Answer :
### Question 1: Calculate the value of inventory listed on the firm's balance sheet.
Step 1: Understand the Given Information
- Current liabilities = \[tex]$15 million - Current ratio (Current Assets / Current Liabilities) = 2.1 - Cash makes up 10% of current assets. - Accounts receivable makes up 40% of current assets. Step 2: Calculate Current Assets The current ratio is defined as: \[ \text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} \] Thus, \[ 2.1 = \frac{\text{Current Assets}}{15} \] Solving for Current Assets: \[ \text{Current Assets} = 2.1 \times 15 = 31.5 \text{ million dollars} \] Step 3: Calculate the Value of Cash and Accounts Receivable - Cash is 10% of current assets. - Accounts receivable is 40% of current assets. \[ \text{Cash} = 0.1 \times 31.5 = 3.15 \text{ million dollars} \] \[ \text{Accounts Receivable} = 0.4 \times 31.5 = 12.6 \text{ million dollars} \] Step 4: Calculate the Value of Inventory Inventory is the remaining portion of current assets after accounting for cash and accounts receivable. \[ \text{Inventory} = \text{Current Assets} - (\text{Cash} + \text{Accounts Receivable}) \] \[ \text{Inventory} = 31.5 - (3.15 + 12.6) \] \[ \text{Inventory} = 31.5 - 15.75 \] \[ \text{Inventory} = 15.75 \text{ million dollars} \] So, the value of inventory listed on the firm's balance sheet is \$[/tex]15.75 million.
### Question 2: Evaluate projects A and B based on given decision rules.
Given Information:
- The initial investment for each project is \[tex]$105,000. - Expected cash inflows for Project A: - Year 1: \$[/tex]55,000
- Year 2: \[tex]$43,000 - Year 3: \$[/tex]61,000
- Expected cash inflows for Project B:
- Year 1: \[tex]$5,000 - Year 2: \$[/tex]10,000
- Year 3: \[tex]$144,000 - Required rate of return: 9% Step 1: Profit Maximization Profit maximization involves comparing the net cash inflows over the lifetime of the projects. \[ \text{Net Cash Inflows for Project A} = \$[/tex]55,000 + \[tex]$43,000 + \$[/tex]61,000 - \[tex]$105,000 = \$[/tex]54,000 \]
[tex]\[ \text{Net Cash Inflows for Project B} = \$5,000 + \$10,000 + \$144,000 - \$105,000 = \$54,000 \][/tex]
Since both projects have identical net cash inflows (\[tex]$54,000), you can choose either based on other qualitative factors, as profit maximization alone does not differentiate them. Step 2: Wealth Maximization Wealth maximization involves calculating the Net Present Value (NPV) of each project. NPV accounts for the time value of money. \[ \text{NPV} = \sum_{t=1}^{n} \frac{\text{Cash Inflow}_t}{(1 + r)^t} - \text{Initial Investment} \] where \( r \) is the required rate of return (9%). NPV for Project A: \[ \text{NPV}_A = \frac{55000}{(1 + 0.09)^1} + \frac{43000}{(1 + 0.09)^2} + \frac{61000}{(1 + 0.09)^3} - 105000 \] NPV for Project B: \[ \text{NPV}_B = \frac{5000}{(1 + 0.09)^1} + \frac{10000}{(1 + 0.09)^2} + \frac{144000}{(1 + 0.09)^3} - 105000 \] After calculating: \[ \text{NPV}_A = 28754.15 \text{ (approximately) } \] \[ \text{NPV}_B = 19198.38 \text{ (approximately) } \] Decision: a. Profit Maximization Decision: - Profit maximization yields the same net cash inflows of \$[/tex]54,000 for both projects. Therefore, based on this rule, either project could be chosen.
b. Wealth Maximization Decision:
- Wealth maximization indicates that Project A should be chosen, as it has a higher NPV (\[tex]$28,754.15) compared to Project B (\$[/tex]19,198.38).
Step 1: Understand the Given Information
- Current liabilities = \[tex]$15 million - Current ratio (Current Assets / Current Liabilities) = 2.1 - Cash makes up 10% of current assets. - Accounts receivable makes up 40% of current assets. Step 2: Calculate Current Assets The current ratio is defined as: \[ \text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} \] Thus, \[ 2.1 = \frac{\text{Current Assets}}{15} \] Solving for Current Assets: \[ \text{Current Assets} = 2.1 \times 15 = 31.5 \text{ million dollars} \] Step 3: Calculate the Value of Cash and Accounts Receivable - Cash is 10% of current assets. - Accounts receivable is 40% of current assets. \[ \text{Cash} = 0.1 \times 31.5 = 3.15 \text{ million dollars} \] \[ \text{Accounts Receivable} = 0.4 \times 31.5 = 12.6 \text{ million dollars} \] Step 4: Calculate the Value of Inventory Inventory is the remaining portion of current assets after accounting for cash and accounts receivable. \[ \text{Inventory} = \text{Current Assets} - (\text{Cash} + \text{Accounts Receivable}) \] \[ \text{Inventory} = 31.5 - (3.15 + 12.6) \] \[ \text{Inventory} = 31.5 - 15.75 \] \[ \text{Inventory} = 15.75 \text{ million dollars} \] So, the value of inventory listed on the firm's balance sheet is \$[/tex]15.75 million.
### Question 2: Evaluate projects A and B based on given decision rules.
Given Information:
- The initial investment for each project is \[tex]$105,000. - Expected cash inflows for Project A: - Year 1: \$[/tex]55,000
- Year 2: \[tex]$43,000 - Year 3: \$[/tex]61,000
- Expected cash inflows for Project B:
- Year 1: \[tex]$5,000 - Year 2: \$[/tex]10,000
- Year 3: \[tex]$144,000 - Required rate of return: 9% Step 1: Profit Maximization Profit maximization involves comparing the net cash inflows over the lifetime of the projects. \[ \text{Net Cash Inflows for Project A} = \$[/tex]55,000 + \[tex]$43,000 + \$[/tex]61,000 - \[tex]$105,000 = \$[/tex]54,000 \]
[tex]\[ \text{Net Cash Inflows for Project B} = \$5,000 + \$10,000 + \$144,000 - \$105,000 = \$54,000 \][/tex]
Since both projects have identical net cash inflows (\[tex]$54,000), you can choose either based on other qualitative factors, as profit maximization alone does not differentiate them. Step 2: Wealth Maximization Wealth maximization involves calculating the Net Present Value (NPV) of each project. NPV accounts for the time value of money. \[ \text{NPV} = \sum_{t=1}^{n} \frac{\text{Cash Inflow}_t}{(1 + r)^t} - \text{Initial Investment} \] where \( r \) is the required rate of return (9%). NPV for Project A: \[ \text{NPV}_A = \frac{55000}{(1 + 0.09)^1} + \frac{43000}{(1 + 0.09)^2} + \frac{61000}{(1 + 0.09)^3} - 105000 \] NPV for Project B: \[ \text{NPV}_B = \frac{5000}{(1 + 0.09)^1} + \frac{10000}{(1 + 0.09)^2} + \frac{144000}{(1 + 0.09)^3} - 105000 \] After calculating: \[ \text{NPV}_A = 28754.15 \text{ (approximately) } \] \[ \text{NPV}_B = 19198.38 \text{ (approximately) } \] Decision: a. Profit Maximization Decision: - Profit maximization yields the same net cash inflows of \$[/tex]54,000 for both projects. Therefore, based on this rule, either project could be chosen.
b. Wealth Maximization Decision:
- Wealth maximization indicates that Project A should be chosen, as it has a higher NPV (\[tex]$28,754.15) compared to Project B (\$[/tex]19,198.38).
