Question

The technique for calculating a bid price can be extended to many other types of problems. Answer the following questions using the same technique as setting a bid price; that is, set the project NPV to zero and solve for the variable in question. Guthrie Enterprises needs someone to supply it with 145,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost $1,850,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that in five years this equipment can be salvaged for $155,000. Your fixed production costs will be $270,000 per year, and your variable production costs should be $9.90 per carton. You also need an initial investment in net working capital of $135,000. The tax rate is 25 percent and you require a return of 11 percent on your investment. Assume that the price per carton is $16.50. a. Calculate the project NPV. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the minimum number of cartons per year that can be supplied and still break even? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) c. What is the highest fixed costs that could be incurred and still break even? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

NPV = Present Value of Cash Inflows – Present Value of Cash Outflows

Year	0	1	2	3	4	5
Cost of Equipment	-1,850,000
Working Capital	-135,000
Revenue per Carton		16.50	16.50	16.50	16.50	16.50
Variable Cost per Carton		9.90	9.90	9.90	9.90	9.90
Contribution Margin per Carton		6.6	6.6	6.6	6.6	6.6
Total Contribution Margin		957,000	957,000	957,000	957,000	957,000
Less: Fixed Costs		270,000	270,000	270,000	270,000	270,000
Less: Depreciation = Cost/5		370,000	370,000	370,000	370,000	370,000
Profits		317,000	317,000	317,000	317,000	317,000
Tax @ 25%		79,250	79,250	79,250	79,250	79,250
Profits after Tax		237,750	237,750	237,750	237,750	237,750
Cash Flows = Profits + Dep		607,750	607,750	607,750	607,750	607,750
Working Capital Recovery						135,000
Salvage Value Net of Tax						116,250

NPV = -1,850,000 – 135,000 + 607,750*PVAF(11%, 5 years) + 251,250*PVF(11%, 5 years)

= -1,985,000 + 607,750*3.696 + 251,250*0.593

= $410,235.25

b.Let minimum number be x

To break even, NPV = 0

0 = -1,985,000+{(6.6x – 640,000)0.75 + 370,000}3.696 + 251,250*0.593

0 = -1,985,000 + 18.2952x – 406,560 + 148,991.25

X = 122,576.89 or 122,577 cartons

c. Let highest fixed cost be x

0 =-1,985,000+{(957,000-x-370,000)0.75 + 370,000}3.696 + 251,250*0.593

0 = -1,985,000 + 2,994,684 – 2.772x + 148,991.25

X = $417,992.51