A project cost $1 million and has a base-case NPV of exactly zero (NPV = 0). What is the projects' APV in the following cases?

a. If the firm invests, it has to raise $500,000 by a stock issue. Issue costs are 15% of net proceeds.

b. If the firm invests, its debt capacity increases by $500,000. The present value of interest tax shield on this debt is $76,000.

a. Well, if I were a firm trying to raise $500,000 through a stock issue, I would probably dress up as a clown and juggle some stocks to get people's attention. But hey, that's just me! Now, as for the project's APV, let's calculate it. The base-case NPV is zero, so we add the net proceeds from the stock issue, which is $500,000 minus 15% for issue costs. So, we're looking at an APV of $500,000 minus a clownish 15% of net proceeds.

b. Ah, debt capacity! It's like trying to balance on a tightrope while wearing oversized clown shoes. Anyway, the present value of the interest tax shield on the increased debt capacity is $76,000. So, we add this amount to the base-case NPV of zero, giving us an APV of $76,000. Just be careful not to trip on those clown shoes!

To find the APV (Adjusted Present Value) for the project, we need to consider the additional cash flows or benefits associated with the investment. Let's calculate the APV for each case:

a. If the firm invests and raises $500,000 by a stock issue, we need to calculate the net proceeds after deducting the issue costs.

Step 1: Calculate the issue costs:
Issue costs = 15% of net proceeds
Issue costs = 15% * $500,000 = $75,000

Step 2: Calculate the net proceeds:
Net proceeds = Amount raised - Issue costs
Net proceeds = $500,000 - $75,000 = $425,000

Step 3: Calculate the APV:
APV = NPV + Net proceeds
APV = $0 + $425,000
APV = $425,000

Therefore, in this case, the project's APV is $425,000.

b. If the firm invests and its debt capacity increases by $500,000, we need to consider the present value of the interest tax shield on this debt.

Step 1: Calculate the APV:
APV = NPV + Present value of the interest tax shield

Step 2: Calculate the present value of the interest tax shield:
Present value of the interest tax shield = $76,000

Step 3: Calculate the APV:
APV = $0 + $76,000
APV = $76,000

Therefore, in this case, the project's APV is $76,000.

To find the APV (Adjusted Present Value) of a project, we need to take into account the effect of financing decisions on the project's value. Let's calculate the APV in both cases:

a. If the firm invests and raises $500,000 through a stock issue, we need to consider the issue costs. Issue costs are 15% of the net proceeds, so we subtract 15% of $500,000 from the $500,000 raised to determine the net amount invested.

Net amount invested = $500,000 - (15% * $500,000) = $500,000 - $75,000 = $425,000

Now, we need to calculate the NPV of the project, taking into account the net amount invested. Since the base-case NPV is zero, the NPV will also be zero in this case.

APV = NPV + Net amount invested = 0 + $425,000 = $425,000

Therefore, the project's APV in this case is $425,000.

b. If the firm invests and its debt capacity increases by $500,000, we need to consider the present value of interest tax shield on this debt. The present value of interest tax shield represents the tax savings resulting from deducting interest payments on the debt from taxable income.

Given that the present value of interest tax shield on this debt is $76,000, we need to add this amount to the base-case NPV of zero.

APV = NPV + Present value of interest tax shield = 0 + $76,000 = $76,000

Therefore, the project's APV in this case is $76,000.