Question

Litchfield Design is evaluating a 3-year project that would involve buying a new piece of equipment for 430,000 dollars today. The equipment would be depreciated straight-line to 40,000 dollars over 2 years. In 3 years, the equipment would be sold for an after-tax cash flow of 52,000 dollars. In each of the 3 years of the project, relevant revenues are expected to be 259,000 dollars and relevant costs are expected to be 95,000 dollars. The tax rate is 50 percent and the cost of capital for the project is 10.22 percent. What is the NPV of the project?

Answer 1

Solution:

Given:

3-Year Project having Cash Flow = $ 430,000 or Cash Flow of Year 0 = $ 430,000

Depreciation = $ 40,000

After-tax Cash Flow = $ 52,000

Expected Revenues = $ 259,000

Expected Relevant Cost = $ 95,000

Tax Rate = 50 %

Cost of Capital = 10.22 %

To Calculate:

The NPV of the Project.

Calculation of Net Present Value:

Step:1 Calculation of Net Cash Flow:

Particulars	Calculation	Amount in $
Gross Profit = Revenue - Cost	$ 259,000 - $ 95,000 = 164,000	$ 164,000
EBIT (Earnings Before Interests and Taxes) = Gross Profit - Depreciation	$ 164,000 - $ 40,000 = 124,000	$ 124,000
Tax Amount = EBIT × Tax Rate	$ 124,000 × 50 % = 62,000	$ 62,000
EAT (Earnings After Taxes) = EBIT – Tax Amount	$ 124,000 – $ 62,000 = 62,000	$ 62,000
Net Cash Flow = EAT + Depreciation	$ 62,000 + $ 40,000 = 102,000	$ 102,000

Note: The Net Cash Flow is the Cash Flow for Year 1, Year 2 & Year 3 while the Cash Flow for Year 0 is initial investment in buying the equipment of project i.e. $ 430,000

Step: 2 Calculation of Present Value of Cash Flows for Year 0:

Year	Cash Flow	Discounted Cash Flow = Net Cash Flow × (1 / 1+Cost of Capital) ^n	Amount of Discounted Cash Flows or Present Value of Cash Flows
0	$ 430,000	430,000 (1/ 1 + 0.1022) ^ 0 = $ 430,000 ×1	= $ 430,000
Total of Present Value of Cash Flow for Year 0	= $ 430,000

Step: 3 Calculation of Present Value of Cash Flows from Year 1 to 3:

Year	Cash Flow	Discounted Cash Flow = Net Cash Flow × (1 / 1+Cost of Capital) ^n	Amount of Discounted Cash Flows or Present Value of Cash Flows
1	$ 102,000	102,000 (1/ 1 + 0.1022) ^ 1 = $ 102,000 ×0.9072763564	= $ 92,542.19
2	$ 102,000	102,000 (1/ 1 + 0.1022) ^ 2 = $ 102,000 ×0.8231503868	= $ 83,961.34
3	$ 102,000	102,000 (1/ 1 + 0.1022) ^ 3 = $ 102,000 × 0.7468248837	= $ 76,176.14
Total Present Value of Cash Flows from Year 1 to 3	= $ 252,679.67

Step: 4 Calculation of Present Value of Cash Flows After-Tax for Year 3:

Year	After-Tax Cash Flow	Discounted After-Tax Cash Flow = Net Cash Flow × (1 / 1+Cost of Capital) ^n	Amount of After-Tax Discounted Cash Flows or Present Value of After-Tax Cash Flows
3.	$ 52,000	$ 52,000 (1/ 1 + 0.1022) ^ 3 = $ 52,000 × 0.7468248837	= $ 38,834.89
Total of Present Value of After-Tax Cash Flows for Year 3	= $ 38,834.89

Final Step 4: Calculation of Net Present Value of the Project:

Now, we calculate the NPV of Project by putting the values in the following formula:

Net Present Value of Project = (Total Present Value of Cash Flows from Year 1 to 3 + Total of Present Value of After-Tax Cash Flows for Year 3) - Total of Present Value of Cash Flow for Year 0

NPV = ($ 252,679.67 + $ 38,834.89) - $ 430,000

NPV = $ 291,514.56 - $ 430,000

NPV of the Project = - $ 138,485.44

Ans: The NPV (Net Present Value) of the Project = - $ 138,485.44