Sziasztok, külföldi közgazdaság tudomány karon tanulok, ezért a feladat angolul van (elég könnyű szöveg). Van hozzá mások által megoldott eredményeim, de egyszerűen nem értem, hogyan jöttek ki (lásd alul)
Feladat:
The National Institutes of Health (NIH) is considering funding a grant for a promising research project that aims to cure a rare disease. The time frame of the research is five years. The grant would fund the hiring of 20 scientists making $150,000 per year for five years, a one-time investment in new lab equipment of $3 million during the first year, and $1 million per year for five years in lab supplies and materials. If successful, the cure would be available upon completion of the project, starting in Year 6. As the scientist reviewing the proposal for the NIH, you estimate that the probability of success for this project is only 2%. However, if it were successful, it would immediately cure all patients with the disease, which is fatal within one year of diagnosis, and kills approximately 15 people annually. To answer the following questions, assume the NIH uses a 7% discount rate, and is risk neutral.

A. Conduct a formal cost-benefit analysis for this project, weighing the costs of funding the proposal and the benefits of a possible cure for the disease. Use the figure of $9.6 million for the value of a life, and assume that the cure will work indefinitely. Do the costs outweigh the benefits? Do you recommend funding the grant? (Note: use the attached spreadsheet to conduct the cost-benefit analysis. Assume you are conducting these calculations in Year 0, and that funding and project costs would begin in Year 1. Set up your spreadsheet in such a way that it is easy to change the value of life, discount rate and the % of success. Useful to remember that the present discounted value for an infinite stream of payments is = $/r. Since benefits occur after year 5, need to discount it further: = $benefits/r)/[(1+r)^5]).

B. One of your colleagues argues that a 2% chance of success is possibly an overestimate—the chance of the research being a success may more realistically be around 1%. If your colleague is right, how does this change the calculations you arrived at in part (a)?

Megoldás másoktól:
A) to conduct a formal cost-benefit analysis, we need to calculete the total costs and benefits of the projekt and then compare them.
Total costs = hiring 20 scientis for five years at 150 000 dollar per year * 5 years + $3 million as onetime investment in new lab equipment + $1 million per year for lab supplies and materials * 5 years = 43 million
MIÉRT NEM 23 000 000 ????????

Total benefits = number of lives saved * value of life = 15 * 9,6 million = 144 million

To calculate the present value of costs and benefits, we use the discount rate of 7% and assume the benefits will accrue in 6 year (when the cure is available).

Present value of costs = $43 million / (1 + 0,07)^5 = $29,6 million
Present value of benefits = $144 million / (1+ 0,07)^6 = $105,5 million
ANSWER: the present value of benefits exceeds the present value of costs, which means the the projekt has positive net present value(NPV). Therefor it is recommended to fund the grant.

B) if the chance of success is only 1% the expected number of lives saved would be:
Expected number of lives saved = 1% * 15 = 0,15
Total benefits = number of lives saved * value of a life = 0,15 * 9,6 million = 1,44 million
Present value of benefits = $14,4 million / (1+ 0,07)^6 = $1,05 million
ANSWER: as the expected benefits are now much lower, the projekt has a negative NPV and the costs outweitgh the benefits. Therefore, it is not recommended to fund the grant.

Szóval nagyjából értem csinálunk, de ha én akarom kiszámolni akkor nem jönnek ki ugyanazok az eredemények.
Köszönöm!