# Least common multiple of project lives long problem

2 Projects Project A: \$35,000,000 NPV, Life in years 8 Project B: \$35,000,000 NPV, Life in years 5 Cost for each project is \$30,000,000 Find NPVs under least common multiples approach. Answer: A=75.25, B=77.83 I can’t seem to get to these numbers. I get 73.37 million for use using the following combinations on my calc: C01: 35,000,000, F01: 1, C02:0, F02: 7, C03: 35,000,000, F03: 7 etc… and I repeat 5 times but cannot get the correct anser of 75.25, (instead I get 73.37). What am I entering wrong and is there an easier way to do replacement chain questions that are this long?

LCM: 40 Project A: CFo = -30 CF of NPV1-5 = 35 *The trick seems to be that you discount each NPV, so if over 8 years you realize 35m, you actually realize the 35m 5 diff times. Project B: CFo = -30 CF1-8 = 35 You realize the 35 8 times since the life is only 5 years I cant do the calc since I dont have the discount rate. But this is what I see it as, hope it helps

What is the rate of return given for these 2 projects?

My bad, the discount rate is 7.5%

lets do for Project A, Project B will be similar. Since the LCM is 40, to compare this project with B, we will keep doing the project 5 times. And the NPV of this project is already given as 35m. Which means, Now and at the end of every 8th year, we will be getting 35m (and because we already know NPV for 1 such term, we dont have to bother about any intermediate cashflows from the project). So, cashflows would be like: CF0 = 35 CF1 = 0, F01 = 7 CF2 = 35 – Cashflow at the end of 8th year CF3 = 0, F03 = 7 CF4 = 35 – Cashflow at the end of 16th year CF5 = 0, F05 = 7 CF6 = 35 – Cashflow at the end of 24th year CF7 = 0, F07 = 7 CF8 = 35 – Cashflow at the end of 32th year NPV of this cashflow at discount rate of 7.5% is 75.25

got it, thanks for your help.

So i cant get the correct answer for part b…wtf CF0 = 35 CF1 = 0, F01 = 4 CF2 = 35 – Cashflow at the end of 5th year CF3 = 0, F03 = 4 CF4 = 35 – Cashflow at the end of 10th year CF5 = 0, F05 = 4 CF6 = 35 – Cashflow at the end of 15th year CF7 = 0, F07 = 4 CF8 = 35 – Cashflow at the end of 20th year CF9 = 0, F01 = 4 CF10 = 35 – Cashflow at the end of 25th year CF11 = 0, F03 = 4 CF12 = 35 – Cashflow at the end of 30th year CF13 = 0, F05 = 4 CF14 = 35 – Cashflow at the end of 35th year NPV of this cashflow at discount rate of 7.5% is 108.95 Anyone help??

all i see is your CFo should be -30 NOT +35

I guess there is a problem with the question itself. Dtrynoski, can you please recheck the question. Is there any missing information there.

Northeastern Student Wrote: ------------------------------------------------------- > all i see is your CFo should be -30 NOT +35 No buddy. He is right in saying that the “NET” cash flows at CF0 = 35. This is net cash flow from CF0 to CF5 after deducting the starting cash flow of 30 NPV = Intermediate cash flow - Starting cash flow 35 = dont know - 30 Since NPV =35 is already given we dont use the 30 as starting cash flow.

i see now, just took at the example in the book, thanks for the correction