Question

13. To solve the bid price problem presented in the text, we set the project NPV equal to zero and found the required price using the definition of OCF. Thus the bid price represents a financial break-even level for the project. This type of analysis can be extended to many other types of problems. Martin Enterprises needs someone to supply it with 140,000 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 you $985,000 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 $130,000. Your fixed production costs will be $560,000 per year, and your variable production costs should be $18.85 per carton. You also need an initial investment in net working capital of $120,000. Assume your tax rate is 25 percent and you require a return of 12 percent on your investment.

1. Assuming that the price per carton is $29.00, what is the NPV of this project?
2. Assuming that the price per carton is $29.00, find the quantity of cartons per year you can supply and still break even.
3. Assuming that the price per carton is $29.00, find the highest level of fixed costs you could afford each year and still break even?

Answer 1

Answer (a):

Year 0 cash flow:

Year 0 cash flow = cost of equipment + net working capital = 985000 + 120000 = $1,105,000

Year 1 to 5:

Annual depreciation = (cost of equipment - salvage value) / useful life = (985000 - 0) / 5 = $197,000

Annual depreciation tax shied = 197000* 25% = $49,250

Annual cash flow = ((sale price - variable cost) * units - Fixed cost) * (1 - Tax rate) + depreciation tax shield

= ((29 - 18.85) * 140000 - 560000) * (1 - 25%) + 49250

= 695000

Terminal cash flow in Year 5:

Terminal cash flow = Salvage value net of tax + Recovery of net working capital = 130000 * (1 - 25%) + 120000

= $217500

Hence:

NPV = Annual cash flow * PV factor of annuity + Terminal cash flow * PV of 41 - Year 0 cash flow

= 695000 * (1 - 1/(1+12%)^5)/12% + 217500 * 1 / (1 + 12%)^5 - 11050000

= $1,523,734.80

NPV = $1,523,734.80

Answer (b):

At break even NPV = 0

ΔNPV / ΔQ = (sale price - variable cost) * (1 - Tax rate) * PV factor of annuity

=(29 - 18.85) * (1 - 25%) * (1 - 1 /(1+12%)^5)/12%

= $27.44135884

Reduction in quantity sold for NPV amount of $1,523,734.80 = $1,523,734.80 /27.44135884 = 55,526.94 units

Hence:

Break-even quantity = 140000 - 55526.94 = 84,473.06

Break-even quantity = 84,473

Answer (c):

Current NPV = $1,523,734.80

For NPV = 0,

Possible reduction in annual cash flow = 1523734.80 / ((1 - 1 /(1+12%)^5)/12%) = $422698.86

Possible increase in Fixed cost = 422698.86/ (1 - 25%) =563598.48

Maximum possible fixed to break-even = 560000 + 563598.48 =$1123598.48

Highest level of fixed costs you could afford each year and still break even = $1,123,598.48