Question

A public hospital would like to reduce breast cancer mortality by 20% every year. In order to do that it has two different options:

1. To buy technology X that allows detecting breast cancer at an earlier stage reducing breast cancer mortality by 20% every year.

Technology X will be bought at the beginning of 2020 (year 0) and it will be operative right away, meaning that mortality will be reduced by 20% already in 2020. The technology will be operative 10 years (until 2029, year 2029 included). However, every three years it needs to be checked and the hospital needs to pay the inspection costs. The following table summarizes all the costs:

Year	Cost
2020	100000
2023	2000
2026	3000
2029	4000

2. To buy technology Y that allows treating breast cancer in a less aggressive manner reducing breast cancer mortality by 20% every year.

Technology Y will be bought at the beginning of 2020 (year 0) and it will be operative right away, meaning that mortality will be reduced by 20% already in 2020. The technology costs 75000 dollars paid at the beginning (year 0). The technology will be operative 10 years (until 2029, 2029 included). These technology should be updated after 5 years. The update cost is 20000 dollars. The following table summarizes all the costs:

Year	Cost
2020	75000
2025	20000

With this information, which option is the most cost-effective technology to reduce breast cancer mortality by 20% per year (in 2020, meaning 2020 is year 0)? The discount rate is the one used by the Canadian Federal government as the social time preference rate(8%). Show your calculations and explain your answer.

Answer 1

Present Worth of Technology X

Initial Cost =100000

PW of next cost at year 2023= P/(1+r)^n = 2000/(1+8%)^3 = 2000/1.08^3 = 2000/1.2597 = 1587.66

PW of next cost at year 2026= P/(1+r)^n = 3000/(1+8%)^6 = 3000/1.08^6 = 3000/1.5869 = 1890.51

PW of next cost at year 2029= P/(1+r)^n = 4000/(1+8%)^9 = 4000/1.08^9 = 3000/1.999 = 2001

Total Cost of Technology X = 100000+1587.66+1890.51+2001= 105479.17

Present Worth of Technology Y

Initial Cost =75000

PW of update cost at year 2025= P/(1+r)^n = 20000/(1+8%)^5 = 20000/1.08^3 = 20000/1.4693 = 13611.66

Total Cost of Technology Y = 75000+13611.66= 88611.66

Since Technology Y PW of cost is lower Technology Y shall be selected