Math questions - need explaination

Hi,

I would appreciate of someone elaborate/explain the answers for following questions -

1) A company has to make a choice between two projects, because the available resources in money and kind are not sufficient to run both at the same time. Each project would take 9 months and would cost $250,000. The first project is a process optimization which would result in a cost reduction of $120,000 per year. This benefit would be achieved immediately after the end of the project.The second project would be the development of a new product which could produce the following net profits after the end of the project:

1. year:       $     15,000
2. year:     $     125,000
3. year:     $     220,000

Assumed is a discount rate of 5% per year. Looking at the present values of the benefits of these projects in the first 3 years, what is true?
1) Both projects are equally attractive.
2) The first project is more attractive by app. 7%.
3) The second project is more attractive by app. 5%.
4) The first project is more attractive by app. 3%.


2) You are running a project for a customer based on a cost-reimbursable contract with the following terms:
 
Target costs:     $     1,000,000
Fixed fee:     $     100,000
Benefit/cost sharing:     80% / 20%
Price ceiling:     $     1,200,000

Which is the PTA (= point of total assumption, break point) of the project?
1) $1,300,000
2) $1,500,000
3) $80,000
4) $1,125,000

First question requires you to calculate PV for both projects and then find out which one is better.

In case of project 1,

1st year = 120000/(1+0.05)^1 = $ 114286
2nd year = 120000/(1+0.05)^2 = $ 108844
3rd year = 120000/(1+0.05)^3 = $ 103661

Total = $326,791

Project 2

 

1st year = 15000/(1+0.05)^1 = $ 14286
2nd year = 125000/(1+0.05)^2 = $ 113379
3rd year = 220000/(1+0.05)^3 = $ 190044

Total = $317,709
 
Since Project 1 offers better return it is clearly winner.
How much better?
 
(326791 - 317709)/317709*100 = 2.85 %
So answer 4 is correct
 
In the second question, it is a simple case of filling in the formula values:
 
PTA = ((ceiling price - target price)/buyer/seller ratio) + target cost
 
target price = target cost + fixed fee
target price = 1,000,000 + 100,000 = 1,100,000
 
PTA = ((1,200,000 - 1,100,000)/0.8)+1,000,000
PTA = 1,125,000
 
So option 4 is correct answer.
 

Thank you very much !