Revenues generated by a new fad product are forecast as follows: Year Revenues 1 $40,000 2 30,000 3 20,000 4 5,000 Thereafter 0 Expenses are expected to be 40% of revenues, and working capital required in each year is expected to be 20% of revenues in the following year. The product requires an immediate investment of $49,000 in plant and equipment. a. What is the initial investment in the product? Remember working capital. Initial investment $ b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 20%, what are the project cash flows in each year? (Enter your answers in thousands of dollars. Do not round intermediate calculations. Round your answers to 2 decimal places.) Year Cash Flow 1 $ 2 3 4 c. If the opportunity cost of capital is 10%, what is project NPV? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) NPV $ d. What is project IRR? (Do not round intermediate calculations. Round your answer to 2 decimal places.) IRR %

a. $57,000

b.

c. - $3,047.64

d. IRR =  7%

Explanation:

a. What is the initial investment in the product?

We have: the initial investment in the product is the sum of investment in plant, equipment and the initial required working capital.

+) Investment in plant and equipment is given as $49,000

+) Required working capital each year is 20% of revenue of the following year

=> The initial working capital required is 20% of revenue of year 1

=> Initial working capital required = 20% x 40,000 = $8,000

So that: The initial investment = $49,000 + $8,000 = $57,000

b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 20%, what are the project cash flows in each year?

We have the formula to calculate the cash flow of each year as following:

CF = Net Operating Profit - Taxes - Net Change in Working Capital  = P - T - ΔCw

According to the straight-line depreciation, as the plant and equipment are depreciated over 4 years, so that the depreciation of investment in plant and equipment each year is:

D = Depreciation = (Total Investment in Plant and Equipment)÷Its useful life = $49,000 ÷4 = $12,250

We have, expenses (E) are expected to be 40% of revenues (R).

=> Expense of each year is: E = 0.4 R

Net profit of each year (P)= Revenue - Expense

=> Net profit of each year is:  P = R - E = R - 0.4 R = 0.6R

The tax each year is imposed on the profit of the company after depreciation, so that taxes each year of the company with the rate of 20% is:

T = 0.2(P - D) = 0.2 (0.6R - 12,250) = 0.12R - 2,450

We have, working capital change for each year is the difference in working capital of current and the previous year.  

We have, working capital (Cw) of each year is:

+) Initial Cw = $8,000

+) Cw1 = 20% x Revenue Year 2 = 0.2 x 30,000 = $6,000

+) Cw2 = 20% x Revenue Year 3 = 0.2 x 20,000 = $4,000

+) Cw3 = 20% x Revenue Year 4 = 0.2 x 10,000 = $2,000

+) Cw4 = 20% x Revenue Year 5 = 0.2 x 0 = 0

So that the change in Cw each year is:

+) ΔCw1 = Cw1 - Initial Cw = 6,000 - 8,000 = -2,000

+) ΔCw2 = Cw2 - Cw1 = 4,000 - 6,000 = -2,000

+) ΔCw3 = Cw3 - Cw2 = 2,000 - 4,000 = -2,000

+) ΔCw4 = Cw4 - Cw3 = 0 - 2,000 = -2,000

Now we can write the cash flow formula as following:

CF = P - T - ΔCw = 0.6R - (0.12R -2,450) - (-2000) = 0.48R +4,450

c. If the opportunity cost of capital is 10%, what is project NPV?

Assume that cost of capital is r, so that r = 10% = 0.1

We have:

PV = ∑[CF Year i/(1+r)^i] (with i = 1 to 4) = ∑[CF Year i/(1+0.1)^i]

= CF1/(1+0.1)^1 + CF2/(1 + 0.1)^2 + CF3/(1+0.1)^3 + CF4/(1+0.1)^4

Replace the value of CF as the previous part in the equation, we have:  

PV ≈ $53,952.36

We have,Net Present Value (NPV) = Present Value (PV) - Initial Investment (I)

=> NPV = $53,952.36 - $57,000 = - $3,047.64

d. What is project IRR?

IRR is the discount rate r in the equation:

+) PV = ∑[CF Year i/(1+r)^i] (with i = 1 to 4)

The value of IRR has to satisfy the equation:

NPV = 0

⇔ PV - I = 0

+) PV = ∑[CF Year i/(1+r)^i] = Initial Investment = $57,000

However, the IRR can only be calculated by tool. Here, we can use Excel spreadsheet to calculate the value of IRR.

The input can be describe as following:

Column A values:                                    Column B

A1: -57,000 (Initial Investment)             B1: =IRR(A1:A5)

A2: 23,650  (CF1)

A3: 18,850 (CF2)

A4: 14,050  (CF3)

A5: 9,250 (CF4)

=> IRR = B1 =  7%

the u.s. census bureau produces data on the population and economy nationwide. it can you to analyze the kind of people living in your neighborhood. it does not show you the market of people willing to buy your product or an existing market for your product. that will require more market research. the census bureau only gives you an insight to the demographics in your area.