Given: WACC= 12%, NPV=+1,491.39, IRR=14.87378%, your all-equity firm has 5,000 common shares outstanding, and the cash flows are: CF0= -18,000, CF1= 3,000 CF2= 3,000, CF3=7,000, CF4?, CF5= 10,000. What is the cash flow at time-point 4.
To find the cash flow at time-point 4 (CF4), we can use the Net Present Value (NPV) formula and the Internal Rate of Return (IRR) formula.
1. Start with the NPV formula:
NPV = CF0 + CF1/(1+WACC)^1 + CF2/(1+WACC)^2 + CF3/(1+WACC)^3 + CF4/(1+WACC)^4 + CF5/(1+WACC)^5
Given values: NPV = +1,491.39, WACC = 12%, CF0 = -18,000, CF1 = 3,000, CF2 = 3,000, CF3 = 7,000, CF5 = 10,000.
We want to find CF4, so we can rearrange the formula:
CF4/(1+WACC)^4 = NPV - (CF0 + CF1/(1+WACC)^1 + CF2/(1+WACC)^2 + CF3/(1+WACC)^3 + CF5/(1+WACC)^5)
2. Now use the IRR formula to find the value of (1+WACC)^4:
IRR = (1+WACC)^4
Given value: IRR = 14.87378%
Rearrange the formula to find (1+WACC)^4:
(1+WACC)^4 = IRR
3. Substituting the values into the formulas:
(1+WACC)^4 = (1+0.12)^4 = 1.57351904
CF4/(1+WACC)^4 = NPV - (CF0 + CF1/(1+WACC)^1 + CF2/(1+WACC)^2 + CF3/(1+WACC)^3 + CF5/(1+WACC)^5)
CF4/1.57351904 = 1,491.39 - (-18,000 + 3,000/(1+0.12)^1 + 3,000/(1+0.12)^2 + 7,000/(1+0.12)^3 + 10,000/(1+0.12)^5)
4. Solve for CF4:
CF4/1.57351904 = 1,491.39 + 18,000 - 3,000/(1+0.12)^1 - 3,000/(1+0.12)^2 - 7,000/(1+0.12)^3 - 10,000/(1+0.12)^5
CF4/1.57351904 = 1,491.39 + 18,000 - 2,678.57 - 2,386.07 - 5,356.65 - 5,072.01
CF4/1.57351904 = 3,998.09
Multiply both sides by 1.57351904 to isolate CF4:
CF4 = 3,998.09 * 1.57351904
CF4 ≈ 6,298.40
Therefore, the cash flow at time-point 4 (CF4) is approximately $6,298.40.