i = r_debt = 10% OCF₀ = −$100,000 K_u = r_assets = 15% OCF_1-4= $39,800 = 25,000 × ($5 − $3) × (1 − 0.34) + $20,000 × 0.34
K_l = r_equity = 24.9% OCF₅ = $43,100 = $39,800 + $5,000 × (1 − 0.34) K = r_WACC = 11.20% Tax rate = 34% Debt-to-equity ratio = 3 Risk-free rate = 2%
The 5-year project requires equipment that costs $100,000.If undertaken,the shareholders will contribute $25,000 cash and borrow $75,000 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.
When using the APV methodology,what is the NPV of the depreciation tax shield?

Question

Quizplus · Accepted Answer

The NPV of the depreciation tax shield is calculated by taking the annual depreciation tax shield (depreciation expense multiplied by the tax rate) and discounting it at the unlevered cost of capital (Ku). The depreciation expense is $20,000 per year ($100,000/5 years), and the tax shield is $20,000 * 0.34 = $6,800 per year. Discounting this at 15% over 5 years gives an NPV of $25,777.35.

I = Rdebt = 10% OCF0 = −$100,000 Ku =

I = R_debt = 10% OCF₀ = −$100,000 K_u =