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 for tax straight-line over 10 years. In each of years 1 to 10, the project is forecast to produce sales of $100,000 and to incur variable costs of 50% of sales and fixed costs of $30,000. The corporate tax rate is 30%, and the cost of capital is 10%


a. Calculate the NPV break-even levels of fixed costs. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Please find FIXED COST at NPV breakeven! not just NPV

Answer 1

Let x be the breakeven level of fixed costs, at which NPV is zero.

So, After tax cashflows every year will be:

Revenue	100000
Variable Costs(50%)	50000
Fixed Costs	x
Depreciation(90000/10)	9000
EBIT(Rev-Var-Fix-Dep)	41000-x
Tax(30%)	12300-0.3x
Net Income	28700-0.7x
After Tax Cashflow(Add back Deprec)	37700-0.7x

NPV for a time period of n can be calculated using the formula: -C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n; where C is the initial investment, C1 to Cn are cash inflows and r is the required rate of return.

NPV= -90000+(37700-0.7x)/(1+10%)+(37700-0.7x)/(1+10%)^2+.....(37700-0.7x)/(1+10%)^10.

we can use present value of annuity formula for cashinflows which is P*(1-(1+r)^-n)/r; where P is the annual cashflow, r is the discount rate and n is the number of years.

NPV= -90000+((37700-0.7x)*(1-1.1^-10)/10%)= 0.

(37700-0.7x)*(6.1446)= 90000

x= $32932.73

So, breakeven level of fixed costs is $32932.73