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

CF0=-Cost of equipment-working capital
CF1, CF2, CF3, CF4, CF5=((number of cartons*(price per carton-variable cost per carton)-fixed costs per year-depreciation)*(1-tax rate)+depreciation)
Additional cash flow in year 5=Salvage value*(1-tax rate)+working capital
Depreciation=Initial cost of equipment/5
NPV=CF0+CF1/(1+r)+CF2/(1+r)^2+CF3/(1+r)^3+CF4/(1+r)^4+CF5/(1+r)^5+Additional cash flow in year 5/(1+r)^5

a. Assuming that the price per carton is $30.00, what is the NPV of this project?

NPV=-1010000+145000*(1-25%)/1.10^5-130000+130000/1.10^5+((145000*(30-19.35)-585000-1010000/5)*(1-25%)+1010000/5)/10%*(1-1/1.10^5)
=1926913.854

b. Assuming that the price per carton is $30.00, find the quantity of cartons per year you can supply and still break even.

Let quantity be Q
At breakeven NPV=0
Hence,
-1010000+145000*(1-25%)/1.10^5-130000+130000/1.10^5+((Q*(30-19.35)-585000-1010000/5)*(1-25%)+1010000/5)/10%*(1-1/1.10^5)=0
=>Q=81361.186800

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.

Let fixed costs be F
At breakeven NPV=0
Hence,
-1010000+145000*(1-25%)/1.10^5-130000+130000/1.10^5+((145000*(30-19.35)-F-1010000/5)*(1-25%)+1010000/5)/10%*(1-1/1.10^5)=0
=>F=1262753.360578