A project requires an initial investment of $10,000, straight-line depreciable to zero over four years. The discount rate is 10%. Your tax bracket is 34% and you receive a tax credit for negative earnings
In the year in which the loss occurs. Additional information for variables with forecast error are
Shown below. What is the base case NPV for the project?
A) $1,523
B) $4,974
C) $5,247
D) $6,529
E) $8,281

Question

A project requires an initial investment of $10,000, straight-line depreciable to zero over four years. The discount rate is 10%. Your tax bracket is 34% and you receive a tax credit for negative earnings
In the year in which the loss occurs. Additional information for variables with forecast error are
Shown below.  What is the base case NPV for the project?
A) $1,523 
B) $4,974 
C) $5,247 
D) $6,529 
E) $8,281

Quizplus · Accepted Answer

To calculate the NPV, we need to first calculate the cash flows for each year.

Year 0: 
Initial investment: -$10,000

Year 1-4: 
Depreciation = $10,000/4 = $2,500 
Tax credit = -$850 (34% of -$2,500) 
Net cash flow = -$2,500 - (-$850) = -$1,650

Discount rate = 10%

Using these cash flows, we can calculate the NPV:

NPV = -$10,000 + ($1,650/(1+0.1)^1) + ($1,650/(1+0.1)^2) + ($1,650/(1+0.1)^3) + ($1,650/(1+0.1)^4)

NPV = -$10,000 + $1,500 + $1,239 + $1,019 + $839 
NPV = $597

However, we also need to consider the forecast errors for variables. Since we do not have specific numbers for the errors, we can use the range given in the table: -15% to +20%.

To calculate the worst-case NPV, we use the bottom end of the range for all variables:

NPV worst-case = -$16,250 + ($1,312.50/(1+0.1)^1) + ($1,312.50/(1+0.1)^2) + ($1,312.50/(1+0.1)^3) + ($1,312.50/(1+0.1)^4) 
NPV worst-case = -$16,250 + $1,192 + $911 + $699 + $537 
NPV worst-case = -$12,911

To calculate the best-case NPV, we use the top end of the range for all variables:

NPV best-case = -$8,500 + ($1,950/(1+0.1)^1) + ($1,950/(1+0.1)^2) + ($1,950/(1+0.1)^3) + ($1,950/(1+0.1)^4) 
NPV best-case = -$8,500 + $1,676 + $1,416 + $1,198 + $1,017 
NPV best-case = $2,207

Therefore, the base case NPV for the project is $597, but the best choice(s) depend on the risk appetite of the investor. If the investor is risk-neutral or risk-seeking, they may choose to invest in the project since even the worst-case NPV is positive. However, if the investor is risk-averse, they may not invest in the project since the worst-case NPV is negative.

A Project Requires an Initial Investment of $10,000, Straight-Line Depreciable