Question

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. Romo Enterprises needs someone to supply it with 113,000 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 $800,000 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 $63,000. Your fixed production costs will be $318,000 per year, and your variable production costs should be $9.60 per carton. You also need an initial investment in net working capital of $68,000. Assume your tax rate is 34 percent and you require a 10 percent return on your investment. a. Assuming that the price per carton is $16.30, what is the NPV of this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ b. Assuming that the price per carton is $16.30, find the quantity of cartons per year you need to supply to break even. (Do not round intermediate calculations and round your answer to nearest whole number.) Quantity of cartons c. Assuming that the price per carton is $16.30, find the highest level of fixed costs you could afford each year and still break even. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Fixed costs $

Answer 1

Answer a:

Price per carton = $16.30

Variable cost per carton = $9.60

Hence, contribution per carton = $16.30 - $9.60 = $6.70

Depreciation per year (SLM) = Equipment cost / Useful life = $800,000 / 5 = $160,000

Initial investment = Equipment cost + net working capital = $800,000 + $68,000 = $868,000

Annual operating cash flow = (Contribution per carton * Quantity - Fixed production costs) * (1 -Tax rate) + Depreciation tax shield

= (113000 * 6.70 - 318000) * (1 - 34%) + 160000 * 34%

= $344,206

Terminal cash flow = Salvage value - (Salvage value - Book Value) * Tax rate + Recovery of working capital

= 63000 - (63000 - 0) * 34% + 68000

= $109,580

PV Factors for One Dollar Discounted at 12% for 5 Periods = 1 / (1 + k) ⁿ = 1 / (1 + 10%) ⁵

PV Factors for One-Dollar Annuity Discounted at 10% for 5 Periods = [1 - 1/ (1 + k) ⁿ ] / k

NPV = PV of annual cash flows + PV of terminal cash flow - Initial investment

= 344206 * (1 - 1/(1 +10%) ⁵) / 10% + 109580 * 1 / (1 + 10%) ⁵ - 868000

= $504,852.11

NPV of this project = $504,852.11

Answer b:

At Break-even, NPV = 0

Let us assume break-even quantity = X

Hence,

NPV sensitivity per carton = Contribution per carton * (1 - Tax rate) * PV annuity factor

= 6.70 * (1 - 34%) * (1 - 1/(1 +10%) ⁵) / 10%

= $16.7628591

Hence break-even quantity =113,000 - 504,852.11 / 16.7628591= 82,883

Quantity of cartons = 82,883

Answer c:

Current fixed cost = $318,000 per year

NPV = $504,852.11

At break-even NPV = $0

Hence possible increase in fixed cost for break-even = (NPV / PV Annuity factor) / (1- tax rate) = [504852.11 / {(1 - 1/(1 +10%) ⁵) /10%}] /(1- 34%) = $201,785.93

Highest level of fixed costs you could afford each year and still break even = $318,000 + $201,785.93 = $519,785.93

Fixed cost = $519,785.93