I need to perform a break-even analysis of moving from one system design to another.
Definitions
$M_0, M_1$ = one-time initial manufacturing cost of currently deployed system design and new system design, respectively.
$O_0, O_1$ = operational cost of running the application on the currently deployed system design and new system design, respectively.
$L$ = lifetime of system (e.g., in terms of number of times the hard disk can be used before failure, 10^6 uses)
$T$ = system component usage of the application, given a specific system design (e.g., hard disk is used 100 times within the application runtime)
Therefore, number of application invocations during lifetime = $L/T$
Assume $L$ remains the same no matter the system design change. But component usage may differ on the new system design. e.g., ($T_1 < T_0$)
Also, the operational cost of the new system design may also differ (e.g., new design may be more efficient: $O_1 < O_0$)
Assume the old design is abandoned and the system is switched to the new design midway through its lifetime.
Assume the initial manufacturing cost can be amortized across the lifetime of the system
Then, the total cost per application invocation = $C = O + (\frac{T}{L} \times M)$
Problem
Using break-even analysis, what is the formula to find $t_B$, the break-even point where the new design offsets both the (a) unamortized manufacturing cost of the old system and (b) manufacturing cost of the new system design can be amortized within the lifetime L ?
(Note: here the units of $t_B$ should be number of application invocations of the new design after the switch)
I'm thinking of following the general definition of breakeven: $t_B$ = fixed cost / savings per invocation
if so, should savings per invocation only consider operational savings per invocation ($O_1 - O_0$) or to total savings per invocation ($C_1 - C_0$) ? (because the new design may also have lower $T$
