In the spreadsheet for problem1.xls you will nd the specications for two project
ID: 2680935 • Letter: I
Question
In the spreadsheet for problem1.xls you will nd the specications for two projects. This includes how much will be received or invested and at which time. Some of the values are unknown, specically X; t1; t2; t3. Investigate what values for these variables will make project 2 preferable to project 1. You may impose restrictions on your variables to attain closed form solutions if you like. Assume money is earned at the compound interest rate given in the spreadsheet.Project 1 Investment Time
-10000 at 0
-10000 at 1
-5000 at 2
3000 at 4
5000 at 5
10000 at 6
30000 at 7
30000 at 15
Project 2 Investment Time
-13000 at 0
-18000 at 1
10000 at 2
X at 4
27000 at t1
21000 at t2
6000 at t3
Compound interest rate: 0.1
I've been able to solve this far:
PV1 = -10,000(1.10^0) + -10,000(1.10^-1) + -5,000(1.10^-2) + 3000(1.10^-4) + 10,000(1.10^-6) + 30,000(1.10^-7) + 30,000(1.10^-15) = 7,047.14
PV2 = -13,000(1.10^0) + -18,000(1.10^-1) + -10,000(1.10^-2) + X(1.10^-4) + 27,000(1.10^-t1) + 21,000(1.10^-t2) + 6,000(1.10^-t3)
I'm just unsure where to progress from here...
Explanation / Answer
Project#1 seems to have year-end flows as following: 1: negative at first...start-up costs and the likes, I assume 2: then positives, thus revenue... If so, then you will have $42,407 at end of 15th year (10% annual). (the Future Value) Problem seems to be to compare this to Project#2; so I assume that we use 15 years again, to make it a sensible comparison... We need to calculate x as the required amount at end of year#4, that will result in an ending balance of $42,407 after taking in consideration that 3 more flows will be received: 27000,21000,6000. I see no reason for making that a $54,000 amount received at end of 15th year: nothing prevents that a per problem's wording. Right before x is received at end of year#4, the balance will be $(30,891) ... in the red! So we have: 1.10^11(x - 30891) + 54000 = 42407 x = 26,827 Well, that at least tells you that 2nd project will be equal to the 1st project after 15 years if $26,827 is 4th year flow, and if 27000+21000+6000 = $54,000 is the 15th year flow (none in between).