Annual Before-Tax Cash Flow Calculation for Scott Corporation's Project | CFA Level 1 Exam Prep

Explanation

X = after-tax cash flow.

Y = before-tax cash flow.

X = Y(1 - T).

$10,000 = X(PVIFA(15%,10))

$10,000 = X(5.0188)

X = $1,992.51.

$1,992.51 = Y(1 - 0.40)

Y = $3,320.85 = $3,321.

To determine the annual before-tax cash flow for each year, we can use the internal rate of return (IRR) to calculate the cash flows that would result in a 15% rate of return over the 10-year period. Since the cash flows are evenly distributed, we need to find the constant cash flow that would yield an IRR of 15%.

Step 1: Calculate the initial investment The project requires an investment of $10,000.

Step 2: Calculate the annual before-tax cash flow Let's assume the annual before-tax cash flow is X dollars.

Year 0: Initial investment: -$10,000

Years 1-10: Annual before-tax cash flow: X

Step 3: Calculate the net present value (NPV) To calculate the NPV, we need to discount the cash flows at the project's IRR of 15%. The NPV should equal zero for the IRR.

NPV = 0 = -10,000 + X / (1 + 0.15) + X / (1 + 0.15)^2 + ... + X / (1 + 0.15)^10

Step 4: Solve for X To solve for X, we can rearrange the equation and solve for X.

0 = -10,000 + X / (1 + 0.15) + X / (1 + 0.15)^2 + ... + X / (1 + 0.15)^10

Simplifying the equation, we get:

0 = -10,000 + X * [(1 + 0.15)^-1 + (1 + 0.15)^-2 + ... + (1 + 0.15)^-10]

Using the formula for the sum of a geometric series, we can simplify the equation further:

0 = -10,000 + X * [1 / (1 + 0.15) * (1 - (1 + 0.15)^-10) / (1 - (1 + 0.15)^-1)]

0 = -10,000 + X * [1 / 1.15 * (1 - 0.3225) / 0.15]

0 = -10,000 + X * [0.8696]

10,000 = 0.8696X