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. Show your calculations and explain your answer.

Answer 1

Solution

The social discount rate used by the Canadian Federal Govt. is 10%

Given that in both the cases,the instruments become operative in the year 2020 itself,if chosen.If we take the present value of future cash outflows,then the Technology Y is the best option (although even by observation ,we can say the same)

Technology X

= -1,00,000 - (2000 / (1.10 ^3)) - (3000 / (1.10 ^ 6)) - (4000 / (1.10 ^9))

since the amounts 2000,3000 and 4000 are planned to be expended in the years 3,6 and 9 respectively,the denominator is raised to the respective powers according to the formula for calculating the present value.

= -1,00,000 - 1502.27 - 1693.42 - 1696.39

= -$1,04,892.08

Technology Y

= -75,000 - (20000 / (1.10 ^ 5))

= -75,000 - 12418.42

= - $87,418.42