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ial Estrmated Estimated capital required receipts disbursements annual annual Estimated life years) 12 Investment 300,000 130,000 140,000 175,000 120,000 56,000 25,000 62,000 126.000 Note: Assume equal replacement conditions for this problem. Approach 2. Assume equal replacement conditions (costs and incomes) for each alter- native and compute the discounted present worth on the basis of the least common multiple of lives for all alternatives. First, draw a detailed sketch of the cash flow diagram for each alternative using Approach 2. Then, using each cash flow diagram, create a NPV formula for each alternative: interest rate is an unknown variable in each NPV formua. Finally attempt to solve for the interest rate that makes the NPV equal to zero; this is the rate of return

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1. Cash flow diagram using Least Common Multiple Approach Write Up: The present value analysis is done for 2 or more projects to evaluate which machine or investment proposal provides more positive cash flow. An inherent assumption here is that the duration of all the projects that are being compared is same. So if the duration of projects being compared is not same, simple present value worth would give incorrect result. That is because project with longer duration would always give more cash flows. To overcome this issue, we have one tool of using Least Common Multiple Assumptions of LCM Approach: Selected alternative can be repeated over each cycle of LCM in excactly same manner and that cash flow estimates are same for each life cycle Considering the duration of the given projects o 12, 6& 8 years, LCM would be 24 years

Cash flows for various alternatives for 24 years INVESTMENT M INVESTMENT P INVESTMENT S Original Duration 12 Yrs Original Duration 6 Yrs Original Duration 8 Yrs Year Net Cash Flow Year Net Cash Flow 0 140,000 49,000 6 (140,000 49,000 1 (140,000 49,000 18 (140,000 49,000 Year Net Cash Flow 0 5 (120,000 31,000 8 120,000 31,000 1 (120,000 31,000 0 (300,000 68,000 1 to 12 $ 1 to 6 $ 1 to 8 12 (300,000 68,000 13 to 24S 7 to 12 S 9 to 16 $ 13 to 18S 17 to 24 S 19 to 24S

Construction and meaning of cash flows In case of Investment M, Original duration being 12 years, since durations are uneven, we would consider 2 periods of 12 years. Accordingly, in case of Investment P, Original duration being 6 years, we would consider 4 periods of 6 years. Likewise, for Investment s, we would be considering 3 periods of 8 years It is like we are investing in Investment M 2 times. Therefore, we have to consider the cash flows twice (ignoring time value of money). Therefore we are considering dual cash outflows of initial nature and corresponding cash flows2. NPV Formula for each alternative MASTER FORMULA PWM--Initial Investment + Annual Cash inflow x (1 t i-1 lnitial lnvestment at time t-1 INVESTMENT M PWM-$3,00,000 $68,000 x (1-1-$3,00,000 INVESTMENT P PWM- $1,40,000 $49,000 x (1-1 - S1,40,000 S1,40,0001,40,000 INVESTMENT S PWM- $1,20,000 $31,000x (1-1 S1,20,000 1.20,000

3. Calculation of IRR Write up: IRR is such a rate at which NPV is zero. While evaluating projects using IRR, higher the better principle is applicable i.e., higher the IRR, Better it is for the company IRRH 20.17% IRRP 26.43% RRs 19.71% Year Flows Year Flows Year Flows 01$ 〔300,000〕 1 $68,000 2 68,000 3$68,000 468,000 5 68,000 6 68,000 7$68,000 8 68,000 968,000 1068.000 11$68,000 12(232.000 13 68.000 1 68.000 15$68,000 1668,000 1768.000 168,000 19$68,000 20 $68,000 21 68,000 22 $68,000 23 $68,000 24$68,000 01$ 〔140,000) 1 $49,000 249,000 3$49,000 449,000 549,000 6 $(91,000) 749,000 8 49,000 9$49,000 1049,000 11$49,000 12 $ 〔91,000 13$49,000 14| 49,000 1549,000 16$49,000 17$49,000 18| $ (91,000) 19$49,000 20 $49,000 21 $49,000 22 $49,000 23 $49,000 24$49,000 01$ 〔120,000 1 $31,000 231,000 3 $31,000 4$31,000 5 31,000 6 31,000 731,000 8 (89,000) 9$31,000 1031,000 11$31,000 1231,000 1331,000 1431,000 1531,000 161 $ (89,000) 171 $ 31,000 181 $ 31,000 19$31,000 20 $31,000 21 $31,000 22 $31,000 23 $31,000 24$31,000

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