Question

You are financial managers of a company which makes printers. Currently you are using NPV method to evaluate a 10-year project that produces a new model.

The WACC is 10% and the tax rate is 21%. (2 points)

1. The project needs a set of machine that is worth $5 million. The company uses 10-year straight-line depreciation.
2. In the past two years, the company spent $800,000 in R&D in developing the new model.
3. The project will be partially financed with debt, and the interest to be paid every year is $100,000.
4. If the new project is taken, it is expected that the current inventory level will increase by $1,500,000, account receivable will increase by $1 million, account payable increases by $800,000, and the minimum cash balance will increase by $0.5 million.
5. The sales from this project will be $8 million per year of which 20 percent will be from lost sales of existing products.
6. The variable costs of the production will be 30% of the sales.
7. The project will require hiring a new manager, who will cost $100,000 per year. In addition, the firm needs to rent a new office for $50,000 a year.
8. Currently, the overhead of the firm is $500,000. And the accounting department will allocate 20% of it to the new project.

Question 1: How much is the initial investment at t=0?

Question 2: How much is the operating cash flow for the first year?

Question 3: How much is the non-operating cash flow at the end of the last year?

Question 4: How much is the NPV?

Answer 1

1. Initial Investment at t=0

a. Cost of the machine = $5,000,000

b. Working capital requirements = Increase in Inventory + Increase in receivables - Increase in payables + Increase in minimum cash = $1,500,000+$1,000,000-$800,000+$500,000 = $2,200,000 (this is a net working capital investment resulting in cash-outflow)

Total Initial Investment at t=0 = $5,000,000 +$2,200,000= $7,200,000

R&D spend of $800,000 which is already incurred is a sunk cost and not relevant in the decision making.

2. Operating Cash flow:

a. Total Sales per year = $8,000,000.

% being lost sales of existing products = 20%

Thus, net sales per year = $8,000,000*(100%-20%) = $6,400,000 per annum

b. Variable cost = 30% of sales = 30% * $6,400,000 = $1,920,000 per annum

c. Cost of new manager hired = $100,000 per annum

d. Rental of new office = $50,000 per annum

e. Overhead of the firm = $500,000 per annum

Allocation to the project = 20%

Overhead of the project = $500,000*20% = $100,000 per annum

f. Interest on debt = $100,000 per annum

g. Depreciation on straight line basis for 10 years

Cost of the machine = $5,000,000

Depreciation per annum = $5,000,000/10 = $500,000

h. Profit Before Tax = Net Sales - Variable cost - Cost of new manager hired - Rental of new office - Overhead of the project - Interest on debt - Depreciation = $6,400,000 - $1,920,000-$100,000-$50,000-$100,000-$100,000-$500,000 = $3,630,000

i. Tax rate = 21%

Thus, tax = Profit Before Tax * tax rate = $3,630,000*21% = $762,300

j. Profit After Tax = Profit Before Tax - Tax = $3,630,000 - $762,300 = $2,867,700

k. Operating cash flow = Profit after tax + Depreciation = $2,867,700+$500,000 = $3,367,700 (for years 1 to 10)

3. Non operating cash-flow at the end of the last year

Net working capital investment at year 0 = $2,200,000

Recovery of net working capital at year 10 = $2,200,000 (recovery is a cash-inflow).

Though the question is silent on working capital recovery, generally working capital gets recovered at the end of the project and hence this is a fair assumption to make when the question is silent.

4. Net Present Value =

a. Discount factor at 10% =

Year 1 = 1/(100%+10%)^1 = 0.909

Year 2 = 1/(100%+10%)^2 = 0.826

Year 3 = 1/(100%+10%)^3 = 0.751

Year 4 = 1/(100%+10%)^4 = 0.683

Year 5 = 1/(100%+10%)^5 = 0.621

Year 6 = 1/(100%+10%)^6 = 0.564

Year 7 = 1/(100%+10%)^7 = 0.513

Year 8 = 1/(100%+10%)^8 = 0.467

Year 9 = 1/(100%+10%)^9 = 0.424

Year 10 = 1/(100%+10%)^10 = 0.386

Total of discount factor of 10 years = (sum of 10 years rates) = 6.145 (cumulative discount factor for 10 years)

b. Net Present Value = - Initial Investment at year 0 + (Operating cash flow per year * 10 years * cumulative discount factor for 10 years) + (Net working capital recovery at year 10 * discount factor of year 10)

=-$7,200,000 +($3,367,700*10*6.145)+($2,200,000*0.386) = -$7,200,000+$20,693,059+$848,195 = $14,341,254

Thus, NPV of the project = $14,341,254

Since the NPV is positive, the project can be undertaken.