Using the High$-$Low Method to Estimate Variable and Fixed Costs

Located on Swiftcurrent Lake in Glacier National Park, Many Glacier Hotel was built in $1915$ by the Great Northern Railway. To supplement its lodging revenue, the hotel decided to begin manufacturing and selling small wooden canoes decorated with symbols hand painted by Native Americans living near the park. The canoes were a great success, so a couple of years later the hotel began manufacturing and selling paddles. Many hotel guests purchase a canoe and paddles for use in self$-$guided tours of Swiftcurrent Lake. Because production of the two products began in different years, the canoes and paddles are produced in separate production facilities and employ different laborers. Each canoe sells for $\backslash (\backslash$$ $540\backslash ),$ and each paddle sells for $\backslash (\backslash$$ $60\backslash ).$ About $15$ years ago, a fire destroyed the hotel's accounting records. A new system put into place before the next season provides the following aggregated data for the hotel's canoe and paddle manufacturing and marketing activities $($Years $1$ through $12$ give the data for the years in which the new accounting system was active$)$: $\backslash$begin$\{$tabular$\}\{$c$|$c$|$c$|$c$|$c$|$c$\}$

$\backslash$hline $6$ & $380$ & $132,000$ & $6$ & $1,700$ & $66,500\backslash \backslash$

$\backslash$hline $7$ & $415$ & $146,500$ & $7$ & $1,720$ & $66,300\backslash \backslash$

$\backslash$hline $8$ & $430$ & $132,000$ & $8$ & $1,850$ & $71,750\backslash \backslash$

$\backslash$hline $9$ & $450$ & $146,100$ & $9$ & $1,900$ & $72,000\backslash \backslash$

$\backslash$hline $10$ & $470$ & $155,000$ & $10$ & $2,020$ & $78,900\backslash \backslash$

$\backslash$hline $11$ & $480$ & $136,000$ & $11$ & $2,050$ & $78,200\backslash \backslash$

$\backslash$hline $12$ & $500$ & $167,000$ & $12$ & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Marketing Data

$\backslash$begin$\{$tabular$\}\{$c$|$c$|$c$|$c$|$c$|$c$\}$

$\backslash$hline Year & $\backslash$begin$\{$tabular$\}\{$c$\}$

Number $\backslash \backslash$

of Canoes $\backslash \backslash$

Sold

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Total $\backslash \backslash$

Canoe $\backslash \backslash$

Marketing $\backslash \backslash$

Costs

$\backslash$end$\{$tabular$\}$ & Year & $\backslash$begin$\{$tabular$\}\{$c$\}$

Number $\backslash \backslash$

of Paddles $\backslash \backslash$

Sold

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Total $\backslash \backslash$

Paddle $\backslash \backslash$

Marketing $\backslash \backslash$

Costs

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $250$ & $\backslash (\backslash$$ $45,000\backslash )$ & $1$ & $900$ & $\backslash (\backslash$$ $7,500\backslash )\backslash \backslash$

$\backslash$hline $2$ & $240$ & $47,000$ & $2$ & $1,200$ & $9,000\backslash \backslash$

$\backslash$hline $3$ & $275$ & $43,000$ & $3$ & $1,000$ & $8,000\backslash \backslash$

$\backslash$hline $4$ & $310$ & $51,000$ & $4$ & $1,100$ & $8,500\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Required:

$1.$ High$-$Low Cost Estimation Method

a$.$ Use the high$-$low method to estimate the per$-$unit variable costs and total fixed costs for the canoe product line.

b$.$ Use the high$-$low method to estimate the per$-$unit variable costs and total fixed costs for the paddle product line.

$2.$ Cost$-$Volume$-$Profit Analysis, Single$-$Product Setting

Use CVP analysis to calculate the break$-$even point in units for

a$.$ The canoe product line only $($i$.$e$.,$ single$-$product setting$)$

b$.$ The paddle product line only $($i$.$e$.,$ single$-$product setting$)$

$3.$ Cost$-$Volume$-$Profit Analysis, Multiple$-$Product Setting The hotel's accounting system data show an average sales mix of approximately $300$ canoes and $1,200$ paddles each season. Significantly more paddles are sold relative to canoes because some inexperienced canoe guests accidentally break one or more paddles, while other guests purchase additional paddles as presents for friends and relatives. In addition, for this multiple$-$product CVP analysis, assume there is an additional $\backslash (\backslash$$ $28,000\backslash )$ of common fixed costs for a customer service hotline used for both canoe and paddle customers. Use CVP analysis to calculate the break$-$even point in units for both the canoe and paddle product lines combined $($i$.$e$.,$ the multiple$-$product setting$).$

$4.$ Cost Classification

a$.$ Classify the manufacturing costs, marketing costs, and customer service hotline costs either as production costs or period costs.

b$.$ For the period costs, further classify them into either selling expenses or general and administrative expenses.

$5.$ Sensitivity Cost$-$Volume$-$Profit Analysis and Production Versus Period Costs, MultipleProduct Setting

If both the variable and fixed production costs $($refer to your answer to Requirement $1)$ associated with the canoe product line increased by $5\backslash \%($beyond the estimate from the high$-$low analysis$),$ how many canoes and paddles would need to be sold in order to earn a target income of $\backslash$$$96,000?$ Assume the same sales mix and additional fixed costs as in Requirement $3.$

$6.$ Margin of Safety

Calculate the hotel's margin of safety $($both in units and in sales dollars$)$ for Many Glacier Hotel, assuming the same facts as in Requirement $3,$ and assuming that it sells $650$ canoes and $2,400$ paddles next year.