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# Abel and Family Perfumes wants to add one or more of four new products to its current line of colognes. Historically, Abel has used a 5-year project recovery period and a MARR of 20% per year. (a) Determine which of the four options the company should undertake on the basis of a present worth analysis, provided the total amount of investment capital available is $800,000. Use a hand solution, unless assigned otherwise. (b) What products are selected if the investment limit is increased to$900,000? Use a spreadsheet, unless assigned otherwise. (All cash flows are in $1000 units.)$ $$\begin{matrix} \text{Product Line} & \text{R1} & \text{S2} & \text{T3} & \text{U4}\\ \hline \text{Investment, \} & \text{-200} & \text{-400} & \text{-500} & \text{-700}\\ \text{M&O cost, \/year} & \text{-50} & \text{-200} & \text{-300} & \text{-400}\\ \text{Revenue, \/year} & \text{150} & \text{450} & \text{520} & \text{770}\\ \hline \end{matrix}$$ \$

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a) Hand solution:

\begin{align*} \text{PW}_{\text{DN}}&=0\\[20pt] \text{PW}_{\text{R}1}&=-200{,}000+(150{,}000-50{,}000)(P/A, 20\%, 5)\\[7pt] &=-200{,}000+100{,}000(2.9906)\\[7pt] &= \boxed{\99{,}060}\\ \end{align*}

\begin{align*} \text{PW}_{\text{S}2}&=-400{,}000+(450{,}000-200{,}000)(P/A, 20\%, 5)\\[7pt] &=-400{,}000+250{,}000(2.9906)\\[7pt] &= \boxed{\347{,}650}\\ \end{align*}

\begin{align*} \text{PW}_{\text{T}3}&=-500{,}000+(520{,}000-300{,}000)(P/A, 20\%, 5)\\[7pt] &=-500{,}000+220{,}000(2.9906)\\[7pt] &= \boxed{\157{,}932}\\ \end{align*}

\begin{align*} \text{PW}_{\text{U}4}&=-700{,}000+(770{,}000-400{,}000)(P/A, 20\%, 5)\\[7pt] &=-700{,}000+370{,}000(2.9906)\\[7pt] &= \boxed{\406{,}522}\\ \end{align*}

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