Question

Digital Organics (DO) has the opportunity to invest $1.23 million now (t = 0) and expects after-tax returns of $700,000 in t = 1 and $800,000 in t = 2. The project will last for two years only. The appropriate cost of capital is 12% with all-equity financing, the borrowing rate is 8%, and DO will borrow $200,000 against the project. This debt must be repaid in two equal installments of $100,000 each. Assume debt tax shields have a net value of $.30 per dollar of interest paid. Calculate the project’s APV. (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations. Round your answer to the nearest whole number.) Adjusted present value

Answer 1

Initial investment = $1.23 million = CF₀ = 1.23 x 1000000 = 1230000

After tax return in year 1 = CF₁ = $700000

After tax return in year 2 = CF₂ = $800000

We know that

APV of a project = Base case NPV or NPV of a all equity project + Present value of interest tax shields discounted at cost of debt

Cost of of capital with all equity financing = Unlevered cost of capital = 12%

Base Case NPV = NPV of project financed entirely with equity = - Initial investment + Sum of present value of after tax return discounted at unlevered cost of capital = -1230000 + 700000 / (1 + 12%) + 800000 / (1 + 12%)²

Initial debt or debt at beginning of year 1 = 200000

As debt is repaid in equal installments of $100000, hence $100000 will paid in year 1 and year 2

Debt at end of year 1 or at beginning of year 2 = Initial debt or debt at beginning of year 1 - Debt repaid = $200000 - $100000 = 100000

Debt at end of year 2 = Debt at end of year 1 or at beginning of year 2 - Debt repaid = 100000 - 100000 = 0

Interest for a year = debt at Beginning of year x interest rate

Interest for year 1 = initial debt or debt at beginning of year 1 x 8% = 200000 x 8% = 16000

Interest for year 2 = Debt at end of year 1 or at beginning of year 2 x 8% = 100000 x 8% = 80000

Debt Tax shield or interest tax shield = 0.30 for a dollar interest paid = 0.30 x interest paid

Interest tax shield for year 1 = Interest for year 1 x 0.30 = 16000 x 0.30 = 4800

Interest tax shield for year 2 = Interest for year 2 x 0.30 = 8000 x 0.30 = 2400

Year	0	1	2
Debt	200000	100000	0
Interest		16000	8000
Interest tax shield		4800	2400

Present value of interest tax shield discounted at cost of debt = 4800 / (1 + 8%) +2400 / (1 + 8%)²

Now

APV of project = Base case NPV + Present value of interest tax shield discounted at cost of debt

= -1230000 + 700000 / (1 + 12%) + 800000 / (1 + 12%)² + 4800 / (1 + 8%) +2400 / (1 + 8%)²

= -1230000 + 625000 + 637755.1020 + 4444.4444 + 2057.6131 = 39257.1595 = $39257 (rounded to nearest whole number

Hence APV of the project = $39257