Cost-Benefit analysis question.

[-King-]

I have a feeling that this question should be easy, but I can't get it. I'm thinking that the benefits is supposed to outweigh the cost, but I keep getting the opposite. Any help?

[alnorth]

Cool problem. I'll restate the conditions first.

#1 Peace corps stint would last for 3 years
#2 In those 3 years, your food and lodging is paid for, and you would get $10,000 per year.
#3 Alternatively, you can forget the peace corps and start working right away. $50,000 per year, minus $15,000 expenses for paying for your own room and board, net $35,000 per year
#4 If you join the peace corps, you will receive emotional enjoyment worth the equivalent to you of $15,000 per year in those 3 years.
#5 If you join the peace corps, you incur a one-time cost in the first year of $8,000
#6 This condition is worded vaguely. (eg "lifetime pay at 1,000 per year" could mean the present value of your life earnings is reduced by 3,000, or that your starting salary after the peace corps will be 49,000, or that it will be 47,000, or some other interpretation) I decided to assume that after you get back from the peace corps, you will be working for 49,000 per year.
#7 You will retire 30 years after you are done with the peace corps, or 33 years from today. So you'll either be working at your job for 30 years or 33 years.
#8 If you work for the peace corps, you will gain $50,000 of present value.

Join peace corps
Year 1: 10k - 8k + 15k + 50k = 67k
Years 2 and 3: 10k + 15k = 25k
Years 4 through 33: 49k - 15k = 34k
Total: 1.137MM

Don't join peace corps
Years 1 through 33: 50k - 15k = 35k
Total: 1.155MM

It's very close, but I'm also coming up with no. Since we are including non-monetary "emotional" gains, I don't know that it would be appropriate to evaluate what happens when you introduce an interest rate. (otherwise with the numbers this close and that lump sum for joining the peace corps, there could be some interest rate that makes them equal)

Even though you might think the answer "should be" join the peace corps, I wouldn't be surprised if it was no. This seems like a clever way to fool the student into thinking one answer just has to be right and twisting the numbers around to fit that conclusion instead of just doing the math.

edit: going back to condition 6, if that merely meant your present value is reduced by 3000, then you should join the peace corps.

[jbwm89]

Originally Posted by -King-

Yeah, I'm thinking that I'm going to learn more out of the weekly tutoring sessions that at the actual lecture.

that econ help lab thing helps, there is usually a pretty massive curve too.

[Rain Man]

Peace Corps Benefits
Pay - $30,000
Personal - $15,000 x 3 = $45,000
Language - $50,000

Total Benefits - $125,000


Peace Corps Costs

Lost Pay - $35,000 x 3 = $105,000
Physical - $8,000
Lost Lifetime Pay - $30,000

Total Costs $143,000


Become a corporate drone.

[jbwm89]

Originally Posted by alnorth

Cool problem. I'll restate the conditions first.

#1 Peace core stint would last for 3 years
#2 In those 3 years, your food and lodging is paid for, and you would get $10,000 per year.
#3 Alternatively, you can forget the peace core and start working right away. $50,000 per year, minus $15,000 expenses for paying for your own room and board, net $35,000 per year
#4 If you join the peace core, you will receive emotional enjoyment worth the equivalent to you of $15,000 per year in those 3 years.
#5 If you join the peace core, you incur a one-time cost in the first year of $8,000
#6 This condition is worded vaguely. (eg "lifetime pay at 1,000 per year" could mean the present value of your life earnings is reduced by 3,000, or that your starting salary after the peace corp will be 49,000, or that it will be 47,000, or some other interpretation) I decided to assume that after you get back from the peace corp, you will be working for 49,000 per year.
#7 You will retire 30 years after you are done with the peace corp, or 33 years from today. So you'll either be working at your job for 30 years or 33 years.
#8 If you work for the peace core, you will gain $50,000 of present value.

Join peace core
Year 1: 10k - 8k + 15k + 50k = 67k
Years 2 and 3: 10k + 15k = 25k
Years 4 through 33: 49k - 15k = 34k
Total: 1.112MM

Don't join peace core
Years 1 through 33: 50k - 15k = 35k
Total: 1.115MM

It's very close, but I'm also coming up with no. Since we are including non-monetary "emotional" gains, I don't know that it would be appropriate to evaluate what happens when you introduce an interest rate. (otherwise with the numbers this close and that lump sum for joining the peace core, there could be some interest rate that makes them equal)

Even though you might think the answer "should be" join the peace core, I wouldn't be surprised if it was no. This seems like a clever way to fool the student into thinking one answer just has to be right and twisting the numbers around to fit that conclusion instead of just doing the math.

edit: going back to condition 5, if we assume that it meant reduce the lifetime earnings by 3k, then you should join the peace corp.

I took it as reduce the lifetime earnings by 1k per year for the 30 years you work afterwards.

[-King-]

Originally Posted by alnorth

Cool problem. I'll restate the conditions first.

#1 Peace core stint would last for 3 years
#2 In those 3 years, your food and lodging is paid for, and you would get $10,000 per year.
#3 Alternatively, you can forget the peace core and start working right away. $50,000 per year, minus $15,000 expenses for paying for your own room and board, net $35,000 per year
#4 If you join the peace core, you will receive emotional enjoyment worth the equivalent to you of $15,000 per year in those 3 years.
#5 If you join the peace core, you incur a one-time cost in the first year of $8,000
#6 This condition is worded vaguely. (eg "lifetime pay at 1,000 per year" could mean the present value of your life earnings is reduced by 3,000, or that your that your starting salary after the peace corp will be 49,000, or that it will be 47,000, or some other interpretation) I decided to assume that after you get back from the peace corp, you will be working for 49,000 per year.
#7 You will retire 30 years after you are done with the peace corp, or 33 years from today. So you'll either be working at your job for 30 years or 33 years.
#8 If you work for the peace core, you will gain $50,000 of present value.

Join peace core
Year 1: 10k - 8k + 15k + 50k = 67k
Years 2 and 3: 10k + 15k = 25k
Years 4 through 33: 49k - 15k = 34k
Total: 1.112MM

Don't join peace core
Years 1 through 33: 50k - 15k = 35k
Total: 1.115MM

It's very close, but I'm also coming up with no. Since we are including non-monetary "emotional" gains, I don't know that it would be appropriate to evaluate what happens when you introduce an interest rate. (otherwise with the numbers this close and that lump sum for joining the peace core, there could be some interest rate that makes them equal)

Even though you might think the answer "should be" join the peace core, I wouldn't be surprised if it was no. This seems like a clever way to fool the student into thinking one answer just has to be right and twisting the numbers around to fit that conclusion instead of just doing the math.

edit: going back to condition 5, if we assume that it meant reduce the lifetime earnings by 3k, then you should join the peace corp.

The reason I'm thinking the answer should be yes is because question 2 says: "Now suppose you have finished your peace corps service and you find the following things occurred that you had not expected. Suppose you were correct about all your other expectations"

So I'm thinking that the benefit must have been more than the cost for him to join. Maybe I'm overthinking this.

[jbwm89]

Originally Posted by -King-

The reason I'm thinking the answer should be yes is because question 2 says: "Now suppose you have finished your peace corps service and you find the following things occurred that you had not expected. Suppose you were correct about all your other expectations"

So I'm thinking that the benefit must have been more than the cost for him to join. Maybe I'm overthinking this.

possibly, micro down here is pretty confusing and inconsistent as far as which approach is necessary.

[alnorth]

you guys reply fast. I made several corrections to fix some minor errors.

It all boils down to condition 6. If it means you'll be working for 49,000 per year for 30 years, then don't join the peace corps. If it means you merely lose a grand total of $3,000 over your entire working life, then join the peace corps.

[-King-]

Yeah, the wording on this problem really messes it up.

[alnorth]

condition 6 is screwing this up. I'm now beginning to think it just meant take off 3000 total instead of 1 grand per year (or 30k total). The reason is the word "lifetime". If the question writer wanted to say your salary is reduced to 49,000, then if that word is removed, the intent is much clearer. "lifetime" does not need to be there if that was the intent.

If the question meant to say you'll lose 3,000 over the course of your life, then the value of joining the peace corps is $1.164MM

edit: yep, after reading it again I change my mind, I'm going with the alternate interpretation, and I'd make it very clear what I was doing and why. So yes, join the peace corps.

[-King-]

Originally Posted by alnorth

condition 6 is screwing this up. I'm now beginning to think it just meant take off 3000 total instead of 1 grand per year (or 30k total). The reason is the word "lifetime". If the question writer wanted to say your salary is reduced to 49,000, then if that word is removed, the intent is much clearer. "lifetime" does not need to be there if that was the intent.

If the question meant to say you'll lose 3,000 over the course of your life, then the value of joining the peace corps is $1.164MM

edit: yep, after reading it again I change my mind, I'm going with the alternate interpretation, and I'd make it very clear what I was doing and why. So yes, join the peace corps.

I think I'm going to go with that since thats the only way question 2 would make sense.

It wouldn't make sense to go to the peace corp in question 2 if the benefit was lower than the cost.

[-King-]

Wait, am I supposed to calculate it for his working career?

Benefits

30,000 peace corp
49,000 per year for 30 years
50,000 french
15,000 per year for 3 years for satisfaction in the peace corps

Total= $1,545,000

Costs
50,000 a year for 30 years
8,000 for the transportation and physical
15000 room and board

Total = $1,523,000

I have never overthunk a problem like this

[alnorth]

Originally Posted by -King-

Wait, am I supposed to calculate it for his working career?

Benefits

30,000 peace corp
49,000 per year for 30 years
50,000 french
15,000 per year for 3 years for satisfaction in the peace corps

Total= $1,545,000

Costs
50,000 a year for 30 years
8,000 for the transportation and physical
15000 room and board

Total = $1,523,000

I have never overthunk a problem like this

I assumed that if you dont join the peace corps, then you work for 33 years. The problem said his retirement age was 30 years after peace corps.

Given that and what we said above, I'm getting

peace corps = $1,164,000
no peace corps = $1,155,000

edit: I'm sure there's a clean way to divide it between cost/benefit, but thats unintuitive, unnecessary, and more likely to make mistakes.

You have two different people, one who joined, and one who did not join. How much will each make? Higher value wins. Simple.

[-King-]

Emailed a TA. She said that the cost SHOULD outweigh the benefit.

[alnorth]

Originally Posted by -King-

Emailed a TA. She said that the cost SHOULD outweigh the benefit.

in that case, my original interpretation of condition 6 might be right, the values in that post might be right, and the way the question was worded sucks. The word "lifetime" should have been excluded.

[-King-]

So all in all do I calculate it for her whole career, or calculate it for 3 years?