Question

Integrative Multiple leverage measures Play-More Toys produces inflatable beach balls, selling 380,000 balls per year. Each ball produced has a variable operating cost of $0.86 and sells for $1.25. Fixed operating costs are $32,000. The firm has annual interest charges of $6,300, preferred dividends of $1,900, and a 40% tax rate. a. Calculate the operating breakeven point in units. b. Use the degree of operating leverage (DOL) formula to calculate DOL. c. Use the degree of financial leverage (DFL) formula to calculate DFL. d. Use the degree of totalleverage (DTL) formula to calculate DTL. Compare this to the product of DOL and DFL calculated in parts (b) and (c)

Answer 1

a.

Operating Break-even point = Fixed cost /Contribution margin

                               = Fixed cost / (Sales – Variable cost)

                               = $ 32,000/ ($ 1.25 - $ 0.86)

                               = $ 32,000/ $ 0.39 = 82,051.282051282 or 82,051 balls

b.

Degree of operating leverages = Q (P – V)/ Q (P – V) – F

Q = Number of units =

P = Price per unit = $ 1.25

V = Variable cost per unit = $ 0.86

F = Fixed cost = $ 32,000

Degree of operating leverages = 380,000 ($ 1.25 - $ 0.86)/ 380,000 ($ 1.25 - $ 0.86) – $ 32,000

= 380,000 x $ 0.39 / (380,000 x $ 0.39 – $ 32,000)

= $ 148,200/ ($ 148,200 - $ 32,000)

= $ 148,200/ $ 116200 = 1.27538726333907 or 1.28

3.

DFL = EBIT/ [EBIT – I – (PD x 1/(1-T))]

I = Interest charges = $ 6,300

PD = Proffered dividend = $ 1,900

T = Tax rate = 0.4

EBIT = (P x Q) – FC – (Q x VC)

         = $ 1.25 x 380,000 - $ 32,000 - 380,000 x $ 0.86

         = $ 475,000 - $ 32,000 - $ 326,800

         = $ 116,200

DFL = $ 116,200/ [$ 116,200 – $ 6,300 – ($ 1,900 x 1/ (1-0.4))]

       = $ 116,200/ [$ 116,200 – $ 6,300 – ($ 1,900 / 0.6)]

       = $ 116,200/ ($ 116,200 – $ 6,300 – $ 3,166.666667)

       = $ 116,200/ 106733.443333

       = 1.088694474 or 1.09

4.

DTL = [Q x (P-VC)]/ [Q x (P-VC) – FC – I – (PD/(1-T)]

= [380,000 x ($ 1.25 - $ 0.86)]/ [380,000 x ($ 1.25 - $ 0.86) – $ 32,000 – $ 6,300 – ($ 1,900 x1/ (1-0.4))]

= (380,000 x $ 0.39)/ [380,000 x $ 0.39 – $ 32,000 – $ 6,300 – ($ 1,900 / 0.6)]

= $ 148,200/ ($ 148,200 – $ 32,000 – $ 6,300 – $ 3,166.666667)

= $ 148,200/ $ 106,733.443333

= 1.388505752 or 1.39

DTL = DOL x DFL = 1.27538726333907 x 1.088694474 = 1.388507066 or 1.39

Computation of DTL using two formulas give the same results.