Question

Break-even calculations are most often concerned with the effect of a shortfall in sales, but they could equally well focus on any other component of cash flow. Dog Days is considering a proposal to produce and market a caviar-flavored dog food. It will involve an initial investment of $90,000 that can be depreciated straight-line over 10 years. In each of years 1-10, the project is forecast to produce sales of $100,000, and to incur variable costs of 50% of sales and some fixed costs. The corporate tax rate is 30%. Assume that the company if entirely financed by equity. The stock price is $20 per share. The dividend per share is expected to be $1 next year and is expected to grow at a rate of 5% each year in the future.

1) Calculate the economic break-even level of fixed cost.

Answer 1

First we estimate the discount rate,

Given Price of stock=P=$20

Growth rate=g=5%

Expected dividend next year=D1=$1

Discount rate=i=?

We know that

P=D1/(i-g)

i=(D1/P)+g=(1/20)+5%=10%

Depreciation per year=(Cost-salvage)/Useful life=(90000-0)/10=$9000

Annual sales=S=$100,000

Variable Cost per year=V=S*50%=100000*50%=$50000

Let the economic fixed cost per year=F

Tax liability per year=T=(S-V-F-D)*Tax rate=(100000-50000-F-9000)*30%=(12300-0.3F)

Net Revenue per year=R=(S-V-F-T)=100000-50000-F-12300+0.3F=37700-0.7F

NPV=-C+R*(P/A,0.10,10)=-90000+(37700-0.7F)*(P/A,0.10,10)

Let us calculate the interest factor

NPV=-90000+(37700-0.7F)*6.144567

NPV=141650.1759-4.3011969F

We know NPV is zero to break even. So,

141650.1759-4.3011969F=0

F=$32932.73 or say $32933 per year