i = r_debt = 6% OCF₀ = −$100,000 K_u = r_assets = 12% OCF_1-4= $39,800 = 25,000 × ($5 − $3) × (1 − 0.34) + $20,000 × 0.34
K_l = r_equity = 27.84% OCF₅ = $43,100 = $39,800 + $5,000 × (1 − 0.34) K = r_WACC = 8.74% π = Tax rate = 34% Debt-to-equity ratio = 4 Risk-free rate = 2%
The 5-year project requires equipment that costs $100,000.If undertaken,the shareholders will contribute $20,000 cash and borrow $80,000 at 6 percent with an interest-only loan with a maturity of 5 years and annual interest payments.The equipment will be depreciated straight-line to zero over the 5-year life of the project.There will be a pre-tax salvage value of $5,000.There are no other start-up costs at year 0.During years 1 through 5,the firm will sell 25,000 units of product at $5; variable costs are $3; there are no fixed costs.
What is the NPV of the project using the WACC methodology?

Question

Quizplus · Accepted Answer

To calculate the NPV of the project, we need to calculate the annual free cash flow (FCF) and discount it back to present value using the WACC methodology.

Annual FCF = Revenue - Variable Costs - Interest Expense - Depreciation Expense - Taxes

Year 0: 
Initial Investment = -$100,000 (outflow) 
Shareholders' Equity = $20,000 (inflow) 
Debt = $80,000 (inflow)
Total Cash Flows = -$100,000 + $20,000 + $80,000 = $0

Year 1-5: 
Revenue = 25,000 x $5 = $125,000 
Variable Costs = 25,000 x $3 = $75,000 
Interest Expense = $80,000 x 6% = $4,800 
Depreciation Expense = $100,000 / 5 = $20,000 
Taxable Income = Revenue - Variable Costs - Interest Expense - Depreciation Expense = $25,200 
Taxes = $25,200 x 34% = $8,568 
Free Cash Flow = $25,200 - $4,800 - $20,000 - $8,568 = -$8,168

Salvage Value at the end of Year 5 = $5,000

Now, we can discount the annual FCF and salvage value using the WACC of 8.74%:

NPV = (-$100,000 + ∑ ($8,168 / (1+8.74%)^t) + $5,000 / (1+8.74%)^5)

NPV = -$100,000 + $20,469.80 + $22,129.91

NPV = $49,599.71

Therefore, the NPV of the project using the WACC methodology is $49,599.71.

The best choice is B because it has the highest NPV and is therefore the most financially attractive option.

I = Rdebt = 6% OCF0 = −$100,000 Ku =

I = R_debt = 6% OCF₀ = −$100,000 K_u =