CMA September 2024 Examination Solutions

Solution:

The correct answer is **(d) To maximize the owner's wealth**. While minimizing risk and maximizing return are important, they are sub-goals of the primary objective. The ultimate goal of financial management is to make decisions that increase the value of the firm, which directly translates to maximizing the wealth of the owners or shareholders, often measured by the stock price.

Solution:

The correct answer is **(c) Return on equity ratio**. Return on equity (ROE) measures the net income earned per dollar of shareholders' equity. It is a key measure of profitability and directly reflects how efficiently management is using the capital provided by shareholders to generate profits.

Solution:

The correct answer is **(d) Future value of a perpetuity**. A perpetuity is an annuity that continues forever. Because the cash flows extend to infinity, the future value of a perpetuity would also be infinite, making it impossible to compute a finite number.

Solution:

The correct answer is **(e) Using long-term bank credit to reduce payables**. Net working capital is defined as current assets minus current liabilities. By using a long-term liability (long-term bank credit) to pay off a current liability (payables), the firm decreases its current liabilities without affecting its current assets, which results in a direct increase in net working capital.

Solution:

First, we need to determine the total dividends paid. The retention ratio is the percentage of earnings retained by the company, so the dividend payout ratio is $1 - \text{retention ratio}$.

Dividend Payout Ratio = $1 - 0.80 = 0.20$ or $20\%$

Total Dividends = Net Income $\times$ Dividend Payout Ratio

= $155,000 \times 0.20 = \text{Tk. } 31,000$

Then, we can calculate the dividend per share:

Dividend per Share = $\frac{\text{Total Dividends}}{\text{Number of Shares Outstanding}} = \frac{31,000}{31,000} = \text{Tk. } 1.00$

The correct answer is **(c) Tk. 1.00**.

Solution:

First, we need to find the company's total assets using the BEP ratio.

$0.10 = \frac{40,000,000}{\text{Total Assets}}$

Total Assets = $\frac{40,000,000}{0.10} = \text{Tk. } 400,000,000$

Next, we need to find the net income to calculate the ROA. To do this, we first find the interest expense using the TIE ratio.

$8.0 = \frac{40,000,000}{\text{Interest Expense}} \implies \text{Interest Expense} = \frac{40,000,000}{8.0} = \text{Tk. } 5,000,000$

Now, calculate net income:

EBIT = Tk. 40,000,000

Interest Expense = Tk. 5,000,000

Earnings Before Tax (EBT) = $40,000,000 - 5,000,000 = \text{Tk. } 35,000,000$

Tax = $35,000,000 \times 0.40 = \text{Tk. } 14,000,000$

Net Income = EBT - Tax = $35,000,000 - 14,000,000 = \text{Tk. } 21,000,000$

Finally, calculate the Return on Assets (ROA):

The correct answer is **(e) 5.25%**.

Solution:

The correct answer is **(b) Will decrease the WACC of a firm with debt in its capital structure**. The cost of debt is calculated on an after-tax basis: $k_d(1-T)$. A higher corporate tax rate ($T$) increases the tax shield on debt, which lowers the after-tax cost of debt. Since the cost of debt is a component of the WACC, a lower after-tax cost of debt will decrease the overall WACC of the firm.

Solution:

The correct answer is **(e) Retained earnings**. The pecking order theory of capital structure suggests that firms prefer to finance new projects with internal funds (retained earnings) first. If internal funds are insufficient, they will seek external debt financing (such as bonds or bank loans), and only as a last resort will they issue new equity (common stock).

Solution:

The correct answer is **(b) Depreciation**. While depreciation is a non-cash expense, it is relevant for capital budgeting because it creates a **tax shield**. The tax shield is a real cash flow benefit that must be included in the project's cash flow analysis. Sunk costs, allocated common costs, and interest costs are generally not considered relevant incremental cash flows for a project evaluation.

Solution:

The net investment is the initial outlay for the new asset, adjusted for any tax implications of selling the old asset.

Purchase price of new bailer = Tk. 10,000

Installation/transport cost = Tk. 750

Total Cost of New Asset = $10,000 + 750 = \text{Tk. } 10,750$

Assuming the book value of the old bailer is Tk. 0, the entire sale price is a taxable gain.

Taxable Gain on Sale of Old Bailer = Tk. 2,000

Tax on Gain = $2,000 \times 0.40 = \text{Tk. } 800$

Net Cash from Sale of Old Bailer = Sale Price - Tax on Gain

= $2,000 - 800 = \text{Tk. } 1,200$

Net Investment = Cost of New Asset - Net Cash from Sale of Old Asset

= $10,750 - 1,200 = \text{Tk. } 9,550$

The correct answer is **(c) Tk. 9,550**.

Solution:

True. Financial leverage is the use of debt in a company's capital structure. The effect of this leverage is seen in how changes in EBIT (Earnings Before Interest and Taxes) are magnified in the firm's earnings per share (EPS). If EBIT is high, financial leverage can significantly increase EPS, but if EBIT is low, it can lead to financial distress.

Solution:

False. The arrangement described is a **fixed-rate exchange** system. A crawling-peg arrangement is a system where a country's currency is allowed to fluctuate within a narrow band of a foreign currency or basket of currencies, but this band is periodically adjusted to maintain a competitive exchange rate.

Solution:

True. The constant growth model (Gordon Growth Model) states that the required return ($k_e$) is equal to the dividend yield ($\frac{D_1}{P_0}$) plus the constant growth rate ($g$). Rearranging the formula ($k_e = \frac{D_1}{P_0} + g$), we get $\frac{D_1}{P_0} = k_e - g$.

Solution:

True. A perpetual bond (or consol) has no maturity date, so it pays interest payments forever. Its intrinsic value is calculated as the annual interest payment divided by the market's required yield on the bond, which is the definition of the capitalized value of an infinite stream of payments.

Solution:

True. The market risk premium is the additional return investors demand for taking on the average level of market risk. When investors become more risk-averse, they require a higher premium to hold risky assets. Therefore, a higher level of risk aversion leads to a larger market risk premium.

Solution:

The correct matches are as follows:

• **(1) Agency cost** matches with **(f) Audit fees**. Agency costs are the costs incurred to ensure that managers act in the best interest of the shareholders, such as the fees paid for external audits.
• **(2) Shareholders** matches with **(i) Residual risk**. Shareholders are the residual claimants of a firm's cash flows; they are entitled to all cash flows that remain after all other claims have been paid. This makes them exposed to the residual risk.
• **(3) Right issue** matches with **(h) Ownership dilution**. A rights issue is a new issue of stock to existing shareholders, which can lead to a dilution of ownership if a shareholder does not exercise their rights.
• **(4) Put option** matches with **(a) Right to sell an asset**. A put option gives the holder the right, but not the obligation, to sell an asset at a specified price.
• **(5) Dividend relevance theory** matches with **(e) Bird in hand argument**. The dividend relevance theory argues that investors prefer a certain dividend today over an uncertain capital gain in the future, which is often referred to as the "bird in the hand" argument.

Solution:

Primary vs. Secondary Offerings in an IPO:

A **primary offering** is when a company sells new shares to the public for the first time. The cash proceeds from this sale go directly to the company, providing it with new capital to fund its operations, expansion, or debt repayment. A **secondary offering** is when existing shareholders sell their shares to the public. In this case, the proceeds from the sale go to the selling shareholders, not to the company. A single IPO can include both primary and secondary offerings.

Benefits of an IPO:

• **Access to Public Capital Markets:** An IPO provides the company with access to a much larger pool of potential investors, enabling it to raise substantial capital for growth and expansion without having to rely on private equity or debt.
• **Liquidity for Founders and Employees:** An IPO allows existing shareholders, such as founders and early employees, to sell their shares and convert their ownership stakes into liquid cash. This serves as a powerful incentive for attracting and retaining top talent.

Solution:

First, we need to calculate the Effective Annual Rate (EAR) for Bank A. The formula is:

For Bank A: $APR = 8\% = 0.08$, compounding frequency ($m$) = 4 (quarterly).

$\text{EAR}_A = (1 + \frac{0.08}{4})^4 - 1 = (1.02)^4 - 1 = 1.082432 - 1 = 0.082432$ or $8.2432\%$

Next, we need to find the nominal rate (APR) for Bank B that results in the same EAR, with monthly compounding ($m=12$).

$(1.082432)^{1/12} = 1 + \frac{APR_B}{12}$

$1.006623 = 1 + \frac{APR_B}{12}$

$\frac{APR_B}{12} = 0.006623 \implies APR_B = 0.006623 \times 12 = 0.079476$ or $7.9476\%$

Bank B must set a nominal rate of approximately **7.95%**.

Comment:

Bank B's nominal rate of 7.95% is **not equal** to Bank A's nominal rate of 8%. The nominal rates are different because the compounding periods are different. To achieve the same effective annual rate, the bank that compounds more frequently (Bank B) must set a lower nominal rate.

Solution:

To find the value of Western Mountain Pizza, we need to discount the incremental cash flows to their present value. The first step is to calculate the appropriate discount rate (the cost of equity, $k_e$) using the Capital Asset Pricing Model (CAPM).

Given: $R_f = 6\% = 0.06$, $\beta = 1.5$, Market Risk Premium = $4\% = 0.04$.

$k_e = 0.06 + 1.5 \times 0.04 = 0.06 + 0.06 = 0.12$ or $12\%$

Next, we calculate the terminal value at the end of Year 4, which is the present value of all cash flows from Year 5 onwards, growing at a constant rate. The terminal value is calculated as of the end of Year 4 using the Gordon Growth Model.

Cash Flow in Year 5 = Cash Flow in Year 4 $\times$ $(1+g) = 5 \text{ million} \times (1.05) = \text{Tk. } 5.25 \text{ million}$.

$\text{Terminal Value}_4 = \frac{5.25 \text{ million}}{0.12 - 0.05} = \frac{5.25}{0.07} = \text{Tk. } 75 \text{ million}$

Finally, we calculate the total present value by discounting the annual cash flows and the terminal value back to the present.

Year (t)	Cash Flow (Tk. million)	PV Factor (12%)	PV of Cash Flow (Tk. million)
1	1.5	$\frac{1}{1.12} = 0.8929$	$1.5 \times 0.8929 = 1.3394$
2	2.0	$\frac{1}{1.12^2} = 0.7972$	$2.0 \times 0.7972 = 1.5944$
3	3.0	$\frac{1}{1.12^3} = 0.7118$	$3.0 \times 0.7118 = 2.1354$
4	$5.0 + 75.0$ (Terminal Value)	$\frac{1}{1.12^4} = 0.6355$	$80.0 \times 0.6355 = 50.8400$

Total NPV = $1.3394 + 1.5944 + 2.1354 + 50.8400 = \text{Tk. } 55.9092 \text{ million}$

The value of Western Mountain Pizza to Pizza Place is approximately **Tk. 55.91 million**.

Solution:

i. Accounts Receivable:

We use the DSO formula to find accounts receivable.

$40.55 = \frac{\text{Accounts Receivable}}{1,000 / 365} \implies \text{Accounts Receivable} = 40.55 \times (2.7397) \approx \text{Tk. } 111.10 \text{ million}$

Accounts receivable is approximately **Tk. 111.10 million**.

ii. Current Liabilities:

First, we need to find the inventory. The difference between the Current Ratio and the Quick Ratio is inventory divided by current liabilities.

We know that Current Assets = Cash + A/R + Inventory. We can express this in a different way to solve the problem:

Current Ratio - Quick Ratio = $\frac{\text{Inventory}}{\text{Current Liabilities}}$

$3.0 - 2.0 = \frac{\text{Inventory}}{\text{Current Liabilities}} \implies \text{Inventory} = \text{Current Liabilities}$

Also, Quick Ratio = $\frac{\text{Cash} + \text{A/R}}{\text{Current Liabilities}}$.

$2.0 = \frac{100 + 111.10}{\text{Current Liabilities}} = \frac{211.10}{\text{Current Liabilities}}$

Current Liabilities = $\frac{211.10}{2.0} = \text{Tk. } 105.55 \text{ million}$

Current liabilities are **Tk. 105.55 million**.

iii. Current Assets:

Current Assets = Current Liabilities $\times$ Current Ratio

= $105.55 \times 3.0 = \text{Tk. } 316.65 \text{ million}$

Current assets are **Tk. 316.65 million**.

iv. Total Assets:

Total Assets = Current Assets + Fixed Assets

= $316.65 + 283.50 = \text{Tk. } 600.15 \text{ million}$

Total assets are **Tk. 600.15 million**.

v. ROA:

ROA = $\frac{50}{600.15} \approx 0.0833$ or $8.33\%$

ROA is approximately **8.33%**.

vi. Common Equity:

We use the ROE formula to find common equity.

$0.12 = \frac{50}{\text{Common Equity}} \implies \text{Common Equity} = \frac{50}{0.12} = \text{Tk. } 416.67 \text{ million}$

Common equity is **Tk. 416.67 million**.

Solution:

We need to evaluate the net present value (NPV) of each possible combination of projects and select the combination with the highest positive NPV. The NPV is calculated as the present value of future cash flows minus the investment required.

• **Project 1 Only:** $NPV_1 = 290,000 - 200,000 = \text{Tk. } 90,000$
• **Project 2 Only:** $NPV_2 = 185,000 - 115,000 = \text{Tk. } 70,000$
• **Project 3 Only:** $NPV_3 = 400,000 - 270,000 = \text{Tk. } 130,000$
• **Projects 1 & 2 Combined:**

  Investment = $200,000 + 115,000 = \text{Tk. } 315,000$

  PV of CF = $290,000 + 185,000 = \text{Tk. } 475,000$

  $NPV_{1+2} = 475,000 - 315,000 = \text{Tk. } 160,000$

• **Projects 1 & 3 Combined:**

  Investment = Tk. 440,000

  PV of CF = $290,000 + 400,000 = \text{Tk. } 690,000$

  $NPV_{1+3} = 690,000 - 440,000 = \text{Tk. } 250,000$

• **Projects 2 & 3 Combined:**

  Investment = $115,000 + 270,000 = \text{Tk. } 385,000$

  PV of CF = Tk. 620,000

  $NPV_{2+3} = 620,000 - 385,000 = \text{Tk. } 235,000$

• **Projects 1, 2, & 3 Combined:**

  Investment = (Investment of 1+2) + Investment of 3 - economies + plant extension

  = $315,000 + 270,000 + 125,000 - \text{economies}$

  Let's use the individual investments and economies to calculate total investment and PV of cash flows for all three.

  Investment = (Inv 1 + Inv 2 + Inv 3) - Inv savings from 1&3 + cost of plant extension

  = $(200,000+115,000+270,000) - ((200,000+270,000) - 440,000) + 125,000$

  = $585,000 - 30,000 + 125,000 = \text{Tk. } 680,000$

  PV of CF = (PV of 1+PV of 2+PV of 3) + PV gains from 2&3

  = $(290,000+185,000+400,000) + (620,000 - (185,000+400,000))$

  = $875,000 + 35,000 = \text{Tk. } 910,000$

  $NPV_{1+2+3} = 910,000 - 680,000 = \text{Tk. } 230,000$

Comparing the NPVs of all possible combinations, the highest is **Tk. 250,000** from undertaking **Projects 1 and 3**. Therefore, this is the optimal choice.

Solution:

We need to calculate a separate WACC for each division, using their respective betas to find the cost of equity. The cost of debt and preferred stock, as well as the capital structure weights, are the same for both divisions.

First, let's find the costs of each capital component:

• **Cost of Debt ($k_d$):** After-tax cost of debt = $15\% \times (1 - 0.40) = 9\%$
• **Cost of Preferred Stock ($k_p$):** Given as 13%.
• **Cost of Equity ($k_e$):** We use CAPM.

  Market Risk Premium ($R_M - R_f$) = $17\% - 12\% = 5\%$

Next, let's find the capital structure weights:

Weight of Debt ($W_d$) = 30% or 0.30

Weight of Preferred Stock ($W_p$) = 10% or 0.10

Weight of Equity ($W_e$) = $1 - 0.30 - 0.10 = 0.60$ or $60\%$

Finally, we calculate the divisional WACCs:

• **Health Foods Division ($beta = 0.90$):**

  Cost of Equity ($k_{e,HF}$) = $12\% + 0.90 \times (5\%) = 12\% + 4.5\% = 16.5\%$

  WACC = $(W_d \times k_d) + (W_p \times k_p) + (W_e \times k_{e,HF})$

  = $(0.30 \times 9\%) + (0.10 \times 13\%) + (0.60 \times 16.5\%)$

  = $2.7\% + 1.3\% + 9.9\% = 13.9\%$

• **Specialty Metals Division ($beta = 1.30$):**

  Cost of Equity ($k_{e,SM}$) = $12\% + 1.30 \times (5\%) = 12\% + 6.5\% = 18.5\%$

  WACC = $(W_d \times k_d) + (W_p \times k_p) + (W_e \times k_{e,SM})$

  = $(0.30 \times 9\%) + (0.10 \times 13\%) + (0.60 \times 18.5\%)$

  = $2.7\% + 1.3\% + 11.1\% = 15.1\%$

The weighted average required return for the Health Foods division is **13.9%**, and for the Specialty Metals division is **15.1%**.

Solution:

First, we need to calculate the dividends for the growth periods and the price at the end of the supernormal growth phase.

Given: $D_0 = 1.15$, $k_e = 12\%$, $g_1 = 15\%$, $g_2 = 13\%$, $g_c = 6\%$.

• $D_1 = D_0 \times (1+g_1) = 1.15 \times 1.15 = \text{Tk. } 1.3225$
• $D_2 = D_1 \times (1+g_1) = 1.3225 \times 1.15 = \text{Tk. } 1.5209$
• $D_3 = D_2 \times (1+g_2) = 1.5209 \times 1.13 = \text{Tk. } 1.7186$
• $D_4 = D_3 \times (1+g_c) = 1.7186 \times 1.06 = \text{Tk. } 1.8217$

i. Calculate the value of the stock today, one year from now and two years from now.

We start by finding the price at the end of year 3 using the constant growth model:

$P_3 = \frac{D_4}{k_e - g_c} = \frac{1.8217}{0.12 - 0.06} = \frac{1.8217}{0.06} = \text{Tk. } 30.36$

Now, we can find the stock prices at different points in time:

• **Value of the stock today ($P_0$):**

  $P_0 = \frac{D_1}{(1+k_e)^1} + \frac{D_2}{(1+k_e)^2} + \frac{D_3 + P_3}{(1+k_e)^3}$

  $P_0 = \frac{1.3225}{1.12} + \frac{1.5209}{1.12^2} + \frac{1.7186 + 30.36}{1.12^3}$

  $P_0 = 1.1808 + 1.2131 + \frac{32.0786}{1.4049} = 1.1808 + 1.2131 + 22.8336 = \text{Tk. } 25.2375$

• **Value of the stock at Year 1 ($P_1$):**

  $P_1 = \frac{D_2}{(1+k_e)^1} + \frac{D_3 + P_3}{(1+k_e)^2}$

  $P_1 = \frac{1.5209}{1.12} + \frac{1.7186 + 30.36}{1.12^2} = 1.3579 + \frac{32.0786}{1.2544} = 1.3579 + 25.5721 = \text{Tk. } 26.93$

• **Value of the stock at Year 2 ($P_2$):**

  $P_2 = \frac{D_3 + P_3}{(1+k_e)^1}$

  $P_2 = \frac{1.7186 + 30.36}{1.12} = \frac{32.0786}{1.12} = \text{Tk. } 28.64$

The value of the stock today is **Tk. 25.24**, one year from now is **Tk. 26.93**, and two years from now is **Tk. 28.64**.

ii. Calculate the dividend yield and capital gains yield for Years 1, 2, and 3.

Dividend Yield = $\frac{D_t}{P_{t-1}}$

Capital Gains Yield = $\frac{P_t - P_{t-1}}{P_{t-1}}$

Total Return ($k_e$) = Dividend Yield + Capital Gains Yield = 12%

• **Year 1:**

  Dividend Yield = $\frac{D_1}{P_0} = \frac{1.3225}{25.2375} \approx 0.0524$ or $5.24\%$

  Capital Gains Yield = $12\% - 5.24\% = 6.76\%$

• **Year 2:**

  Dividend Yield = $\frac{D_2}{P_1} = \frac{1.5209}{26.93} \approx 0.0565$ or $5.65\%$

  Capital Gains Yield = $12\% - 5.65\% = 6.35\%$

• **Year 3:**

  Dividend Yield = $\frac{D_3}{P_2} = \frac{1.7186}{28.64} \approx 0.06$ or $6.00\%$

  Capital Gains Yield = $12\% - 6.00\% = 6.00\%$ (This makes sense, as year 3 is the start of the constant growth phase where capital gains yield equals the growth rate).

Solution:

Trade-off Theory:

The trade-off theory proposes that a firm's optimal capital structure involves a balance between the benefits of debt (the interest tax shield) and the costs of debt (financial distress costs). The firm's leverage ratio is determined by finding the point where the marginal benefit of adding another dollar of debt is exactly equal to the marginal cost of the associated financial distress. This theory **does imply a target leverage ratio** for firms.

Pecking Order Theory:

The pecking order theory, in contrast, argues that there is no optimal capital structure. Instead, managers follow a hierarchy of financing preferences based on asymmetric information. They prefer internal financing (retained earnings) first, then debt, and finally new equity as a last resort. The leverage ratio is determined by the firm's need for external financing and the availability of retained earnings. This theory **does not imply a target leverage ratio**; instead, it suggests that a firm's debt-to-equity ratio is a result of its accumulated past financing decisions.

Solution:

The agency conflict between shareholders and bondholders arises from their differing objectives. Shareholders have a claim on the firm's residual cash flows and are interested in maximizing the value of their equity, often by taking on risky projects that could yield high returns. Bondholders, on the other hand, hold a fixed claim on the firm's assets and cash flows and are primarily concerned with the firm's ability to pay its debt obligations. They prefer less risky projects to ensure the safety of their investment.

Dividends play a central role in this conflict. When a firm pays a dividend, it distributes cash to shareholders. Bondholders view this as a reduction in the firm's asset base, which serves as their collateral. If a company pays out large dividends, it may leave fewer assets within the firm to cover its debt obligations, thereby increasing the risk for bondholders. For this reason, bondholders often include restrictive covenants in the bond indenture that limit the firm's ability to pay dividends, thereby protecting their investment from being eroded by cash distributions to shareholders.

Solution:

Initial state:

Number of shares outstanding = $\frac{\text{Common Stock}}{\text{Par Value}} = \frac{2,000,000}{8} = 250,000 \text{ shares}$

i. Effect on accounts and shares outstanding:

• **1. 10 percent stock dividend:**

  New shares = $250,000 \times 0.10 = 25,000$ shares

  Total shares = $250,000 + 25,000 = 275,000$ shares

  Value of new shares (from retained earnings) = $25,000 \times \text{Market Price} = 25,000 \times 60 = \text{Tk. } 1,500,000$

  The par value portion is $25,000 \times 8 = \text{Tk. } 200,000$, and the rest is added to additional paid-in capital.

  **New Account Balances:**

  • Common Stock: $2,000,000 + 200,000 = \text{Tk. } 2,200,000$
  • Additional Paid-in Capital: $1,600,000 + (1,500,000 - 200,000) = \text{Tk. } 2,900,000$
  • Retained Earnings: $8,400,000 - 1,500,000 = \text{Tk. } 6,900,000$
  • Total Equity: Tk. 12,000,000 (unchanged)
• **2. 2-for-1 stock split:**

  Total shares = $250,000 \times 2 = 500,000$ shares

  Par value per share = $\frac{8}{2} = \text{Tk. } 4$

  No changes to the account balances, only the number of shares and par value are adjusted.

• **3. 1-for-2 reverse stock split:**

  Total shares = $250,000 \times \frac{1}{2} = 125,000$ shares

  Par value per share = $8 \times 2 = \text{Tk. } 16$

  No changes to the account balances, only the number of shares and par value are adjusted.

ii. Stock price after stock dividend and signaling effect:

In the absence of an informational or signaling effect, the total value of the firm's equity remains the same. The share price would adjust downward proportionally to the increase in the number of shares.

New shares = $250,000 \times 1.10 = 275,000$

New Share Price = $\frac{\text{Old Share Price}}{\text{New Shares}} = \frac{60}{1.10} \approx \text{Tk. } 54.55$

The new share price should be approximately **Tk. 54.55**.

However, if there were a signaling effect, the stock price might not fall proportionally. A stock dividend can be interpreted by the market as a positive signal that management is confident about the firm's future earnings and is expecting a higher dividend stream in the future. As a result, the new share price might fall by a smaller amount than the proportional adjustment, or even rise, reflecting the market's positive reevaluation of the firm's prospects.

Solution:

The **cash conversion cycle (CCC)** represents the amount of time, in days, that a firm's cash is tied up in its operating activities. It measures the time between paying for inventory and receiving cash from the sale of that inventory. A shorter CCC is generally better, as it indicates a more efficient working capital management.

Impact of minimizing the CCC on financial ratios:

• **Inventory turnover:** Minimizing the CCC requires reducing the time inventory is held, which would lead to a **higher inventory turnover** ratio.
• **Average collection period:** A shorter CCC is achieved by collecting receivables faster, which would result in a **lower average collection period** (DSO).
• **Average payment period:** Minimizing the CCC involves stretching out the payment of payables, which would lead to a **higher average payment period**.

Constraints on aggressive strategies:

• **Inventory:** Aggressively minimizing inventory can lead to stock-outs, which can result in lost sales and customer dissatisfaction.
• **Accounts Receivable:** Aggressively collecting receivables (shortening the collection period) may alienate customers and lead to a decline in sales.
• **Accounts Payable:** Aggressively delaying payments to suppliers can damage a firm's credit reputation, potentially leading to a loss of key suppliers, less favorable credit terms, or even a complete cessation of credit.

Solution:

Covered interest arbitrage is a risk-free investment strategy that involves using forward contracts to "cover" the foreign exchange risk. An arbitrageur takes advantage of the discrepancy between the interest rate differential of two countries and the forward premium or discount on their currencies. This is possible when the interest rate parity theorem does not hold.

Strategy for a U.S. trader:

The interest rate in Canada (12%) is higher than in the U.S. (8%). This would normally make borrowing in the U.S. and lending in Canada profitable. However, the Canadian dollar is selling at a 3% forward discount, meaning its value is expected to fall. We must compare the interest rate differential to the forward premium/discount to see if an arbitrage opportunity exists.

• Interest Rate Differential = $i_{Canada} - i_{US} = 12\% - 8\% = 4\%$
• Forward Discount on CAD = 3%

Since the interest rate differential (4%) is greater than the forward discount (3%), an arbitrage opportunity exists. The U.S. trader should perform the following steps:

• 1. **Borrow in the U.S.:** Borrow a certain amount of U.S. dollars at 8%.
• 2. **Convert to CAD:** Convert the borrowed U.S. dollars to Canadian dollars at the current spot rate.
• 3. **Invest in Canada:** Invest the Canadian dollars at the Canadian interest rate of 12%.
• 4. **Cover the Exchange Risk:** Simultaneously enter into a forward contract to sell the Canadian dollars (principal plus interest) back to U.S. dollars at the forward rate, which is at a 3% discount.

By locking in the exchange rate, the trader ensures that the gain from the higher Canadian interest rate (12%) exceeds the cost of borrowing in the U.S. (8%) even after factoring in the 3% loss from the forward exchange rate. The net profit would be the difference between the interest rate differential and the forward discount ($4\% - 3\% = 1\%$).

Solution:

i. Marginal profitability of additional sales:

Marginal Profitability = Additional Sales $\times$ (1 - Variable Cost Ratio)

$= 5,475,000 \times (1 - 0.75) = 5,475,000 \times 0.25 = \text{Tk. } 1,368,750$

Marginal profitability is **Tk. 1,368,750**.

ii. Cost of additional investment in receivables:

Additional Investment in Receivables = (Additional Sales $\times$ Variable Cost Ratio) $\times$ $\frac{\text{Average Collection Period}}{365}$

We need to use the variable cost to determine the investment in receivables. The average collection period is 75 days.

$= (5,475,000 \times 0.75) \times \frac{75}{365} = 4,106,250 \times 0.2055 \approx \text{Tk. } 844,792$

Cost of Investment = Investment in Receivables $\times$ Required Pretax Return

$= 844,792 \times 0.18 = \text{Tk. } 152,063$

The cost of additional investment in receivables is approximately **Tk. 152,063**.

iii. Additional bad-debt loss:

Additional Bad-Debt Loss = Additional Sales $\times$ Bad-Debt Loss Ratio

$= 5,475,000 \times 0.05 = \text{Tk. } 273,750$

Additional bad-debt loss is **Tk. 273,750**.

iv. Cost of additional investment in inventory:

Cost of Investment in Inventory = Additional Inventory Investment $\times$ Required Pretax Return

$= 800,000 \times 0.18 = \text{Tk. } 144,000$

The cost of additional investment in inventory is **Tk. 144,000**.

v. Additional cash discounts:

Additional Cash Discounts = Additional Sales $\times$ Percentage of Customers Taking Discount $\times$ Discount Rate

$= 5,475,000 \times 0.10 \times 0.02 = \text{Tk. } 10,950$

Additional cash discounts are **Tk. 10,950**.

vi. Net change in pretax profits:

Net Change = Marginal Profitability - Cost of Investment in Receivables - Bad-Debt Loss - Cost of Investment in Inventory - Cash Discounts

= $1,368,750 - 152,063 - 273,750 - 144,000 - 10,950 = \text{Tk. } 787,987$

The net change in pretax profits is approximately **Tk. 787,987**.