A well-established coffee shop, the Hot New Café, wants to build a new café for increased capacity. It’s expected sales are $800,000 for the first 5 years. Direct costs including labor and materials will be 50% of sales. Indirect costs are estimated at $100,000 a year. The cost of the building for the new cafe will be a total of $750,000, which will be depreciated straight line over the next 5 years. The firm's marginal tax rate is 37%, and its cost of capital is 12%.
To calculate the net present value (NPV) of this investment, we need to calculate the cash flows for each year and discount them to their present value. Here's how we can do that:
Step 1: Calculate the annual cash flow
To calculate the annual cash flow, we need to subtract the direct and indirect costs from the expected sales.
Annual Cash Flow = Expected Sales - Direct Costs - Indirect Costs
For the first 5 years, the annual cash flow can be calculated as follows:
Year 1: $800,000 - ($800,000 * 50%) - $100,000 = $400,000
Year 2: $800,000 - ($800,000 * 50%) - $100,000 = $400,000
Year 3: $800,000 - ($800,000 * 50%) - $100,000 = $400,000
Year 4: $800,000 - ($800,000 * 50%) - $100,000 = $400,000
Year 5: $800,000 - ($800,000 * 50%) - $100,000 = $400,000
Step 2: Calculate the present value of the cash flows
To calculate the present value of the cash flows, we need to discount each year's cash flow using the cost of capital.
Present Value of Cash Flow = Cash Flow / (1 + Cost of Capital)^Year
For each year, we calculate the present value of the cash flows as follows:
Year 1: $400,000 / (1 + 12%)^1 = $357,142.86
Year 2: $400,000 / (1 + 12%)^2 = $318,877.55
Year 3: $400,000 / (1 + 12%)^3 = $284,885.80
Year 4: $400,000 / (1 + 12%)^4 = $254,300.89
Year 5: $400,000 / (1 + 12%)^5 = $226,749.56
Step 3: Calculate the present value of the building cost
To calculate the present value of the building cost, we need to depreciate the building value straight line over 5 years and discount it using the cost of capital.
Building Depreciation per Year = Building Cost / Number of Years = $750,000 / 5 = $150,000
Present Value of Building Cost = Building Cost / (1 + Cost of Capital)^Year
For each year, we calculate the present value of the building cost as follows:
Year 1: $150,000 / (1 + 12%)^1 = $133,928.57
Year 2: $150,000 / (1 + 12%)^2 = $119,405.15
Year 3: $150,000 / (1 + 12%)^3 = $106,594.34
Year 4: $150,000 / (1 + 12%)^4 = $95,004.46
Year 5: $150,000 / (1 + 12%)^5 = $84,669.48
Step 4: Calculate the NPV
To calculate the NPV, we sum up the present value of the cash flows and subtract the present value of the building cost.
NPV = Sum of Present Value of Cash Flows - Present Value of Building Cost
NPV = ($357,142.86 + $318,877.55 + $284,885.80 + $254,300.89 + $226,749.56) - ($133,928.57 + $119,405.15 + $106,594.34 + $95,004.46 + $84,669.48)
NPV = $4,176.56
Therefore, the net present value (NPV) of the investment for the new café is $4,176.56.