7-1 Break-even Example 1 A firm produces radios with a fixed cost of $7,000 per month and a variable cost of $5 per radio. If radios sell for $8 each: 1a) What is the break-even point? TR = TC so 8x = x x = 7000/3 = 2, radios per month 1b) What output is needed to produce a profit of $2,000/month? Profit = 2000/month so TR - TC = 8x - ( x) = 2000 x = 9000/3 = 3,000 radios per month

7-2 Break-even Example 1 - continued 1c) What is the profit or loss if 500 radios are produced each week? First, get monthly production: 500  52/12 = 2, radios per month Then calculate profit or loss TR - TC = 8  (  ) = $-500 per month ($500 loss per month)

7-3 Break-even Example 2 A firm produces radios with a fixed cost of $7,000 per month and a variable cost of $5 per radio for the first 3,000 radios produced per month. For all radios produced each month after the first 3,000 the variable cost is $10 per radio (for added overtime and maintenance costs). If radios sell for $8 each: 2a) What are the break-even point(s)? Now TC has two parts depending on the level of production: For x  3000/month: TC = x For x > 3000/month: TC = (3000) + 10(x-3000) = x For any x : TR = 8x

7-4 Break-even Example 2 - continued For x  3000/month: TC = x For x > 3000/month: TC = x For any x : TR = 8x For x  3000/month: x = 8x so x = 2, /month This is < 3000/month, so it is a valid break-even point. For x > 3000/month: x = 8x so x = 4000 /month This is > 3000/month, so it is also a valid break-even point.

7-5 Break-even Example 2 Total cost line Total revenue line 1000 Break-even points Volume (units/month) Dollars (Thousands)

7-6 Break-even Example 3 A firm produces radios with a fixed cost of $7,000 per month and a variable cost of $5 per radio for the first 2,000 radios produced per month. For all radios produced each month after the first 2,000 the variable cost is $10 per radio (for added overtime and maintenance costs). If radios sell for $8 each: 3a) What are the break-even point(s)? Again TC has two parts depending on the level of production: For x  2000/month: TC = x For x > 2000/month: TC = (2000) + 10(x-2000) = x For any x : TR = 8x

7-7 Break-even Example 3 - continued For x  2000/month: TC = x For x > 2000/month: TC = x For any x : TR = 8x For x  2000/month: x = 8x so x = 2, /month This is not < 2000/month, so it is not a break-even point!! For x > 2000/month: x = 8x so x = 1500 /month This is not > 2000/month, so it is not a break-even point!! THERE ARE NO BREAK-EVEN POINTS!

7-8 Break-even Example 3 Total cost line Total revenue line 1000 Volume (units/month) Dollars (Thousands)

7-9 Other Break-even Possibilities Total cost line Total revenue line 1000 Volume (units/month) Dollars (Thousands)

7-10 Crossover Chart Total cost - Process C Total cost - Process B Total cost - Process A Process A: Low volume, high variety Process B: Repetitive Process C: High volume, low variety Process C Process B Process A Lowest cost process

7-11 Crossover Example Process A: F A = $5000/week V A = $10/unit Process B: F B = $8000/week V B = $4/unit Process C: F C = $10000/week V C = $3/unit Over which range of output is each process best? 1. At x = 0 A is best ( F A is smallest fixed cost). 2. As x gets larger, either B or C may become better than A: B 3000/6 or x > 500 /week C 5000/7 or x > /week so B is best for x > 500/week 3. Eventually, C will become better than B ( V C < V B ). C 2000 /week

7-12 Crossover Example Summary: A is best for output of units per week. B is best for output of units per week. C is best for output greater than 2000 units per week A<B A<C B<C A<B A<C B<C A<B<C B<A C<A B<C B<C<A B<A A<C B<C B<A<C B<A C<A C<B C<B<A

7-13 Crossover Chart Fixed cost - Process A Fixed cost - Process B Fixed cost - Process C Total cost - Process C Total cost - Process B Total cost - Process A Process A: low volume, high variety Process B: Repetitive Process C: High volume, low variety Process CProcess BProcess A Lowest cost process

7-14 Cost of Wrong Process Found Via Breakeven Analysis Fixed cost $ Variable cost Fixed cost $ Variable cost Fixed cost $ Variable cost Low volume, high variety process Repetitive processHigh volume, low variety process A B Volume B1 B2 B3 Total cost for low volume high variety Total cost for repetitive process Total cost for high volume, low variety process

7-15 Time Value of Money - Net Present Value  Future cash receipt of amount F is worth less than F today. F = Future value N years in the future. P = Present value today. i = Interest rate.

7-16 Annuities  An annuity is a annual series of equal payments. R = Amount received every year for N years. S = Present value today. S = RX where X is from Table 7.5 (page 264). Example: What is present value of $1,000,000 paid in 20 equal annual installments? For i =6%/year, S =  = $573,500 For i =14%/year, S =  = $331,150

7-17 Limitations of Net Present Value  Investments with the same NPV will differ:  Different lengths.  Different salvage values.  Different cash flows.  Assumes we know future interest rates!  Assumes payments are always made at the end of the period.

7-18 Limitations of Net Present Value  Investments with the same present value may have significantly different project lives and different salvage values  Investments with the same net present values may have different cash flows  We assume that we know future interest rates - which we do not  We assume that payments are always made at the end of the period - which is not always the case