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%

answerattainable;