Comparing Projects 1 and 2: Finding Optimal Values for Financial Math Problem

[rayven1lk]

1)Hey guys i really need some help on this project I'm doing...i hope there's someone who could help me out and i'd really appreciate it...even if its some kinda hint its still fine...i just need some ideas...here's the question:

In the spreadsheet for problem1.xls you will nd the speci cations for two projects.
This includes how much will be received or invested and at which time. Some of the
values are unknown, speci cally 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 0
-10000 1
-5000 2
3000 4
5000 5
10000 6
30000 7
30000 15

Project 2 Investment Time
-13000 0
-18000 1
10000 2
X 4
27000 t1
21000 t2
6000 t3

Compound interest rate 0.1

2) Present Value of Project 1 = -10000-10000*1.001^(-1)-5000*1.001^(-2)+3000*1.001^(-4)+5000*1.001^(-5)+10000*1.001^(-6)+30000*1.001^(-7)+30000*1.001^(-15)

Present Value of Project 2 =-13000-18000*1.001^(-1)+10000*1.001^(-2)+X*1.001^(-4)+27000*1.001^(-t1)+21000*1.001^(-t2)+6000*1.001^(-t3)

3) I'm nopt sure how to advance from this point

 

[Ray Vickson]

1)Hey guys i really need some help on this project I'm doing...i hope there's someone who could help me out and i'd really appreciate it...even if its some kinda hint its still fine...i just need some ideas...here's the question:

In the spreadsheet for problem1.xls you will nd the speci cations for two projects.
This includes how much will be received or invested and at which time. Some of the
values are unknown, speci cally 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 0
-10000 1
-5000 2
3000 4
5000 5
10000 6
30000 7
30000 15

Project 2 Investment Time
-13000 0
-18000 1
10000 2
X 4
27000 t1
21000 t2
6000 t3

Compound interest rate 0.1

2) Present Value of Project 1 = -10000-10000*1.001^(-1)-5000*1.001^(-2)+3000*1.001^(-4)+5000*1.001^(-5)+10000*1.001^(-6)+30000*1.001^(-7)+30000*1.001^(-15)

Present Value of Project 2 =-13000-18000*1.001^(-1)+10000*1.001^(-2)+X*1.001^(-4)+27000*1.001^(-t1)+21000*1.001^(-t2)+6000*1.001^(-t3)

3) I'm nopt sure how to advance from this point

If your compound interest rate is yearly (that is, 10% per annum) and your times are in years, you should have factors like 1.10^(-2), 1.10^(-4), etc. The formula you wrote assumes an interest rate of (1/10)% per annum, which is awfully small. Anyway, you are supposed to vary X4, t1, t2 and t3 to find values that give NPV(Proj1) > NPV(Proj2), etc. Personally, I would take the advice given, and get closed-form formulas for the values of the NPVs, or at least, as close to closed-form as I could get. For example, you can set y2 = 27000*1.1^(-t1), y2 = 2100*1.1^(-t2), etc. Now NPV(Proj2) is a simple linear function of x, y1, y2 and y3. If you assume that 4 < t1 < t2 < t3 you have some inequalities between x, y1, y2 and y3.

RGV