To determine the combined value $X$ of the two buildings, we will calculate the present value (PV) of each building based on the expected future cash flows and the respective costs of capital, then sum them together. The formula to compute the present value is:

$PV = \frac{CF}{(1 + r)^t}$ Where:

• $PV$ is the present value,
• $CF$ is the future cash flow,
• $r$ is the cost of capital (expressed as a decimal),
• $t$ is the time in years until the cash flow is received.

Step 1: Calculate the present value of Building A

For Building A:

• Future cash flow $CF_A = 430,000$
• Cost of capital $r_A = 14.78\% = 0.1478$
• Time $t_A = 6$ years

$PV_A = \frac{430,000}{(1 + 0.1478)^6} = \frac{430,000}{(1.1478)^6}$

Step 2: Calculate the present value of Building B

For Building B:

• Future cash flow $CF_B = 780,000$
• Cost of capital $r_B = 9.12\% = 0.0912$
• Time $t_B = 4$ years

$PV_B = \frac{780,000}{(1 + 0.0912)^4} = \frac{780,000}{(1.0912)^4}$

Step 3: Add the two present values together to get the total value $X$:

$X = PV_A + PV_B$

Let me calculate the exact values.The combined total value of the two buildings is approximately $X = 738,194.05$.

Would you like more details on this calculation or have any questions?

Here are 5 related questions to explore further:

1. How does the present value change if the cash flow is expected in fewer or more years?
2. How does the cost of capital affect the present value of each building?
3. What is the significance of using the present value for investment decisions?
4. How would changes in future cash flows impact the total value $X$?
5. What would happen to $X$ if both buildings had the same cost of capital?

Tip: Present value decreases as the time to receive cash increases or as the cost of capital rises.