CT1 Sep 2009 Q 10

[Sunil Sanga]

Three doubts in this question:
1st - Cost of communities:
Communities affected by climate change will incur costs of $20bn per annum
incurred continuously, increasing at a continuous rate of 1% per annum.

This is increasing annuity with increasing continuous rate and resolved by taking integral. Please suggest is the only way to obtain this annuity??

2nd - Corbon technology

The experts are considering whether to recommend investment in a carbon storing
technology which, it is believed, will reduce all the costs and benefits listed above to
zero.


When it is believed that it will reduce all the costs and benefits to zero then why it is assumed that total cost would be benefits in solution


3rd: NPV at real rate :

Since in both part 3rd and 4th NPV needs to be calculated on real rate. How does this formula utilize for interest rate

Please help me to understand this question. All others suggestions and comments are most welcome.

 

[Darrell Chainey]

A very tricky question.
1. Yes, working from first principles you can use an annuity with the rate of payment including the term 1.01^t. But given we then discount using the term (1+i)^(-t) then when i=1% these two terms just cancel and we're integrating a constant. When i=4% you can use substitution to convert the integral into a continuous annuity (a bar) as they do in the solution.

2. The examiners' report suggests that lots of people missed this. The starting position is that the community incurs the costs outlined at the start of the question. If we then introduce the new technology these costs are removed and so they can be considered a benefit of investing in the new technology. (If we don't then we'd have no benefits and the project wouldn't be worth doing.)

3. In the first paragraph of the question it says that the numbers are given in 2009 dollars, implying they are all real (inflation adjusted) cashflows, brought back to 2009 monetary values. So we can directly use the real rates given with these given cashflows. (The actual cashflows would increase with inflation from the values given.)

Hope this helps a little.

 

[Sunil Sanga]

A very tricky question.
1. Yes, working from first principles you can use an annuity with the rate of payment including the term 1.01^t. But given we then discount using the term (1+i)^(-t) then when i=1% these two terms just cancel and we're integrating a constant. When i=4% you can use substitution to convert the integral into a continuous annuity (a bar) as they do in the solution.

2. The examiners' report suggests that lots of people missed this. The starting position is that the community incurs the costs outlined at the start of the question. If we then introduce the new technology these costs are removed and so they can be considered a benefit of investing in the new technology. (If we don't then we'd have no benefits and the project wouldn't be worth doing.)

3. In the first paragraph of the question it says that the numbers are given in 2009 dollars, implying they are all real (inflation adjusted) cashflows, brought back to 2009 monetary values. So we can directly use the real rates given with these given cashflows. (The actual cashflows would increase with inflation from the values given.)

Hope this helps a little.

 

[Sunil Sanga]

Thanks !!