# The Comparison of Irr and Npv

**Topics:**Net present value, Internal rate of return, Rate of return

**Pages:**10 (2887 words)

**Published:**September 20, 2011

(i) Calculation for Project 13

(ii) Calculation for Project 24

(iii) Calculation for Project 35

(iv) Calculation for Project 46

(v) Calculation for Project 57

(vi) Calculations summary8

Question 2. Assessment of the proposals9

Question 3. Other factors to be considered11

Question 4. The comparison of IRR and NPV12

References14

Bibliography15

Question 1. Calculation of Payback, NPV and IRR.

(i) Calculation for Project 1:

Year| Net cash flow (£) | Cumulative net cash flow (£)| Discount factors| Present value (£)| | | | 10%| 20%| 25%| 10%| 20%| 25%|

1-2| 0| 0| | | | | | |

3| 73,000| 73,000| 0.751| 0.579| 0.512| 54,823| 42,267| 37,376| 4| 73,000| 146,000| 0.683| 0.482| 0.410| 49,859| 35,186| 29,930| 5| 73,000| 219,000| 0.621| 0.402| 0.328| 45,333| 29,346| 23,944| Total present value| 150,015| 106,799| 91,250|

Less: Initial investment | 100,000| 100,000| 100,000|

Net present value (NPV) = Total present value - Initial investmentNPV@10% = £50,015| 50,015| 6,799| (8,750)| Payback period=3+ £100,000-£73,000£73,000= 3.37 years or 0.37 * 12 months = 3 year and 4.4 months | Internal rate of return (IRR)

=positive rate+(positive NPVpositive NPV + negative NPV* × range of rates)* ignore the negative sign=20%+£6,799£6,799 + £8,750 × (25% - 20%)= 22.2%|

Conclusion:

As the NPV of £50,015 is positive, the project 1 can be accepted. The IRR of 22.2% which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 3 years and 4.4 months is necessary for the project to pay back initial investment of £100,000. (ii) Calculation for Project 2:

Year| Net cash flow (£)| Discount factors| Present value (£)| | | 10%| 20%| 25%| 10%| 20%| 25%|

Annuity for 5 years| 66,000| 3.791| 2.991| 2.690| | | | Initial investment| 180,000| 180,000| 180,000|

Net present value (NPV) of an annuity= Net cash flow * Discount factor – Initial investment = £66,000 * Discount factor - £180,000NPV@10% = £70,206| 70,206| 17,406| (2,460)| Payback period of an annuity=Initial investmentNet cash flow per year=£180,000£66,000= 2.7 years or 0.7 * 12 months = 2 years and 8.4 months| Internal rate of return (IRR)

=positive rate+(positive NPVpositive NPV + negative NPV* × range of rates)* ignore the negative sign=20%+£17,406 £17,406 + £2,460 × (25% - 20%)= 24.4%|

Conclusion:

As the NPV of £70,206 is positive, the project 2 can be accepted. The IRR of 24.4% which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 2 years and 8.4 months is necessary for the project to pay back initial investment of £180,000.

(iii) Calculation for Project 3:

Year| Net cash flow (£)| Cumulative net cash flow (£)| Discount factors| Present value (£)| | | | 10%| 30%| 35%| 10%| 30%| 35%|

1| 145,000| 145,000| 0.909| 0.780| 0.740| 131,805| 113,100| 107,300| 2| 145,000| 290,000| 0.826| 0.600| 0.550| 119,770| 87,000| 79,750| 3-5| 0| 0| | | | | | |

Total present value| 251,575| 200,100| 187,050|

Less: Initial investment | 200,000| 200,000| 200,000|

Net present value (NPV) = Total present value - Initial investmentNPV@10% = £51,575| 51,575| 100| (12,950)| Payback period=1+ £200,000 - £145,000£145,000 = 1.4 years or 0.4 * 12 months = 1 year and 4.8 months| Internal rate of return (IRR)

=positive rate+(positive NPVpositive NPV + negative NPV* × range of rates)* ignore the negative sign=30%+£100£100 + £12,950 × (35% - 30%)= 30.0%|

Conclusion:

As the NPV of £51,575 is positive, the project 3 can be accepted. The IRR of 30% which is above the minimum rate of return (10%) bring us to the same conclusion. Payback period shows that 1 year and 4.8 months is necessary for the project to pay back initial...

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