15% | ||||||||
| PV of terminal cash flow @ 15% | = | 3,480,400 | ||||||
| NPV @ 15% | = | PV of Initial cash flows+PV of annual cash flows+ PV of terminal cash flows | ||||||
| = | (65,778,380) | |||||||
| Project yields negative NPV at all considered rate of returns therefore it is highly infeasible to adopt and should be discarded. | ||||||||
| d) | Critical evaluation of Capital budgeting techniques | |||||||
| 1) | Payback period | |||||||
| It can be defined as the number of years required to recover the initial investment in project (Rustagi,2003). | ||||||||
| Advantages | ||||||||
| – | The payback period is quite easy and simple to adopt. | |||||||
| – | It indicates liquidity by emphasizing on earlier cash inflows. | |||||||
| Disadvantages | ||||||||
| – | Payback period technique might be misleading as it ignores the cash inflows generated after the payback period. | |||||||
| – | It ignores the time value of money. | |||||||
| – | It also ignores the salvage value and whole business life of the project leading to rejection of more profitable projects in favor of a project with higher initial cash inflows. | |||||||
| – | It only focuses on recovering the capital employed. | |||||||
| IRR | ||||||||
| It is a percentage expected rate of return which brings cash outflows and inflows of a project into equality(Dhirender. et al, n.d.). i.e. here, PV of cash inflows=PV of cash outflows. | ||||||||
| Advantages | ||||||||
| – | It takes into account time value of money by using discounted cash flows. | |||||||
| – | IRR technique takes into consideration all the cash inflows and outflows expanding over the total life of the project. | |||||||
| – | It is easier to interpret as it gives rate of return in percentage rather than in amounts. | |||||||
| Disadvantages | ||||||||
| – | It is quite tedious to calculate as it involves hit and trial procedure. | |||||||
| – | It might give conflicting results when timings of cash flows differ between two projects (Investment decisions-Capital budgeting, nd). | |||||||
| – | IRR technique is biased towards smaller projects which are more likely to give higher rate of return over larger projects. | |||||||
| ARR | ||||||||
| It might be defined as the annual net income earned on the average funds invested. | ||||||||
| Its merit is that it is simple to adopt and easy to calculate as the data required for calculating ARR is easily available. | ||||||||
| Disadvantages | ||||||||
| – | It ignores the time value of money. | |||||||
| – | ARR is based on accounting profits rather than cash flows. | |||||||
| – | ARR does not take into account the economic life of the project and salvage value. | |||||||
| – | It also does not recognise amount of investment required. | |||||||
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| Project evaluation in Practice | ||||||||
| Answers | ||||||||
| a) | Effective annual rate of return | = | (1+i/n)^n-1 | |||||
| where i= stated rate of return = 12% | ||||||||
| n=compounding frequency = 12 | ||||||||
| EAR | = | (1+0.12/12)^12-1 | ||||||
| = | 0.12682503 | |||||||
| = | 12.68% | |||||||
| Although the rate of return for the project is 12% but the firm compounds it monthly so the effective rate of return is actually a little higher at 12.68%. | ||||||||
| b) | Initial cash outflows | |||||||
| factory and machine | -145000000 | |||||||
| purchase of raw material(cash blocked) | -15000000 | |||||||
| Total initial outflow (PV of cash outflows) | -160000000 | |||||||
| Annual cash flows | Amounts in $ | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | ||
| Inflows | ||||||||
| Annual revenue | 60,000,000 | 60,000,000 | 60,000,000 | 60,000,000 | 60,000,000 | |||
| Less reduction in existing sales | 24,000,000 | 24,000,000 | 24,000,000 | 24,000,000 | 24,000,000 | |||
| Incremental revenue | 36,000,000 | 36,000,000 | 36,000,000 | 36,000,000 | 36,000,000 | |||
| Outflows | ||||||||
| Cost of goods sold and other operating expenses | (18,000,000) | (18,000,000) | (18,000,000) | (18,000,000) | (18,000,000) | |||
| Less Reduction in existing variable expenses | (11,000,000) | (11,000,000) | (11,000,000) | (11,000,000) | (11,000,000) | |||
| Incremental operating expenses | (7,000,000) | (7,000,000) | (7,000,000) | (7,000,000) | (7,000,000) | |||
| Maintenance expenses | (2,000,000) | (2,200,000) | (2,400,000) | (2,600,000) | ||||
| Depreciation | (29,000,000) | (29,000,000) | (29,000,000) | (29,000,000) | (29,000,000) | |||
| Total operating expenses | (38,000,000) | (38,200,000) | (38,400,000) | (38,600,000) | (36,000,000) | |||
| EBIT | (2,000,000) | (2,200,000) | (2,400,000) | (2,600,000) | – | |||
| Tax @30% | – | – | – | – | – | |||
| PAT | (2,000,000) | (2,200,000) | (2,400,000) | (2,600,000) | – | |||
| Add back depreciation | 29,000,000 | 29,000,000 | 29,000,000 | 29,000,000 | 29,000,000 | |||
| Cash inflows | 27,000,000 | 26,800,000 | 26,600,000 | 26,400,000 | 29,000,000 | |||
| PVF for 12.68% | 0.8875 | 0.7876 | 0.6990 | 0.6203 | 0.5505 | |||
| PV of cash inflows @ 12.68% | 23962500 | 21107680 | 18592655.2 | 16376342.4 | 15964819 | 96,003,996.60 | ||
| PV of total annual cash flows | ||||||||
| Terminal Cash Inflows | ||||||||
| scrap value of machine | 10,000,000 | |||||||
| depreciated value of machine | – | |||||||
| Long term capital gain | 10,000,000 | |||||||
| Tax on LTCG @ 30% | 3,000,000 | |||||||
| Net cash inflow on sale of factory and machine | 7,000,000.00 | |||||||
| PV of terminal cash inflow @12.68% | 3,853,577 | |||||||
| NPV of project @ 12.68% effective rate of return | = | PV of Initial cash flows+PV of annual cash flows+ PV of terminal cash flows | ||||||
| = | (60,142,426) | |||||||
| Since the NPV of this project is negative at effective rate of return of 12.68%, hence this project should be discarded. | ||||||||
| c) | Sensitivity analysis | |||||||
| Variable | Optimistic | Effective annual rate of return | Pessimistic | |||||
| Rate of Return | 8% | 12.68% | 15% | |||||
| NPV | (47,003,588) | (60,142,426) | (65,778,380) | |||||
| Assuming Optimistic rate of return 8% | ||||||||
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | ||||
| Annual Cash inflows | 27,000,000 | 26,800,000 | 26,600,000 | 26,400,000 | 29,000,000 | |||
| PVF for 8% | 0.9259 | 0.8573 | 0.7938 | 0.7350 | 0.6806 | |||
| PV of cash inflows @ 8% | 24,999,300 | 22,975,640 | 21,115,080 | 19,404,792 | 19,737,400 | 108,232,212 | ||
| PV of total annual cash flows @ 8% | ||||||||
| Net cash inflow on sale of factory and machine | 7,000,000.00 | |||||||
| PV of terminal cash flow @8% | 4764200 | |||||||
| NPV @ 8% | = | PV of Initial cash flows+PV of annual cash flows+ PV of terminal cash flows | ||||||
| = | (47,003,588) | |||||||
| Assuming Pessimistic rate of return 15% | ||||||||
| Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | ||||
| Annual Cash inflows | 27,000,000 | 26,800,000 | 26,600,000 | 26,400,000 | 29,000,000 | |||
| PVF for 15% | 0.8696 | 0.7561 | 0.6575 | 0.5716 | 0.4972 | |||
| PV of cash inflows @ 15% | 23,479,200 | 20,263,480 | 17,489,500 | 15,090,240 | 14,418,800 | 90741220 | ||
| PV of total annual cash flows @ 15% | ||||||||
| PV of terminal cash flow @ 15% | = | 3,480,400 | ||||||
| NPV @ 15% | = | PV of Initial cash flows+PV of annual cash flows+ PV of terminal cash flows | ||||||
| = | (65,778,380) | |||||||
| Project yields negative NPV at all considered rate of returns therefore it is highly infeasible to adopt and should be discarded. | ||||||||
| d) | Critical evaluation of Capital budgeting techniques | |||||||
| 1) | Payback period | |||||||
| It can be defined as the number of years required to recover the initial investment in project (Rustagi,2003). | ||||||||
| Advantages | ||||||||
| – | The payback period is quite easy and simple to adopt. | |||||||
| – | It indicates liquidity by emphasizing on earlier cash inflows. | |||||||
| Disadvantages | ||||||||
| – | Payback period technique might be misleading as it ignores the cash inflows generated after the payback period. | |||||||
| – | It ignores the time value of money. | |||||||
| – | It also ignores the salvage value and whole business life of the project leading to rejection of more profitable projects in favor of a project with higher initial cash inflows. | |||||||
| – | It only focuses on recovering the capital employed. | |||||||
| IRR | ||||||||
| It is a percentage expected rate of return which brings cash outflows and inflows of a project into equality(Dhirender. et al, n.d.). i.e. here, PV of cash inflows=PV of cash outflows. | ||||||||
| Advantages | ||||||||
| – | It takes into account time value of money by using discounted cash flows. | |||||||
| – | IRR technique takes into consideration all the cash inflows and outflows expanding over the total life of the project. | |||||||
| – | It is easier to interpret as it gives rate of return in percentage rather than in amounts. | |||||||
| Disadvantages | ||||||||
| – | It is quite tedious to calculate as it involves hit and trial procedure. | |||||||
| – | It might give conflicting results when timings of cash flows differ between two projects (Investment decisions-Capital budgeting, nd). | |||||||
| – | IRR technique is biased towards smaller projects which are more likely to give higher rate of return over larger projects. | |||||||
| ARR | ||||||||
| It might be defined as the annual net income earned on the average funds invested. | ||||||||
| Its merit is that it is simple to adopt and easy to calculate as the data required for calculating ARR is easily available. | ||||||||
| Disadvantages | ||||||||
| – | It ignores the time value of money. | |||||||
| – | ARR is based on accounting profits rather than cash flows. | |||||||
| – | ARR does not take into account the economic life of the project and salvage value. | |||||||
| – | It also does not recognise amount of investment required. | |||||||
