Heating, ventilation, and air$-$conditioning $($HVAC$)$ systems are formed of various components.

The heat supply component is comprised of heat production, heat distribution, and heat transfer

subsystems. The latter system has three main elements: heat exchanger, pipes, and gate valves. A new

$300$ psi shell$/$tube heat exchanger has been installed in a recently renovated $12,000$ square feet building

hosting a data center, with an initial cost of $$800,000($including procurement and installation costs$).$ The

industry benchmarks for data centers point to an average mean time to failure of one year for the heat

exchangers, following an exponential distribution. A combination of preventative and reactive

maintenance programs is envisioned for this heat exchanger and is estimated to cost as follows $($in $$)$ at

year $$t$$:

TCM $($t$)=140,000*(1-$R$($t$))+25,000*$t$+10,000$

Where R$($t$)$ represents the reliability of the heat exchanger at year $$t$.$ The value of the heat

exchanger is expected to decline on a yearly basis due to physical and functional degradations. As such,

the salvage $($remaining$)$ value of the heat exchanger at year $$t$,$ as per industry benchmarks, is

approximated as follows $($in $$)$:

S$($t$)=400,000+300,000*$R$($t$)-50,000*$t

Note: Salvage value can be as low as zero.

Question $1)$ Given an interest rate of $12\%,$ which year would be the best time to replace this heat

exchanger with a new one? $(40$ marks$)$

Question $2)$ If a $6\%$ inflation rate is taken into consideration, at which year the replacement should take

place? How does inflation affect the replacement decision? $(40$ marks$)$

Question $3)$ For taxation purposes, a heat exchanger is considered a Class $8$ asset by Canada Revenue

Agency corresponding to a depreciation rate of $20\%.$ Report on the expected amount of Capital Cost

Allowance for this heat exchanger in the next $8$ years. $(20$ marks$)$