Find the NPV, IRR, of the cash flows

Question

You are a financial analyst for the firm The Donut Co., hired to evaluate whether the firm should enter the wine market. The Donut Co. has already spent $10,000,000 developing an assortment of non-alcoholic wine cocktails. Entering the wine market requires an initial investment in production equipment of $400,000,000. You expect that the wine department will generate $395,000,000 in sales revenue if the economy is in a recession and $283,000,000 in sales revenue if the economy is booming. The probability of the economy booming is 40%, and the probability of a recession is 60%. The Donut Co. plans to operate the wine department for a total of 6 years before selling off all equipment associated with the project. You expect that the equipment will sell for $90,000,000 in year 6. The wine department is also expected to incur Selling, General, and Administrative costs of $21,000,000 per year starting from year 1, and costs of goods sold of $215,000,000 per year starting from year 1. The Donut Co.'s accountants are accustomed to using a straight-line depreciation method for the company's assets, and they plan to use a 6-year straight-line depreciation method for the wine equipment. Starting the wine department requires The Donut Co. to set aside $10,000,000 worth of wine into inventory right now, and they need to add to their inventory an amount equal to 10% of next year's revenues starting from year 1. The Donut Co. has also spent $30,000 today for your financial analysis. You estimated the cost of capital for The Donut Co. to be 12% per year, and the tax rate is 30%.

What is the NPV of the wine department?

What is the IRR of the wine department?

Should the Donut Co. enter the wine market?

Answer 1

Initial Costs:

Development Costs: $10,000,000

Initial Equipment Investment: $400,000,000

Initial Inventory: $10,000,000

Cost of Analysis: $30,000

Total Initial Investment: $10,000,000 + $400,000,000 + $10,000,000 + $30,000 = $420,030,000

Annual Operating Revenues and Expenses:

Revenue in Recession: $395,000,000

Revenue in Boom: $283,000,000

Probability of Recession: 60%

Probability of Boom: 40%

Expected Revenue: 0.6×395,000,000 + 0.4 × 283,000,000 = $347,200,000

Cost of Goods Sold (COGS): $215,000,000

Selling, General, and Administrative Costs (SG&A): $21,000,000

Depreciation:

Initial Equipment: $400,000,000

Depreciation Period: 6 years

Annual Depreciation: $400,000,000 / 6 = $66,666,667 per year

Tax Calculations:

Tax Rate: 30%

Pre-tax Income: Expected Revenue - COGS - SG&A - Depreciation

Taxes: Pre-tax Income × 30%

Net Cash Flows:

Before Tax: Revenue - COGS - SG&A

After Tax: (Revenue - COGS - SG&A - Depreciation) × (1 - Tax Rate) + Depreciation

End of Project:

Salvage Value of Equipment in Year 6: $90,000,000

Net Cash Flow in Year 6: Salvage Value + Final Year Cash Flow

Additional Inventory Requirement:

Each year, additional inventory needed is 10% of the following year's expected revenue.

Net Present Value (NPV) Calculation

To calculate NPV, we sum the present value of all future net cash flows plus the salvage value of the equipment, subtracting the initial investment. The formula for NPV is:

NPV

=

−

Initial Investment

+

∑

𝑡

=

1

6

Net Cash Flow

𝑡

(

1

+

Discount Rate

)

𝑡

NPV=−Initial Investment+∑

t=1

6

​

(1+Discount Rate)

t

Net Cash Flow

t

​

​

Internal Rate of Return (IRR) Calculation

IRR is the discount rate that makes the NPV of all cash flows equal to zero. It will be computed through iterative calculation or using a financial calculator.

Step-by-Step NPV and IRR Calculation

Let's start by computing the annual net cash flows:

Pre-Tax Income for each year.

Tax for each year.

Net Cash Flows including changes in inventory and the salvage value at the end of the project.