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.

Martin 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 you $1,010,000 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 $145,000. Your fixed production costs will be $585,000 per year, and your variable production costs should be $19.35 per carton. You also need an initial investment in net working capital of $130,000. Assume your tax rate is 25 percent and you require a return of 10 percent on your investment.

  

a.	Assuming that the price per carton is $30.00, what is the NPV of this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	Assuming that the price per carton is $30.00, find the quantity of cartons per year you can supply and still break even. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)
c.	Assuming that the price per carton is $30.00, 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.)

Answer 1

Answer a:

Year 0 cash flow:

Year 0 cash flow = cost of equipment + net working capital = $1,010,000 + $130,000. = $1,140,000

Year 1 to 5:

Annual depreciation = (cost of equipment - salvage value) / useful life = (1010000 - 0) / 5 = $202,000

Annual depreciation tax shied = 202000 * 25% = $50,500

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

= ((30 - 19.35) * 145000 - 585000) * (1 - 25%) + 50500

= $769937.50

Terminal cash flow in Year 5:

Terminal cash flow = Salvage value net of tax + Recovery of net working capital = 145000 * (1 - 25%) + 130000

= $238,750

NPV calculations:

NPV = Annual cash flow * PV of $1 annuity + Terminal cash flow * PV of $1 - Year 0 cash flow

= 769937.50 * (1 - 1/ (1 + 10%) ⁵) /10% + 238750 * 1/ (1+10%) ⁵ - 1,140,000

= $1,926,913.85

NPV = $1,926,913.85

Answer b:

NPV sensitivity:

If we increase quantity by 1 unit:

Increase in NPV = Contribution per unit * (1 - Tax rate) * PV of $1 annuity

= (30 - 19.35) * (1 - 25%) * (1 - 1/ (1 + 10%) ⁵) /10%

=$30.27891

Reduction in units where NPV will be zero = 1926913.85 / 30.27891 = 63638.81

Find the quantity of cartons per year you can supply and still break even = 145000 - 63638.81 =81361.19 or 81,361

Assuming that price per carton is $30, the quantity of cartons per year you can supply and still break even = 81,361

Answer c:

NPV = $1,926,913.85

After tax annual cash flow that can be reduced and still break even = NPV /PV factor of $ annuity

= 1926913.85 / ((1 - 1/ (1 + 10%) ⁵) /10%)

= $508315.0193

Before tax cash flow that can be reduced and still break even = 508315.0193 / (1 - tax rate) = 508315.0193 / (1 - 25%)

= $677753.3591

Hence:

Highest fixed cost that you could afford = 585000 + 677753.3591 = $1,262,753

The highest level of fixed costs you could afford each year and still break even = $1,262,753