Sofa's Tables is planning to sell its Montreal, Toronto, and Calgary stores. The firm expects to sell each of the three stores for the same, positive cash flow of SA. The firm expects to sell its Toronto store in 5 years, its Calgary store in S years, and its Montreal store in T years. The cost of capital for the Toronto store is Y percent, the cost of capital for the Montreal store is Y percent, the cost of capital for the Calgary store is X percent, T>S > 0, and Y > X> 0. The cash flows from the sales are the only cash flows associated with the various stores. Based on the information in the preceding paragraph, which one of the following assertions is true?


Given the information provided, let's summarize and analyze the details to determine which assertion is true.

### Key Information:
1. **Cash Flows:**
   - The firm expects to receive the same cash flow amount, \( SA \), from selling each of the three stores (Montreal, Toronto, Calgary).

2. **Timing of Sales:**
   - Toronto store: Sold in \( 5 \) years.
   - Calgary store: Sold in \( S \) years.
   - Montreal store: Sold in \( T \) years.
   - It's given that \( T > S > 0 \).

3. **Cost of Capital:**
   - Toronto store: \( Y \% \).
   - Montreal store: \( Y \% \).
   - Calgary store: \( X \% \).
   - It's given that \( Y > X > 0 \).

4. **Cash Flows from Sales:**
   - The cash flows from the sales are the only cash flows associated with these stores.

### Analysis:
To determine which assertion is true, we should consider the Present Value (PV) of each store's sale. The present value of a future cash flow is calculated using the formula:

\[
PV = \frac{SA}{(1 + r)^n}
\]

where:
- \( SA \) = Sale amount (cash flow) from the store,
- \( r \) = Discount rate (cost of capital),
- \( n \) = Number of years until the cash flow is received.

Now, let's apply this formula to each store:

- **Toronto Store:**
  \[
  PV_{\text{Toronto}} = \frac{SA}{(1 + Y)^5}
  \]

- **Calgary Store:**
  \[
  PV_{\text{Calgary}} = \frac{SA}{(1 + X)^S}
  \]

- **Montreal Store:**
  \[
  PV_{\text{Montreal}} = \frac{SA}{(1 + Y)^T}
  \]

### Understanding the Relationships:

1. **Cost of Capital Differences:**
   - Since \( Y > X \), the cost of capital for the Montreal and Toronto stores is higher than for the Calgary store.

2. **Timing Differences:**
   - \( T > S > 0 \), so the Montreal store is sold the latest, and the Calgary store is sold earlier than Montreal but later than the Toronto store (which is sold in 5 years).

### True Assertion Analysis:

Given that \( T > S \) and \( Y > X > 0 \), let's analyze the implications:

- **Higher Discount Rate (Y) and Longer Duration (T):**
  - The Montreal store has the highest discount rate (Y) and the longest duration (T). Therefore, its present value will be lower due to both a higher rate and a longer compounding period.

- **Calgary Store with Lower Discount Rate (X):**
  - The Calgary store has a lower discount rate (X) and is sold sooner than the Montreal store. Therefore, its present value will be relatively higher compared to Montreal, assuming \( SA \) is the same.

- **Toronto Store with Higher Discount Rate (Y) and Fixed Duration (5 years):**
  - The Toronto store is sold in 5 years with a higher discount rate (Y). The present value of the Toronto store will be less than that of the Calgary store if \( S \) is relatively low since \( X < Y \).

### Conclusion:

The **true assertion** would be:

1. **The present value of the sale of the Calgary store is greater than the present value of the sale of the Montreal store.**
   - This is because the Calgary store has a lower cost of capital (X) compared to the Montreal store (Y) and is also sold earlier than the Montreal store (since \( S < T \)).

Would you like further details on this analysis or have any additional questions? Here are 5 related questions to consider:

1. How do the differences in cost of capital impact the valuation of future cash flows?
2. What happens to the present value of cash flows if the cost of capital increases?
3. How does the timing of cash flows affect their present value?
4. What other factors could affect the decision to sell these stores at different times?
5. How can sensitivity analysis help in understanding the impact of varying costs of capital?

**Tip:** Remember that the present value decreases as either the discount rate increases or the time period until cash flow receipt increases.

Sofa's Tables is planning to sell its Montreal, Toronto, and Calgary stores. The firm expects to sell each of the three stores for the same, positive cash flow of SA. The firm expects to sell its Toronto store in 5 years, its Calgary store in S years, and its Montreal store in T years. The cost of capital for the Toronto store is Y percent, the cost of capital for the Montreal store is Y percent, the cost of capital for the Calgary store is X percent, T > S > 0, and Y > X > 0. The cash flows from the sales are the only cash flows associated with the various stores. Based on the information in the preceding paragraph, which one of the following assertions is true?

Analyze the present value of cash flows from the sale of Sofa's Tables stores in Montreal, Toronto, and Calgary. Learn how different discount rates and sale timelines impact the valuation of future cash flows. Key concepts include present value calculation and the effect of varying discount rates. Suitable for college-level finance or business studies.

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