A 3-year project will cost $180 at the end of year 1 and is expected to produce operating profit before depreciation and amortization (EBITDA)of $80 in year 1, $100 in year 2, and $60 in year 3. Depreciation, both real and financial, will be calculated using straight-line depreciation over 3 years. The cost of capital is 10%, and the firm's marginal tax rate is 25%.
-Refer to the information above. Assume the firm will issue $100 of debt in year 1 with an expected interest rate of 8%. Interest must be paid each of the 3 years, and the principal is
Repaid at the end of year 3. What is the project NPV? (Ignore any tax laws allowing the carry
Forward or carry back of net operating losses.)

Question

Quizplus · Accepted Answer

To calculate the project NPV, we need to calculate the cash flows for each year and discount them using the cost of capital.

Year 0: -$100 (initial investment in debt)

Year 1: 
EBITDA = $80
Depreciation = $60
Operating profit = $20
Interest expense = $8
Taxable income = $12
Taxes = $3
Operating cash flow = $20 + $60 - $8 = $72
Debt repayment = $100 * 1.1 = $110
Free cash flow = $72 - $110 = -$38

Year 2:
EBITDA = $100
Depreciation = $60
Operating profit = $40
Interest expense = $8
Taxable income = $32
Taxes = $8
Operating cash flow = $40 + $60 - $8 = $92
Debt repayment = $0
Free cash flow = $92

Year 3:
EBITDA = $60
Depreciation = $60
Operating profit = $0
Interest expense = $8
Taxable income = -$8
Taxes = $0
Operating cash flow = $60 + $60 - $8 = $112
Debt repayment = $0
Free cash flow = $112

Now, we need to discount each year's free cash flow using the cost of capital, and sum them up:
NPV = (-$38)/(1+0.1)^1 + $92/(1+0.1)^2 + $112/(1+0.1)^3
NPV = -$27.48 + $79.25 + $56.71
NPV = $ 27.48

Therefore, the project's NPV is positive, so the best choice is C. First, we need to calculate the operating cash flows for each year. We use the EBITDA figures given and adjust for depreciation.

Year 1: 
EBITDA = $80
Depreciation = $60 (180/3)
EBIT = $20
Taxes = $5 (25% x $20)
Operating Cash Flow = $15 (EBIT + Depreciation - Taxes)

Year 2: 
EBITDA = $100
Depreciation = $60 
EBIT = $40
Taxes = $10
Operating Cash Flow = $30

Year 3: 
EBITDA = $60
Depreciation = $60 
EBIT = $0
Taxes = $0
Operating Cash Flow = $60

Next, we need to calculate the cash flows associated with the debt. The firm will receive $100 in year 1, but will have to pay interest and repay the principal in year 3. The interest payments each year will be 8% of the outstanding balance, which declines over time as the principal is repaid.

Year 1: 
Cash Inflow = $100
Interest = $8
Cash Outflow = $8 
Net Cash Flow = $92

Year 2: 
Cash Inflow = $0
Interest = $6.24 (8% x $92)
Cash Outflow = $6.24 
Net Cash Flow = -$6.24

Year 3: 
Cash Inflow = $0
Interest = $3.68 (8% x $46.76)
Principal Repayment = $100
Cash Outflow = $103.68 
Net Cash Flow = -$103.68

Finally, we can calculate the project NPV using a discount rate of 10%.

NPV = -$180 + (15/1.1) + (30/1.1^2) + (60 + (-6.24) - 103.68)/1.1^3
NPV = $27.48

Therefore, the best choice is C, with an NPV of $27.48.

A 3-Year Project Will Cost $180 at the End of Year