SISA Research Paper

Title: Note on discounting benefits

This footnote is about the formula on discounting benefits such as in calculating the discounted YPLL, or to discount health care costs and benefits.

In the literature on discounting current benefits to obtain their future value formula A is often used (Torgerson & Raftery, 1999). However, there are two possibilities, A to calculate the present value of a future benefit; and B to calculate the future value of a current benefit.

A: present value=1/(1+discount rate)(period-1)
formula to calculate the present value of a future benefit in period=t

{note the -1 in period-1. That is because the value of the future benefit is, by definition, a 100% at moment period. If we would have the full future benefit NOW (i.e., in period 1) then: present value=1/(1+discount rate)(period-1) = $/(1+discount rate)(1-1) =$/1=$)}

As an example of A, say someone promises to pay you a 1000 dollars 10 years from now. At an inflation rate of 2% per year, what is the current real value? ($1000/(1+0.02)(10-1))=$1000/1.2=$833.3. The difference between $1000 and $833 is called the discount, the 0.02 the discount rate, 10 the period.

B: future value=(1-discount rate)(period-1)
formula to calculate the future value in period=t of a present benefit

{note the -1 in period-1. NOW is period one and the value of a benefit is a 100%, because by definition we have the full benefit NOW. Thus, present value=1/(1+discount rate)(period-1) = $/(1+discount rate)(1-1) =$/1=$)}

To calculate the future value of a present benefit formula B is used. I own $1000 now, at an inflation rate of 2%, what is the real value ten years from now? $1000(1-0.02)(10-1)=$1000*0.83=$830.

Although for small discount rates the difference between the formula A and B is minimal, the difference will be large for large discount rates or long periods. For example, if a benefit does not have a value beyond the current period, if we use formula A there will remain a value of 50% (1/(1+100%)(2-1)=0.5) in the second period, with formula B the value will be zero ((1-100%)(2-1)=0)

Formula A is mostly the correct one for discounting the YPLL. The benefit from surviving a cause of death today is in the future while the value is obtained now as is the (preventive) investment. If one survives now because of some investment this enables one to enjoy additional years of life next year, five or ten years from now. Again, discounting the YPLL considers that it is highly unlikely that now at this point in taking a decision to invest in ones health and forgo some other benefit one values surviving next year similar to twenty years from now.

Torgerson DJ., Raftery J. Economics notes: Discounting. BMJ 1999; 319: 914.

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SISA Research Paper