#$1$ Single Product CVP

Grand Canyon Adventures sells individual tickets for $$75$ for walking tours of the Grand Canyon. Each ticket has variable costs $($including lunch$)$ of $$15$ per ticket. The company has total fixed costs of $$200,000.$

Required:

a$.$ What is the CM per unit?

$75-15=60$

b$.$ How many tickets must be sold to breakeven?

$60.$x $=200,000$

$=>$ x $=3,334$

c$.$ How many units of tickets must be sold to earn a target income of $$60,000?$

$1000+3,334=4,334$

d$.$ If unit$-$level costs increase to $$20$ per ticket, what decrease in annual fixed costs must be achieved to keep the same breakeven point as calculated in part b$?$

$3,334(75-20)$

e$.$ Back to original assumptions: What is the CM ratio?

$60/75=0\mathrm{.}8$

f$.$ Using the CM ratio, what level of revenue is needed to breakeven?

$200,000.80=250,000$

g$.$ What level of revenue is needed to earn a target income of $$42,000?$

$200,000+42,000=242,000/\mathrm{.}8=302,000$

h$.$ How many tickets must be sold to earn after$-$tax income of $$120,000($with a tax rate of $40\%)$

$666\mathrm{.}7$

i$.$ If $4,000$ tickets are sold $($what is equivalent to $$300,000$ of sales$)$ what is the margin of safety in units? In dollars?

$4000-3,334=666$

j$.$ If $4,000$ tickets are sold, what is the DOL? If $5,000$ units are sold? If $10,000$ units are sold?

k$.$ Assume that $4,000$ tickets are sold, if sales increase by $5\%$ what will happen to profit? Assume that $10,000$ tickets are sold, if sales increase by $5\%$ what will happen to profit?