Feasibility 5 - notes PDF

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Feasibility Lecture (5) *Estimating the IRR via linear interpolation:-To find the IRR of projects with cash flows that extend over more than three points in time, we a fairly good approximation of an investment project’s IRR can be found through the mathematical technique called linear interpolation. -This approach used is to select a pair of discount rates so that one of them produces a positive NPV and the other produces a negative NPV. -We use the linear interpolation method to compare the real discount rate with the discount rate defined by management to to take a decision about accepting or rejecting the project. -The general rule for using linear interpolation is as follows. Select any two discount rates, a lower rate and a higher rate. Calculate the project’s NPV at each discount rate, the use the rule:IRR = LDR + [ LRNPV +(HDR – LDR)] LRNPV+HRNPV LRNPV= NPV calculated at Lower discount rate HRNPV= NPV calculated at higher discount rate LDR= Lower discount rate HDR= Higher discount rate Example:assume the project X using the following cash flows:Year Cash flow 0 - $ 1000 1 + $ 600 2 + $ 500 Calculate IRR using the linear interpolation

assuming to use 4% as a lower discount rate and 12% as a higher

discount rate at 4% discount rate Y Cash Discount factor PV of flow

0 -1000 (1+.04)0 = 1 1 +600 (1+.04)-1 =.9615 2 +500 (1+.04)-2 =.9246

at 12% discount rate

Cash flow

-1000 +576.9 +462.3

Y Cash

Discount factor PV of flow Cash flow 0 0 -1000 (1+.12) = 1 -1000 1 +600 (1+.12)-1 =.8929 +535.74 2 +500 (1+.12)-2 =.7972 +398.6

NPV = +39.2 NPV= - 65.66 IRR= 4% + [ 39.2 × (12% – 4%)] 39.2 – (-65.66) IRR= 4% + [0.37 × 8%] = 6.96% *IRR decision rule:-The decision rule is that only management should define the accepted discount rate (IRR). -Thus to accept the project, a project must generate a return at least equal to the return available elsewhere on the capital market. *IRR and the investment consumption model pages (82-83) for Reading *Discounted payback:-We studied in chapter (3) that the major limitation of payback period that it did not consider the time value of money. However the criticism could be overcome through the use of discounted payback. -It see how quickly a project takes to pay back its outlay in present value cash flow terms.

Example: assume that a company considers to evaluate the new project (009). The management usually uses 12% as a discount rate which reflects the capital market interest for similar projects. The following shows cash flows of the project:Year Cash flow 0 - $ 300000 1 +$ 90000 2 +$ 100000 3 +$ 120000 4 +$ 150000 5 +$ 110000 Calculate the discounted payback period Year 0 1 2 3 4 5

Cash flow Discount factor PV of cash flow - $ 300000 (1+0.12)0= 1 -$ 300000 +$ 90000 (1+0.12)-1=.8929 +$ 80361 +$ 100000 (1+0.12)-2=.7972 +$ 79720 +$ 120000 (1+0.12)-3=.7118 +$ 85416 +$ 150000 (1+0.12)-4=.6355 +$ 95325 +$ 110000 (1+0.12)-5=.5674 +$ 62414

The discounted

payback period will be 4 years. *Appendix: (Compounding and discounting) pages 85-89 for reading

[Chapter 6] Net present value and internal rate of return *in chapter (3):we studied the payback and ROCE/ARR techniques which deal with: 1- Single and independent projects (accept or reject). 2- Mutually exclusive projects (choose the best project). *in chapter (5): we studied the NPV and IRR techniques which deal with the single projects. Now in chapter (6): looking at the NPV and IRR decision rules when faced with mutually exclusive projects and other forms of project decision interdependence. Example: Suppose a company has to make a decision for the two following projects X1, Y1 and the management uses a discount rate 8% :Project X1 Year 0 1 2 3 4

Cash flow - $ 300000 +$ 120000 +$ 150000 +$ 100000 +$ 80000

Project Y1 Year 0 1 2 3

Cash flow - $ 250000 +$ 90000 +$ 120000 +$ 100000...