CMA May 2025 Examination Solutions

Solution:

The correct answer is **(e) Characteristic line**. The characteristic line plots the excess returns of a security against the excess returns of the market portfolio. The slope of this line is the security's beta ($\beta$). While the Security Market Line (SML) also relates return and risk, it is a graphical representation of the CAPM and plots a security's expected return as a function of its beta, not a description of the relationship between their historical returns.

Solution:

The correct answer is **(c) Profitability moves together with risk**. In working capital management, pursuing higher profitability often involves taking on more risk, such as holding lower levels of cash and inventory or offering more generous credit terms. This inverse relationship between liquidity and profitability, and the direct relationship between profitability and risk, is a fundamental trade-off.

Solution:

The correct answer is **(b) The expected return**. The expected return is a forward-looking measure calculated by multiplying the return of each possible outcome by its probability of occurrence and then summing the results. This provides a single-point estimate of a project's future return.

Solution:

The correct answer is **(a) The yield to maturity on the firm's bond**. The cost of debt for a firm is the return required by its creditors. This is best measured by the Yield to Maturity (YTM) on the firm's existing, publicly traded bonds, as it reflects the current market-required return, not the historical coupon rate.

Solution:

First, we need to find the present value of each year's cash flow.

Initial Investment = -Tk. 600,000

Annual Cash Flow = Tk. 200,000

Discount Rate ($r$) = 10% or 0.10

Year	Cash Flow (Tk.)	PV Factor (10%)	PV of Cash Flow (Tk.)	Cumulative PV (Tk.)
1	200,000	$\frac{1}{(1.10)^1} = 0.9091$	$200,000 \times 0.9091 = 181,820$	181,820
2	200,000	$\frac{1}{(1.10)^2} = 0.8264$	$200,000 \times 0.8264 = 165,280$	$181,820 + 165,280 = 347,100$
3	200,000	$\frac{1}{(1.10)^3} = 0.7513$	$200,000 \times 0.7513 = 150,260$	$347,100 + 150,260 = 497,360$
4	200,000	$\frac{1}{(1.10)^4} = 0.6830$	$200,000 \times 0.6830 = 136,600$	$497,360 + 136,600 = 633,960$

The discounted payback period is between year 3 and year 4. We need to find the fraction of the final year.

Fraction of year = $\frac{\text{Initial Investment} - \text{Cumulative PV at Year 3}}{\text{PV of Cash Flow in Year 4}}$

Fraction of year = $\frac{600,000 - 497,360}{136,600} = \frac{102,640}{136,600} \approx 0.75 \text{ years}$

Total Discounted Payback Period = $3 \text{ years} + 0.75 \text{ years} = 3.75 \text{ years}$

This is equivalent to 3 years and $0.75 \times 12 = 9$ months. Therefore, the correct option is **(e) 3 years 9 months**.

Solution:

The value of a levered firm ($V_L$) is given by the formula:

Rearranging the formula to find the PV of the tax shield:

Given:

$V_L = \text{Tk. } 5,000,000$

$V_U = \text{Tk. } 4,780,000$

PV of Financial Distress Costs = Tk. 360,000

Calculation:

$\text{PV of Tax Shield} = 5,000,000 - 4,780,000 + 360,000$

$\text{PV of Tax Shield} = 220,000 + 360,000 = \text{Tk. } 580,000$

The value of the tax shield is **Tk. 580,000**, which corresponds to option **(c)**.

Solution:

The formula for the annual percentage cost of forgoing a cash discount is:

In this case, the customer is forgoing the 1% discount by delaying payment for the difference between the new payment period (70 days) and the previous one (30 days), which is 40 days.

Given:

Discount % = 1%

Days of forgone discount = $70 - 30 = 40$ days

Calculation:

$\text{Cost} = \frac{0.01}{1 - 0.01} \times \frac{365}{40} = \frac{0.01}{0.99} \times 9.125 \approx 0.0101 \times 9.125 \approx 0.09216$ or $9.22\%$

Since 9.22% is closest to 9.5%, and the options are discrete, we should recheck the problem statement. The question implies that the reduction from 70 to 30 days is the new payment period. The original payment terms are not given. Let's assume the terms were something like 1/30 net 70. This would mean they had 30 days to get a discount. The customer is paying on day 70, forgoing the discount. The cost is calculated on the number of additional days of credit taken (70-30=40). The formula is correct. The closest answer is not in the options. This may be an issue with the provided options or problem statement. Let's use the standard formula for a discount, assuming terms are 1/30, net 70. This means a 1% discount if paid within 30 days, otherwise due in 70 days. The customer is taking the full 70 days instead of the 30 days. The credit period for which the discount is foregone is $70 - 30 = 40$ days. The cost is $\frac{1\%}{100\%-1\%} \times \frac{365}{40} = \frac{0.01}{0.99} \times 9.125 = 9.21\%$. None of the answers is a perfect match. The closest option is **9%**, which is **(c)**.

Solution:

We can use linear interpolation to find the approximate IRR.

Given:

$r_1 = 15\% = 0.15$

$r_2 = 18\% = 0.18$

$NPV_1 = \text{Tk. } 3,670$

$NPV_2 = \text{Tk. } -1,390$

Calculation:

$IRR = 0.15 + \frac{3,670}{3,670 - (-1,390)} (0.18 - 0.15)$

$IRR = 0.15 + \frac{3,670}{5,060} (0.03)$

$IRR = 0.15 + 0.7253 \times 0.03 = 0.15 + 0.02176 = 0.17176$

The IRR is approximately 17.18%, which rounds to **17.2%**, corresponding to option **(e)**.

Solution:

The bank's quote is in "indirect" terms from the perspective of the Hong Kong Dollar (HK\$), meaning the US Dollar (the base currency) is quoted in terms of the foreign currency. The bank's offer price is what the bank is willing to sell the base currency (US\$) for, and the bid price is what the bank is willing to buy the base currency (US\$) for.

The exporter wants to sell HK\$ to the bank to get US\$. The bank will be *buying* the HK\$ from the exporter, which means it is *selling* US\$. The bank's offer price is the rate it will sell the base currency (US\$) for. The bank wants to make a profit, so it will use the less favorable rate for the exporter, which is the bid price from its perspective (the rate it is buying the HK\$ at).

The bank is buying HK\$ from the exporter. The bid rate is how many foreign currency units the bank will pay for one unit of the base currency (US\$). Wait, this is confusing. Let's simplify with the bank's perspective. The bank is buying HK\$ from the exporter and paying in US\$. This means the bank is paying less US\$ for each HK\$. The bank's bid price is the price at which the bank is willing to buy the base currency. So, it's the bid price of the US\$ in terms of HK\$. The bank will give the exporter fewer US\$ for their HK\$, so we divide by the higher number, the bank's offer price from the quote. Let's re-examine the quote. The bank's offer price is HK\$7.7000 and the bid price is HK\$7.7425. This quote is in direct terms for the HK\$, which is unusual. Let's assume the quote is in indirect terms from the bank's perspective, meaning 1 US\$ = HK\$X. The bid is what the bank will buy the US\$ for, and the offer is what the bank will sell the US\$ for. The exporter wants to convert HK\$ to US\$. The bank is buying the HK\$ and selling US\$. The bank will use the exchange rate that is most favorable to itself, which means it will give the exporter the least number of US\$. The correct rate to use is the bid price of US\$ from the bank's perspective, which is the higher number in the quote (7.7425). We will divide the amount of HK\$ by the bid price to get the US\$ amount.

Amount in US\$ = $\frac{\text{Amount in HK\$}}{\text{Bank's Bid Price}} = \frac{400,000}{7.7425} \approx \$ 51,662.90$

The exporter will receive **\$ 51,662.90**, which is option **(a)**.

Solution:

The correct answer is **(a) It will increase the initial outflow of cash for the project**. Flotation costs are the fees paid to investment banks for issuing new securities. These costs directly reduce the net proceeds received from financing. When analyzing a new project, these costs increase the initial investment required to raise the necessary funds. This effectively increases the initial cash outflow, which in turn decreases the project's NPV and IRR.

Solution:

False. Unsystematic risk is diversifiable risk, and it is **not** measured by beta. **Systematic risk** is measured by beta factors.

Solution:

False. Common stocks that pay no dividends may be priced **higher** than dividend-paying stocks if they have higher growth potential. Investors would expect to earn a return from capital gains rather than dividends.

Solution:

True. Preferred stock provides financial leverage because it is a fixed-cost security, just like debt. The fixed dividend payments magnify the returns to common stockholders as earnings before interest and taxes (EBIT) change.

Solution:

False. For tax purposes, firms generally prefer an **accelerated depreciation** method because it allows for larger deductions in the early years of an asset's life. This leads to lower taxable income and lower tax payments in the near term, thus increasing the present value of the firm's cash flows.

Solution:

True. In a sale and leaseback arrangement, a firm sells an asset it owns to another party and immediately leases it back. The original owner of the asset is the **seller** and now becomes the **lessee** (the user of the asset). The party that buys the asset is the **buyer** and becomes the **lessor** (the owner who receives lease payments).

Solution:

The correct matches are as follows:

• **1) Earnings per Share (EPS)** matches with **(b) Firm performance**. EPS is a key indicator of a firm's profitability.
• **2) Right share** matches with **(i) Current shareholders**. A rights issue gives existing shareholders the right to buy new shares.
• **3) Cash management** matches with **(c) Baumol model**. The Baumol model is a classical model used for optimizing cash balances.
• **4) Relevant cash flow** matches with **(g) Sunk cost**. A sunk cost is a non-relevant cash flow in capital budgeting decisions.
• **5) Stock exchanges** matches with **(j) Capital market**. Stock exchanges are a key component of the capital market.

Solution:

Relationship between PV and FV:

Present Value (PV) and Future Value (FV) have an inverse relationship. A higher interest rate leads to a lower present value for a given future value, and a higher future value for a given present value. This relationship is defined by the following formula:

where $r$ is the interest rate and $n$ is the number of periods. Rearranging for PV, we get $PV = \frac{FV}{(1+r)^n}$.

Comparing Investments G and H:

We need to find the rate of return ($r$) for each investment. This is the interest rate that makes the present value of the future cash flow equal to the initial cost.

For Investment G:

$65,000 = \frac{125,000}{(1 + r)^6}$

$(1 + r)^6 = \frac{125,000}{65,000} \approx 1.9231$

$1 + r = (1.9231)^{1/6} \approx 1.1147$

$r = 1.1147 - 1 = 0.1147 = 11.47\%$

For Investment H:

$65,000 = \frac{205,000}{(1 + r)^{10}}$

$(1 + r)^{10} = \frac{205,000}{65,000} \approx 3.1538$

$1 + r = (3.1538)^{1/10} \approx 1.1217$

$r = 1.1217 - 1 = 0.1217 = 12.17\%$

**Conclusion:** Investment H has a higher return of **12.17%** compared to Investment G's **11.47%**. Therefore, Investment H has the higher return.

Solution:

1. Impact of market return changes on investment's return.

   The relationship between the investment's return and the market return is given by beta. $\beta = \frac{\%\Delta \text{ Investment Return}}{\%\Delta \text{ Market Return}}$

   If the market return increases by 10%, we can expect the investment's return to change by:

   $\%\Delta \text{ Investment Return} = \beta \times \%\Delta \text{ Market Return} = 1.50 \times 10\% = 15\%$

   If the market return declines by 10%, we can expect the investment's return to change by:

   $\%\Delta \text{ Investment Return} = 1.50 \times (-10\%) = -15\%$

2. Required return using CAPM.

   The CAPM formula is: $R_i = R_f + \beta_i \times (R_M - R_f)$

   Given: $R_f = 7\%$, $R_M = 10\%$, $\beta_i = 1.50$

   $R_i = 7\% + 1.50 \times (10\% - 7\%) = 7\% + 1.50 \times 3\% = 7\% + 4.5\% = 11.5\%$

   The required return on this investment is **11.5%**.

3. Recommendation based on required return.

   The investment is expected to earn 11%, but the CAPM requires a return of 11.5% given its risk. Since the expected return is **less than** the required return ($11\% < 11.5\%$), you should **not recommend** this investment. It does not provide sufficient compensation for the risk taken.

4. Impact of a 1% drop in market return.

   If the market return ($R_M$) drops by 1% to 9%, the new required return would be:

   $R_i = 7\% + 1.50 \times (9\% - 7\%) = 7\% + 1.50 \times 2\% = 7\% + 3\% = 10\%$

   The new required return is 10%. Now, the expected return of 11% is **greater than** the required return ($11\% > 10\%$). Therefore, under this new market condition, you **would recommend** the investment.

Solution:

For a new bond to sell at its par value (Tk. 1,000), its coupon rate must be equal to the current yield to maturity (YTM) of a similar existing bond. The YTM is the market's required rate of return. We need to find the YTM of the existing bonds.

Given for existing bonds:

• Coupon Rate = 5.7% annually, or $\frac{5.7\%}{2} = 2.85\%$ semiannually.
• Par Value (FV) = Tk. 1,000
• Market Price (PV) = Tk. 1,048
• Number of periods (N) = $20 \text{ years} \times 2 = 40$ semiannual periods
• Semiannual Coupon Payment (PMT) = $0.0285 \times 1,000 = \text{Tk. } 28.50$

We need to solve for the semiannual yield ($r$) in the bond pricing formula:

Since this formula cannot be solved directly for $r$, we use a financial calculator or trial and error. By inputting the values, we find that the semiannual rate is approximately 2.65%.

YTM = $2.65\% \times 2 = 5.30\%$.

For the new bonds to sell at par, their coupon rate must be equal to the market's required return, which is the YTM of the existing bonds. Therefore, the company should set the coupon rate on its new bonds at **5.30%**.

Solution:

**No**, a positive NPV after adjusting for political risk and diversification does not automatically mean the project is acceptable. While these adjustments are crucial, there are other factors to consider in international capital budgeting:

• **Foreign Exchange Risk:** The NPV calculation must account for fluctuating exchange rates, which can significantly impact the value of future cash flows when repatriated to the home country.
• **Political and Regulatory Environment:** The discount rate adjustment may not fully capture all political risks, such as expropriation, changes in tax laws, or restrictions on capital repatriation.
• **Strategic Fit:** The project must align with the firm's overall strategic goals and core competencies. A positive NPV project may not be a good fit if it distracts from the company's main business or brand.
• **Financing Risk:** The project may be difficult to finance or may require different capital structures in the host country, which could introduce additional complexities and costs.

Therefore, a positive NPV is a necessary but not sufficient condition for project acceptance. A thorough analysis must also consider all relevant cash flows, the impact of foreign exchange, and strategic fit.

Solution:

First, we calculate the NPV for each project, which is required for the profitability index calculation.

Year	Cash Flow (A)	PV Factor (12%)	PV of CF (A)	PV of CF (B)	PV of CF (C)
1	165,000	0.8929	147,329	267,870	161,622
2	165,000	0.7972	131,538	239,160	107,622
Initial Outlay (Year 0)	(225,000)	1.0000	(225,000)	(450,000)	(225,000)

PV of Cash Inflows:

PV of inflows for A = $147,329 + 131,538 = 278,867$

PV of inflows for B = $267,870 + 239,160 = 507,030$

PV of inflows for C = $161,622 + 107,622 = 269,244$

i. Compute the Profitability Index (PI) for each project.

$PI_A = \frac{278,867}{225,000} = 1.24$

$PI_B = \frac{507,030}{450,000} = 1.13$

$PI_C = \frac{269,244}{225,000} = 1.20$

ii. Compute the NPV for each project.

$NPV_A = 278,867 - 225,000 = \text{Tk. } 53,867$

$NPV_B = 507,030 - 450,000 = \text{Tk. } 57,030$

$NPV_C = 269,244 - 225,000 = \text{Tk. } 44,244$

iii. Which project(s) should PRAN accept based on the PI rule if they are mutually exclusive?

When projects are mutually exclusive, you should accept the project with the highest PI, as long as its PI is greater than 1. In this case, Project A has the highest PI of 1.24. Therefore, PRAN should accept **Project A**.

iv. Which project(s) should PRAN accept if the budget is Tk. 450,000 and projects are not divisible?

With a capital budget constraint, we must rank the projects by their PI and then select the combination that fits within the budget while maximizing total NPV.

• Project A requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 53,867.
• Project C requires Tk. 225,000. Budget remaining: Tk. 225,000. Total NPV: Tk. 44,244.
• Project B requires Tk. 450,000. Budget remaining: Tk. 0. Total NPV: Tk. 57,030.

Project A ($PI=1.24$) and C ($PI=1.20$) both fit in the budget, and their combined cost is $225,000 + 225,000 = 450,000$. Their combined NPV is $53,867 + 44,244 = 98,111$.

Project B ($PI=1.13$) alone costs Tk. 450,000 and has an NPV of Tk. 57,030.

Since the combination of Projects A and C yields a higher total NPV than Project B, PRAN should accept **Projects A and C**.

Solution:

i. Calculate the individual cost of each source of financing.

Cost of Debt ($R_D$):

First, find the YTM of the bond. We are given: PV = Tk. $1,000 - 30 - 20 = 950$ (after discount and flotation cost), FV = Tk. 1,000, PMT = $10\% \times 1,000 = 100$ annually, N = 10 years. Using a financial calculator or trial and error, the YTM is approximately 11.08%. The after-tax cost is $R_D(1 - T_C) = 11.08\% \times (1 - 0.40) = 11.08\% \times 0.60 = 6.65\%$

Cost of Preferred Stock ($R_P$):

Cost of Retained Earnings ($R_{RE}$):

We use the dividend growth model: $R_{RE} = \frac{D_1}{P_0} + g$

Given: $D_1 = \text{Tk. } 6$, $P_0 = \text{Tk. } 80$, $g = 6\%$

Cost of New Common Stock ($R_N$):

The new stock will be underpriced and have flotation costs, so the net proceeds per share ($N_P$) will be $80 - 4 - 4 = 72$.

The firm will use retained earnings until they are exhausted, then new common stock. The cost of equity capital is 13.5% if retained earnings are used, and 14.33% if new stock is issued.

ii. Calculate the firm's weighted average cost of capital (WACC).

Since the problem does not specify if the retained earnings budget is exceeded, we will calculate two WACCs: one using retained earnings and one using new common stock.

WACC (using retained earnings):

$WACC = (0.40 \times 6.65\%) + (0.15 \times 11.46\%) + (0.45 \times 13.5\%)$

$WACC = 2.66\% + 1.72\% + 6.08\% = 10.46\%$

WACC (using new common stock):

$WACC = (0.40 \times 6.65\%) + (0.15 \times 11.46\%) + (0.45 \times 14.33\%)$

$WACC = 2.66\% + 1.72\% + 6.45\% = 10.83\%$

Solution:

We compare the PV cost of leasing to the PV cost of owning. The discount rate is the after-tax cost of debt: $10\% \times (1 - 0.40) = 6\%$.

i. Calculate Tata's PV cost of leasing.

Lease payments are Tk. 10,000 per year, at the beginning of each year.

After-tax lease payment = Lease Payment $\times (1 - T_C) = 10,000 \times (1 - 0.40) = \text{Tk. } 6,000$

Year	After-tax Lease Payment	PV Factor (6%)	PV of Payment
0	6,000	1.0000	6,000
1	6,000	0.9434	5,660.40
2	6,000	0.8900	5,340.00
3	6,000	0.8396	5,037.60
**Total PV Cost of Leasing**	**Tk. 22,038.00**

ii. Calculate Tata's PV cost of owning and make a decision.

Initial Cost = Tk. 40,000

Loan Payments: A 4-year, 10% loan of Tk. 40,000. Using a financial calculator, the annual payment is approximately Tk. 12,618.77. The after-tax loan payment is not a relevant cash flow, as the interest and principal components are different. Instead, we must analyze the cash flows from buying:

• Initial Outlay: Tk. 40,000
• Tax savings from depreciation: Dep. $\times T_C$
• After-tax maintenance costs: Maintenance $\times (1-T_C)$
• After-tax salvage value: Salvage $\times (1-T_C)$

Year	Depreciation	Dep. Tax Shield	Maint. Cost	After-tax Maint.	PV Factor (6%)	PV of CF
0				(40,000)	1.0000	(40,000.00)
1	13,200	5,280	1,000	(600)	0.9434	4,414.71
2	18,000	7,200	1,000	(600)	0.8900	6,051.60
3	6,000	2,400	1,000	(600)	0.8396	1,512.63
4	2,800	1,120	1,000	(600)	0.7921	411.89

Net cash flow for owning, including salvage value at year 4:

PV of owning = PV of (Initial cost + Tax shield + After-tax maintenance + After-tax salvage)

Salvage Value (after-tax) = $10,000 \times (1 - 0.40) = \text{Tk. } 6,000$.

PV of salvage = $6,000 \times 0.7921 = 4,752.60$.

PV cost of owning = $-40,000 + (5,280 - 600) \times 0.9434 + (7,200 - 600) \times 0.8900 + (2,400 - 600) \times 0.8396 + (1,120 - 600 + 10,000) \times 0.7921$

PV cost of owning = $-40,000 + 4,414.71 + 5,874.00 + 1,511.28 + 8,569.21 = \text{Tk. } -19,630.80$

**Correction:** The problem statement for owning is slightly confusing. The PV cost is the total of all outflows and inflows, discounted at the after-tax cost of debt. The PV cost of owning is: $40,000 + \sum(\text{Tax savings from depreciation}) - \sum(\text{After-tax maintenance}) - \text{PV of Salvage}$ $PV_{cost\_own} = -40,000 + 5,280(0.9434) + 7,200(0.8900) + 2,400(0.8396) + 1,120(0.7921) + 10,000(0.7921)$ $PV_{cost\_own} = -40,000 + 4,982.59 + 6,408.00 + 2,015.04 + 887.15 + 7,921 = -17,786.22$. The PV cost of owning is the negative of the net present value, so the NPV is Tk. 17,786.22.

Let's recalculate from scratch to be clear.

PV of Owning = Initial Cost - PV of Dep. Tax Shield - PV of After-tax Salvage + PV of After-tax Maint. Costs

Initial Cost: Tk. 40,000

Year	Dep.	Dep. Tax Shield	PV Factor (6%)	PV of Tax Shield	After-tax Maint.	PV of Maint.
1	13,200	5,280	0.9434	4,982.59	600	566.04
2	18,000	7,200	0.8900	6,408.00	600	534.00
3	6,000	2,400	0.8396	2,015.04	600	503.76
4	2,800	1,120	0.7921	887.15	600	475.26

PV of Depreciation Tax Shield = $4,982.59 + 6,408.00 + 2,015.04 + 887.15 = \text{Tk. } 14,292.78$

PV of After-tax Maintenance = $566.04 + 534.00 + 503.76 + 475.26 = \text{Tk. } 2,079.06$

PV of After-tax Salvage Value = $10,000 \times (1-0.40) \times 0.7921 = \text{Tk. } 4,752.60$

PV cost of owning = Initial Outlay - PV of Dep. Tax Shield - PV of After-tax Salvage + PV of After-tax Maint. Costs

PV cost of owning = $40,000 - 14,292.78 - 4,752.60 + 2,079.06 = \text{Tk. } 23,033.68$

**Decision:** Since the PV cost of leasing (Tk. 22,038) is **less than** the PV cost of owning (Tk. 23,033.68), Tata should **lease** the truck.

Solution:

We will use the projected results for 2025.

To get to the required values, we first need to compute the operating profit (EBIT) and profit before tax for both firms in 2025:

• **Firm A (2025):**
• Sales: Tk. 288.00 million
• Variable costs: Tk. 172.80 million
• Fixed costs: Tk. 60.00 million
• Interest expense: Tk. 35.00 million
• Operating Profit (EBIT) = $288.00 - 172.80 - 60.00 = \text{Tk. } 55.20 \text{ million}$
• Profit Before Tax = $55.20 - 35.00 = \text{Tk. } 20.20 \text{ million}$
• **Firm B (2025):**
• Sales: Tk. 223.20 million
• Variable costs: Tk. 44.64 million
• Fixed costs: Tk. 110.00 million
• Interest expense: Tk. 110.00 million
• Operating Profit (EBIT) = $223.20 - 44.64 - 110.00 = \text{Tk. } 68.56 \text{ million}$
• Profit Before Tax = $68.56 - 110.00 = \text{Tk. } -41.44 \text{ million}$

i. Compute the Degree of Operating Leverage (DOL).

DOL = $\frac{\text{Sales} - \text{Variable Costs}}{\text{Sales} - \text{Variable Costs} - \text{Fixed Costs}} = \frac{\text{Contribution Margin}}{\text{Operating Profit}}$

For Firm A:

Contribution Margin = $288.00 - 172.80 = \text{Tk. } 115.20 \text{ million}$

DOL$_A = \frac{115.20}{55.20} = 2.09$

For Firm B:

Contribution Margin = $223.20 - 44.64 = \text{Tk. } 178.56 \text{ million}$

DOL$_B = \frac{178.56}{68.56} = 2.60$

**Advice:** Firm B has a higher DOL (2.60) than Firm A (2.09). This indicates that Firm B has a higher proportion of fixed costs relative to variable costs, leading to a higher degree of business risk. A given percentage change in sales will result in a larger percentage change in operating profits for Firm B.

ii. Compute the Degree of Financial Leverage (DFL).

DFL = $\frac{\text{Operating Profit}}{\text{Profit Before Tax}}$

For Firm A:

DFL$_A = \frac{55.20}{20.20} = 2.73$

For Firm B:

DFL$_B = \frac{68.56}{-41.44} = -1.65$ (The DFL is negative because the firm is operating at a loss, which indicates extreme financial risk).

**Advice:** Firm B's DFL is highly problematic, as its operating profit is not enough to cover its interest expense. This indicates a very high financial risk due to its large debt burden. Firm A, by contrast, has a positive DFL, meaning its operating profit more than covers its interest expense. The directors should advise Firm B to reconsider its capital structure, potentially by reducing debt to decrease its financial risk. Firm A's capital structure appears more stable.

Solution:

1. Option 1: External Equity Financing

   This option avoids a dividend cut, which is generally viewed positively by investors who rely on dividends. However, raising Tk. 50 million in new common stock can lead to **dilution** of ownership and earnings per share (EPS). Since the stock market primarily values BSRM based on its dividend payout, the maintenance of the dividend policy is a key benefit. The new project's high return (30%) is likely to offset the negative effects of dilution over time, as long as investors believe the project will successfully increase future earnings.

2. Option 2: 50% Internal & 50% External Equity Financing

   This option requires a dividend cut, which is a major negative signal to investors, especially for a company with a stable dividend policy. A dividend cut could lead to a significant drop in the stock's market price. While this option is often considered the cheapest form of equity financing (retained earnings have no flotation costs), the negative market reaction to a dividend cut could outweigh this benefit. This option is likely the least favorable from a stock price perspective.

3. Option 3: Mix of Debt and Equity

   This option maintains the dividend policy, which is a positive. The use of debt introduces financial leverage, which can increase the returns to equity holders, as the project's return (30%) is well above the likely cost of debt. However, using debt also increases the firm's financial risk. Given BSRM's slow and steady growth, a moderate increase in leverage could be beneficial, as it could boost EPS without significantly increasing the risk of financial distress. This is often the most common and balanced approach.

   **Conclusion:** From a stock value perspective, **Option 3** is likely the best choice. It maintains the desired dividend policy, uses a mix of debt and equity that aligns with modern capital structure theory, and leverages the high-return project to increase overall firm value without a painful dividend cut. Option 1 is also a viable but potentially more expensive alternative due to flotation costs and dilution. Option 2 is likely the worst option due to the negative signaling of a dividend cut.

Solution:

Static Trade-off Theory:

The static trade-off theory of capital structure states that a firm chooses its optimal capital structure by balancing the benefits of using debt with the costs of financial distress. The primary benefit of debt is the **tax shield**—the tax deductibility of interest payments. As a firm adds more debt, its value increases due to this tax shield. However, as leverage increases, the probability of financial distress and bankruptcy also increases, leading to a rising cost of debt and equity. The optimal capital structure is reached at the point where the marginal benefit of adding an extra dollar of debt is exactly equal to the marginal cost of financial distress.

Determining Optimal Capital Structure:

Under this theory, the optimal capital structure is determined by finding the mix of debt and equity that **minimizes the firm's Weighted Average Cost of Capital (WACC)** and, consequently, **maximizes the firm's value**. This is an iterative process where the WACC is calculated at different debt-to-equity ratios to find the minimum point.

Challenges in the Real World:

It is difficult to determine the precise optimal capital structure in the real world due to several factors:

• **Difficulty in Measuring Costs:** The costs of financial distress (e.g., agency costs, loss of key customers or employees) are difficult to quantify. These costs are not directly observable and can only be estimated.
• **Tax Shield Limits:** The benefits of the tax shield are not always linear. A firm must have sufficient taxable income to fully utilize the interest tax deduction. A highly leveraged firm with low or negative earnings may not get the full benefit.
• **Asymmetric Information:** Managers often have more information about a firm's prospects than investors. This can lead to signaling effects, where a change in a firm's capital structure is misinterpreted by the market, potentially causing a stock price change that has nothing to do with the "optimal" structure.
• **Industry and Firm-Specific Factors:** The optimal structure is highly dependent on a firm's industry, asset base, and business risk. It is impossible to find a universal formula, and comparisons with competitors are only a guide.

Solution:

Time Trend Analysis:

Time trend analysis is useful because it allows an analyst to observe how a company's performance has changed over time. It can highlight a company's financial strengths and weaknesses and reveal whether a company is improving or deteriorating. This analysis is particularly useful for identifying internal trends and for predicting future performance based on past patterns. It provides insights into management's effectiveness, the impact of strategic decisions, and the firm's overall stability and growth trajectory. For example, a steadily declining current ratio over five years could signal a worsening liquidity position.

Peer Group Analysis:

Peer group analysis is useful because it provides a benchmark for evaluating a company's performance relative to its competitors. Since financial ratios vary significantly across industries, comparing a company's ratios to the industry average or a specific peer group provides a more meaningful context. This analysis can reveal a firm's competitive advantages or disadvantages. For example, a company with a higher profit margin than its peers might be more efficient or have a superior product. It tells you about a company's external financial health and competitive standing within its industry.

Solution:

The "bird-in-the-hand" argument suggests that investors prefer dividends today because they are a certain cash flow, while the future capital gains from retained earnings are uncertain. It argues that a dividend is more valuable than a future capital gain, leading to a higher stock price for firms with higher payout ratios. The fallacy of this argument was challenged by Modigliani and Miller's dividend irrelevance theory.

The fallacy lies in the assumption that a dividend is inherently less risky than a future capital gain. In a perfect market, the value of the firm is determined by its investment policy, not its dividend policy. Any value from a dividend today is offset by a decrease in the firm's capital base, which reduces its ability to invest and generate future earnings. When a firm pays a dividend, its stock price drops by the amount of the dividend, meaning the shareholder is no wealthier. The "certainty" of the dividend is illusory; it is simply a transfer of a portion of the firm's value from the firm to the shareholder. The shareholder could have sold a portion of their stock to achieve the same cash flow without the firm paying a dividend.

In reality, the risk to the shareholder is not about whether a dividend is paid, but about the total future cash flows generated by the firm, whether they are paid out as dividends or reinvested to create capital gains. The risk of the firm's total cash flows is unaffected by how those cash flows are distributed to shareholders.

Solution:

First, let's break down the annual costs based on sales of Tk. 1,500,000. Assume 1 year = 12 months = 50 weeks.

• Direct materials: $1,500,000 \times 0.30 = \text{Tk. } 450,000$
• Direct labor: $1,500,000 \times 0.25 = \text{Tk. } 375,000$
• Variable overheads: $1,500,000 \times 0.10 = \text{Tk. } 150,000$
• Fixed overheads: $1,500,000 \times 0.15 = \text{Tk. } 225,000$
• Selling & Distribution: $1,500,000 \times 0.05 = \text{Tk. } 75,000$

Total Annual Cost of Production = $450,000 + 375,000 + 150,000 + 225,000 = \text{Tk. } 1,200,000$

Working Capital Requirements (Current Assets):

• **Raw Materials:** In inventory for 3 months. Cost = $450,000 \times \frac{3}{12} = \text{Tk. } 112,500$
• **WIP:** 2 months' half-produced goods. Valuation is on materials, labor, and variable overheads.
  • Materials: $450,000 \times \frac{2}{12} = \text{Tk. } 75,000$
  • Labor: $375,000 \times \frac{2}{12} \times \frac{1}{2} = \text{Tk. } 31,250$
  • Variable Overheads: $150,000 \times \frac{2}{12} \times \frac{1}{2} = \text{Tk. } 12,500$
  • Total WIP = $75,000 + 31,250 + 12,500 = \text{Tk. } 118,750$
• **Finished Goods:** 1 month's production. Valued at material, labor, and variable expenses.

  Cost of Finished Goods = $450,000 + 375,000 + 150,000 = \text{Tk. } 975,000$

  Value of Finished Goods = $975,000 \times \frac{1}{12} = \text{Tk. } 81,250$

• **Receivables:** $2\frac{1}{2}$ months. Valued at the cost of production (materials, labor, variable, and fixed overheads, but not S&D).

  Total Cost of Production = $450,000+375,000+150,000+225,000 = \text{Tk. } 1,200,000$

  Value of Receivables = $1,200,000 \times \frac{2.5}{12} = \text{Tk. } 250,000$

Working Capital Requirements (Current Liabilities):

• **Creditors for Materials:** 2 months credit.

  Creditors = $450,000 \times \frac{2}{12} = \text{Tk. } 75,000$

• **Direct Labor:** 1 week credit. Assume 50 weeks in the year.

  Wages Payable = $375,000 \times \frac{1}{50} = \text{Tk. } 7,500$

• **Variable Overheads:** 1 month credit.

  Variable Overheads Payable = $150,000 \times \frac{1}{12} = \text{Tk. } 12,500$

• **Fixed Overheads:** 1 month credit.

  Fixed Overheads Payable = $225,000 \times \frac{1}{12} = \text{Tk. } 18,750$

• **Selling & Distribution:** $\frac{1}{2}$ month credit.

  S&D Payable = $75,000 \times \frac{0.5}{12} = \text{Tk. } 3,125$

Net Working Capital Requirement:

Total Current Assets = Raw Materials + WIP + Finished Goods + Receivables

= $112,500 + 118,750 + 81,250 + 250,000 = \text{Tk. } 562,500$

Total Current Liabilities = Creditors + Wages Payable + Variable Overheads Payable + Fixed Overheads Payable + S&D Payable

= $75,000 + 7,500 + 12,500 + 18,750 + 3,125 = \text{Tk. } 116,875$

Net Working Capital Requirement = Total Current Assets - Total Current Liabilities

= $562,500 - 116,875 = \text{Tk. } 445,625$

The working capital requirement is **Tk. 445,625**.