CMA May 2023 Examination Solutions

Solution:

The correct answer is **(b) inventory is declining**. The current ratio includes inventory, while the quick ratio does not. If the current ratio declines and the quick ratio improves, it means that current assets (excluding inventory) have increased relative to current liabilities, but total current assets have decreased relative to current liabilities. This can be explained if inventory, which is a component of current assets, has decreased significantly. For example, if a firm sells off old, slow-moving inventory at a loss or at a price that generates cash which improves its cash balance, this can boost the quick ratio while the overall current ratio drops due to the loss of a large asset item. It's a nuanced scenario where the decline of one part of current assets (inventory) outweighs the increase in other parts (like cash).

Solution:

The intrinsic value of a perpetual bond (or consol) is calculated by dividing the annual coupon payment by the investor's required rate of return. The face value is only used to calculate the coupon payment.

Annual Coupon Payment = Face Value $\times$ Coupon Rate

= Tk. $1,000 \times 8\% = \text{Tk. } 80$

Intrinsic Value = $\frac{\text{Annual Coupon Payment}}{\text{Required Rate of Return}} = \frac{80}{0.06} = \text{Tk. } 1,333.33$

The correct answer is **(a) Tk. 1,333.33**.

Solution:

The correct answer is **(b) method of project financing used**. The method of project financing (e.g., debt vs. equity) is a cost of capital consideration, not a cash flow for the project itself. Capital budgeting is concerned with the cash flows generated by the project, independent of how the project is financed. The other options directly affect a project's cash flows: depreciation and tax rates affect the tax shield, salvage value is a cash flow at the end of the project, and opportunity cost is a relevant cash outflow.

Solution:

The correct answer is **(b) Sales and EPS**. Combined leverage (also known as total leverage) is the product of operating leverage (Sales and EBIT) and financial leverage (EBIT and EPS). Therefore, it measures the overall impact of a change in sales on a firm's earnings per share (EPS).

Solution:

The book value of common equity is the sum of the common stock at par value, additional paid-in capital, and retained earnings. The book value per share is this total divided by the number of shares outstanding.

Common Stock = 15,000 shares $\times$ Tk. 1 = Tk. 15,000

Total Common Equity = Common Stock + Additional Paid-in Capital + Retained Earnings

= $15,000 + 300,000 + 300,000 = \text{Tk. } 615,000$

Book Value per Share = $\frac{\text{Total Common Equity}}{\text{Shares Outstanding}} = \frac{615,000}{15,000} = \text{Tk. } 41$

The correct answer is **(d) 41**.

Solution:

The formula for future value with continuous compounding is:

Given: PV = Tk. 20,000, r = 8% = 0.08, t = 20 years.

$FV = 20,000 \times e^{0.08 \times 20} = 20,000 \times e^{1.6}$

Using a calculator, $e^{1.6} \approx 4.953032$.

$FV = 20,000 \times 4.953032 \approx \text{Tk. } 99,060.64$

The closest answer is **(d) Tk. 99,061**.

Solution:

The correct answer is **(e) Amount of fixed cost**. Operating leverage is a measure of the sensitivity of operating income to a change in sales. A firm with a higher proportion of fixed costs to variable costs has a higher degree of operating leverage. This means a small change in sales volume can lead to a large change in operating income.

Solution:

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

Given: Discount = 1% = 0.01, Discount Period = 10 days, Credit Period = 35 days.

Approximate Cost = $\frac{1}{100-1} \times \frac{365}{35-10} = \frac{1}{99} \times \frac{365}{25}$

$= 0.010101 \times 14.6 \approx 0.14747$ or $14.75\%$

The closest answer is **(c) 14.7%**.

Solution:

The correct answer is **(a) All sources of finance**. The firm's cost of capital, also known as the Weighted Average Cost of Capital (WACC), is the weighted average of the costs of all the capital components, including debt, equity, and preferred stock. It represents the minimum return a company must earn on its existing asset base to satisfy its creditors, owners, and other providers of capital.

Solution:

The correct answer is **(e) Net working capital**. While net working capital is an amount and not a ratio, it is the only option in the list that is directly related to a firm's liquidity. Liquidity ratios measure a firm's ability to meet its short-term obligations. Equity ratio, proprietary ratio, and debt to equity ratio are all solvency/leverage ratios. Capital gearing ratio is also a form of a leverage ratio.

Solution:

False. The **equity beta** is directly influenced by financial leverage. The **asset beta** is a measure of the firm's business risk and is independent of its financial leverage.

Solution:

False. The receivable-turnover ratio measures how efficiently a firm is collecting its credit sales. This ratio helps in managing **accounts receivable**, not inventory. The inventory-turnover ratio helps in managing inventory.

Solution:

False. The financial structure refers to the mix of both **long-term and short-term funds** used to finance a firm's assets. Capital structure, by contrast, refers only to the mix of long-term funds (debt and equity).

Solution:

False. A firm with high operating leverage will have **higher business risk**. Operating leverage is a function of fixed costs. A high proportion of fixed costs to total costs means that a given change in sales will have a magnified effect on operating profit, thus increasing the firm's business risk.

Solution:

True. According to the Modigliani and Miller (M&M) dividend irrelevance theory, in a perfect capital market, an investor's total return from a stock is not affected by how the firm's earnings are split between dividends and retained earnings. The investor can create "homemade" dividends by selling a portion of their stock, making them indifferent to the firm's dividend policy.

Solution:

The correct matches are as follows:

• **(1) Shareholder wealth** matches with **(a) Market price per share**. The primary goal of financial management is to maximize shareholder wealth, which is directly measured by the market price of the company's stock.
• **(2) Profitability ratio** matches with **(d) Profit margin**. The profit margin ratio measures a firm's profitability by showing what percentage of sales has turned into profits.
• **(3) Capital structure** matches with **(f) Debt and equity**. A firm's capital structure is the specific mix of long-term debt and equity it uses to finance its assets.
• **(4) Money market** matches with **(g) Commercial paper**. The money market is a market for short-term debt instruments. Commercial paper is a type of unsecured short-term debt issued by corporations.
• **(5) Risk-free rate** matches with **(i) Treasury bill**. The risk-free rate is the theoretical rate of return of an investment with zero risk. In practice, the return on a short-term government security like a Treasury bill is used as a proxy for the risk-free rate.

Solution:

The distinction between money markets and capital markets is based on the maturity of the financial instruments traded in them.

• **Money Markets:** These markets are for short-term debt instruments with maturities of one year or less. They are a source of short-term financing for governments, banks, and corporations. The transactions are typically large and involve highly liquid, low-risk securities.

  **Example:** A **Treasury bill** is a short-term debt obligation issued by a government with a maturity of less than one year.

• **Capital Markets:** These markets are for long-term debt and equity-backed securities. They are a source of long-term financing for companies and governments. Securities traded in the capital market, such as stocks and bonds, have a maturity of more than one year.

  **Example:** A **stock exchange**, where company stocks are bought and sold, is a primary component of the capital market.

Solution:

i. Quarterly Installment Calculation:

First, we need to find the quarterly interest rate and the number of periods.

Quarterly Interest Rate ($i$) = $\frac{22\%}{4} = 5.5\%$

Number of Periods ($n$) = $2 \text{ years} \times 4 \text{ quarters/year} = 8 \text{ quarters}$

The loan amount is Tk. 500,000. We can use the present value of an ordinary annuity formula to find the installment amount (PMT).

We rearrange the formula to solve for PMT:

$PMT = PV \times \frac{i}{1 - (1+i)^{-n}} = 500,000 \times \frac{0.055}{1 - (1.055)^{-8}}$

$= 500,000 \times \frac{0.055}{1 - 0.6516} = 500,000 \times \frac{0.055}{0.3484} \approx \text{Tk. } 78,924.97$

The quarterly installment payment is approximately **Tk. 78,925**.

ii. Loan Amortization Schedule:

Quarter	Beginning Balance	Installment	Interest (5.5%)	Principal Repayment	Ending Balance
1	500,000.00	78,924.97	27,500.00	51,424.97	448,575.03
2	448,575.03	78,924.97	24,671.63	54,253.34	394,321.69
3	394,321.69	78,924.97	21,687.69	57,237.28	337,084.41
4	337,084.41	78,924.97	18,539.64	60,385.33	276,699.08
5	276,699.08	78,924.97	15,218.45	63,706.52	212,992.56
6	212,992.56	78,924.97	11,714.60	67,210.37	145,782.19
7	145,782.19	78,924.97	8,017.98	70,906.99	74,875.20
8	74,875.20	78,924.97	4,118.14	74,806.83	68.37

The final balance of Tk. 68.37 is due to rounding in the calculations and is considered paid off.

Solution:

To find the market value of the bonds, we need to find the present value of all future cash flows, discounted at the cost of debt (the market's required rate of return). The cash flows consist of the quarterly interest payments and the final redemption payment.

• Par Value = Tk. 150,000
• Redemption Value (FV) = Tk. 165,000
• Annual Coupon Rate = 12%
• Quarterly Coupon Payment = $150,000 \times \frac{0.12}{4} = \text{Tk. } 4,500$
• Quarterly Cost of Debt ($i$) = 2% = 0.02
• Time to Maturity: From 31 December 2019 to 30 June 2023 is 3 years and 6 months.

  Number of quarters ($n$) = $3 \times 4 + 2 = 14$ quarters

The market value is the present value of the coupon annuity plus the present value of the final redemption payment.

$PV_{bond} = 4,500 \times \left[ \frac{1 - (1.02)^{-14}}{0.02} \right] + \frac{165,000}{(1.02)^{14}}$

$= 4,500 \times [12.288] + \frac{165,000}{1.3195}$

$= 55,296 + 125,047.36 \approx \text{Tk. } 180,343.36$

The market value of the bonds is approximately **Tk. 180,343**.

Solution:

Enamul's Savings Plan:

Enamul makes 10 payments of Tk. 2,000. First, we find the future value of his annuity at the end of his 10th payment (age 30).

$FV_{30} = 2,000 \times \left[ \frac{(1.07)^{10} - 1}{0.07} \right] = 2,000 \times \left[ \frac{1.96715 - 1}{0.07} \right] = 2,000 \times 13.8164 \approx \text{Tk. } 27,632.8$

This amount then compounds for another 35 years (from age 30 to 65).

$FV_{65} = FV_{30} \times (1.07)^{35} = 27,632.8 \times 10.6766 \approx \text{Tk. } 295,081.7$

Enamul's savings will be worth approximately **Tk. 295,082** at retirement.

Rafeed's Savings Plan:

Rafeed makes 35 payments of Tk. 2,000 starting at age 31. This is a 35-year annuity. We find the future value of this annuity at the end of his 35th payment (age 65).

$FV_{65} = 2,000 \times \left[ \frac{(1.07)^{35} - 1}{0.07} \right] = 2,000 \times \left[ \frac{10.6766 - 1}{0.07} \right] = 2,000 \times 138.237 \approx \text{Tk. } 276,474$

Rafeed's savings will be worth approximately **Tk. 276,474** at retirement.

Conclusion:

At retirement, **Mr. Enamul** is better off financially. This highlights the power of early investment and compounding interest.

The difference is: $295,082 - 276,474 = \text{Tk. } 18,608$.

Solution:

No, a company's expected return would **not** double if its beta were to double. The relationship between beta and expected return is linear, but it is not a direct proportionality. The relationship is defined by the Capital Asset Pricing Model (CAPM):

Here, the expected return ($R_i$) is the sum of the risk-free rate ($R_f$) and the market risk premium multiplied by beta. If beta doubles, the risk premium component doubles, but the risk-free rate remains the same. Since the risk-free rate is typically a positive value, the overall expected return will be less than double. For the expected return to double, the risk-free rate would have to be zero, which is not a common scenario.

Solution:

Net Present Value (NPV) Calculation:

First, we calculate the initial investment and the change in working capital.

Initial Outlay (Year 0): Tk. (400,000)

Change in Working Capital (Year 1): Tk. (30,000 + 40,000 - 20,000) = Tk. (50,000)

Depreciation (Straight-line) = $\frac{\text{Cost} - \text{Salvage Value}}{\text{Life}} = \frac{400,000 - 20,000}{5} = \text{Tk. } 76,000$ per year.

Annual Cash Flows (Years 1-5):

Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
Sales Revenue	3,000,000	3,000,000	3,000,000	3,000,000	3,000,000
Direct Cost	(2,000,000)	(2,000,000)	(2,000,000)	(2,000,000)	(2,000,000)
Fixed Cost (excl. dep)	(84,000)	(84,000)	(84,000)	(84,000)	(84,000)
Marketing Cost	(20,000)	(32,000)	0	0	0
Depreciation	(76,000)	(76,000)	(76,000)	(76,000)	(76,000)
**EBIT**	820,000	808,000	840,000	840,000	840,000
Tax (25%)	(205,000)	(202,000)	(210,000)	(210,000)	(210,000)
EBIT(1-T)	615,000	606,000	630,000	630,000	630,000
Add back Depreciation	76,000	76,000	76,000	76,000	76,000
Working Capital Recovery					50,000
Salvage Value					20,000
Tax on Salvage (assuming no gain/loss)					(0)
**Total Cash Flow**	691,000	682,000	706,000	706,000	776,000

Note: Fixed cost without depreciation is $160,000 - 76,000 = \text{Tk. } 84,000$.

Now, we calculate the NPV by discounting all cash flows at 18%.

$NPV = -400,000 + \frac{691,000}{1.18^1} + \frac{682,000}{1.18^2} + \frac{706,000}{1.18^3} + \frac{706,000}{1.18^4} + \frac{776,000}{1.18^5} - 50,000$

We adjust for the initial working capital investment in year 0. So, initial investment is Tk. (450,000). The recovery is at year 5.

$NPV = -450,000 + 585,593 + 489,510 + 430,978 + 364,547 + 338,367 = \text{Tk. } 1,358,995$

The NPV of the project is approximately **Tk. 1,358,995**. Since the NPV is positive, Metro Limited should **acquire** the plant.

Solution:

Assumptions:

For both models, we assume that the given ratios and growth rates are stable and will continue indefinitely. We also assume that the cost of capital is constant and that the market is in equilibrium. The debt is assumed to be risk-free and the firm's beta (systematic risk) is constant.

i. WACC using the Dividend Valuation Model (DVM):

First, we find the cost of equity ($k_e$) using the DVM. We need the dividend yield and the expected growth rate of dividends. The notes provide: Dividend Yield = 7%, Dividend Growth Rate = 11%.

Next, we need the market values and costs of debt and equity.

Market Value of Equity (E) = 1 million shares $\times$ Tk. 3.21 = Tk. 3,210,000

Debt-to-Equity Ratio ($\frac{D}{E}$) = 1:2. So, Market Value of Debt (D) = $0.5 \times E = 0.5 \times 3,210,000 = \text{Tk. } 1,605,000$

Total Firm Value (V) = $E+D = 3,210,000 + 1,605,000 = \text{Tk. } 4,815,000$

Cost of Debt ($k_d$) = Treasury Bill Yield = 12%. After-tax cost of debt = $12\% \times (1-0.30) = 8.4\%$

WACC = $\left( \frac{E}{V} \right) k_e + \left( \frac{D}{V} \right) k_d (1-T)$

$= \left( \frac{3,210,000}{4,815,000} \right) \times 18\% + \left( \frac{1,605,000}{4,815,000} \right) \times 8.4\%$

$= (0.6667 \times 18\%) + (0.3333 \times 8.4\%) = 12\% + 2.8\% = 14.8\%$

WACC using DVM is **14.8%**.

ii. WACC using the Capital Asset Pricing Model (CAPM):

First, we find the cost of equity ($k_e$) using the CAPM.

$R_f = \text{Treasury bill yield} = 12\%$

$R_M = \text{Stock market total return on equity} = 16\%$

Beta ($\beta$) = 14%? This seems to be a typo. Beta is a factor, not a percentage. Let's assume the beta is 1.40 since the value is 14% for systematic risk.

$k_e = R_f + \beta \times (R_M - R_f) = 12\% + 1.40 \times (16\% - 12\%)$

$= 12\% + 1.40 \times 4\% = 12\% + 5.6\% = 17.6\%$

Now, we use the same market values and cost of debt from the DVM calculation.

WACC = $(0.6667 \times 17.6\%) + (0.3333 \times 8.4\%)$

$= 11.73\% + 2.8\% = 14.53\%$

WACC using CAPM is **14.53%**.

Circumstances for similar values:

The two models would produce similar values for the WACC if the assumptions of both models hold true. Specifically, the DVM assumes a constant growth rate, and the CAPM assumes an efficient market where risk is the only factor determining returns. The key link is that the expected return from the DVM model ($k_e = \frac{D_1}{P_0} + g$) should be equal to the required return from the CAPM ($k_e = R_f + \beta \times (R_M - R_f)$). This is a hallmark of a market in equilibrium. If the inputs for both models are accurate and consistent with each other, their resulting WACC values should be very close.

Solution:

The **static trade-off theory** of capital structure suggests that a firm chooses its optimal capital structure by balancing the benefits of debt with the costs of financial distress. The primary trade-off is between the **interest tax shield** from using debt and the **costs of financial distress** that come with higher leverage.

Under this theory's assumptions, a firm's optimal capital structure is determined at the point where the marginal benefit of adding more debt (the tax shield) is exactly equal to the marginal cost of the associated financial distress (e.g., bankruptcy costs, agency costs). This specific debt-to-equity ratio minimizes the firm's weighted average cost of capital (WACC) and, therefore, maximizes its value.

However, it is **not possible** to determine the optimal capital structure in precise terms in the real world. This is because the costs of financial distress and the benefits of the tax shield are difficult to quantify with certainty. These costs are often subjective and depend on a variety of firm-specific and macroeconomic factors that are not easily measurable. As a result, firms in the real world typically refer to a target capital structure, which is a range or a benchmark that they aim for, rather than a single precise optimal point.

Solution:

i. Accounting lease liability immediately after the first payment:

The initial value of the lease liability is the present value of all future lease payments, discounted at the company's incremental borrowing rate (11%) or the lessor's implicit rate (12%), whichever is lower. The problem states the amortization for the first year, which is the principal repayment portion of the lease payment.

The first lease payment is made in advance. So, the lease liability is reduced by the payment amount immediately.

Initial Lease Liability (PV of all payments) = The problem gives us the amortization of the first year (principal repayment), which is the difference between the total payment and the interest portion. This implies we need to find the implicit interest rate. The problem is flawed in that it gives two different interest rates and doesn't clearly state which one to use. Let's use the amortization given to find the initial liability.

Amortization = Payment - Interest

$16,332 = 30,000 - \text{Interest}$

Interest in Year 1 = $30,000 - 16,332 = \text{Tk. } 13,668$

The interest rate that would result in this interest payment is $i = \frac{13,668}{\text{Initial Liability}}$. This doesn't seem to lead to a solution from the information given.

Let's use the standard method. The present value of the lease liability is the present value of the annuity payments. Since payments are in advance (annuity due), the formula is:

Let's use the company's incremental borrowing rate of 11% for the calculation. $n = 6$.

$PV = 30,000 + 30,000 \times \left[ \frac{1 - (1.11)^{-5}}{0.11} \right] = 30,000 + 30,000 \times 3.6959 = 30,000 + 110,877 = \text{Tk. } 140,877$

Initial lease liability = Tk. 140,877. The first payment is made immediately, so the liability is reduced by this amount.

Lease liability after first payment = $140,877 - 30,000 = \text{Tk. } 110,877$

The accounting lease liability immediately after the first payment is **Tk. 110,877**.

ii. Annual lease expense in the first year:

The annual lease expense on the income statement is the sum of the amortization (principal repayment) and the interest expense for that year.

Amortization in first year = Tk. 16,332 (given)

Interest expense in first year = Initial Liability $\times$ Interest Rate. The problem is flawed as it provides a pre-amortization interest amount and a post-amortization interest value. Let's assume the given amortization value is correct and work backwards.

Interest expense is based on the lease liability for the year.

Interest = (Initial Liability - First Payment) $\times$ Interest Rate = $110,877 \times 0.11 = \text{Tk. } 12,196.47$

Lease expense = Amortization + Interest = $16,332 + 12,196.47 = \text{Tk. } 28,528.47$

The annual lease expense in the first year is approximately **Tk. 28,528**.

Solution:

First, we need to find the current market price per share using the dividend growth model. We are given the dividend payout ratio, EPS, growth rate, and cost of equity.

Current Dividend ($D_0$) = EPS $\times$ Payout Ratio = $1.6 \times 0.50 = \text{Tk. } 0.80$

Next year's dividend ($D_1$) = $D_0 \times (1+g) = 0.80 \times (1.05) = \text{Tk. } 0.84$

i. The market price per share:

Using the dividend growth model: $P_0 = \frac{D_1}{k_e - g}$

$P_0 = \frac{0.84}{0.15 - 0.05} = \frac{0.84}{0.10} = \text{Tk. } 8.40$

The market price per share is **Tk. 8.40**.

ii. The capitalization of CBL:

Market Capitalization = Number of shares outstanding $\times$ Market price per share

= $6,000,000 \times 8.40 = \text{Tk. } 50,400,000$

The capitalization of CBL is **Tk. 50,400,000**.

iii. The rights issue price:

The issue price is a 10% discount to the existing market price.

Issue Price = Market Price $\times$ (1 - Discount Rate) = $8.40 \times (1 - 0.10) = 8.40 \times 0.90 = \text{Tk. } 7.56$

The rights issue price is **Tk. 7.56**.

iv. The theoretical ex-right price:

TERP = $\frac{(\text{Number of old shares} \times \text{Old price}) + (\text{Number of new shares} \times \text{Issue price})}{\text{Total number of shares}}$

Rights issue is 1 for 3, so Number of old shares = 3, Number of new shares = 1.

TERP = $\frac{(3 \times 8.40) + (1 \times 7.56)}{3 + 1} = \frac{25.20 + 7.56}{4} = \frac{32.76}{4} = \text{Tk. } 8.19$

The theoretical ex-right price is **Tk. 8.19**.

v. The market capitalization after the rights issue:

Total number of shares after issue = $6,000,000 + (6,000,000 \times \frac{1}{3}) = 6,000,000 + 2,000,000 = 8,000,000$ shares

New Market Capitalization = Total number of shares $\times$ Theoretical ex-right price

= $8,000,000 \times 8.19 = \text{Tk. } 65,520,000$

The market capitalization after the rights issue is **Tk. 65,520,000**.

Solution:

In an environment of high market volatility, financial derivatives like swaps are powerful tools for managing risk.

• **Interest Rate Swap:** This is a contractual agreement between two parties to exchange future interest payments. A company with variable-rate debt can use an interest rate swap to exchange its variable payments for fixed-rate payments from a counterparty. This locks in a predictable cost of debt, protecting the company from the risk of rising interest rates. Conversely, a company with fixed-rate debt that expects rates to fall can swap to receive variable-rate payments.
• **Currency Swap:** A currency swap involves two parties agreeing to exchange principal and interest payments on a loan in one currency for equivalent payments in another currency. This is useful for companies that operate internationally and want to hedge against currency fluctuations. A company with debt in a foreign currency can swap its payments to a counterparty in that currency, while receiving payments in its home currency. This effectively mitigates the risk of an adverse movement in exchange rates.

Solution:

We need to find the expected return on equity (ROE) for each of the three current asset policies. The ROE is calculated as: $ROE = \frac{\text{Net Income}}{\text{Equity}}$.

First, let's find the common financial figures that apply to all three policies.

Sales = Tk. 3,000,000

EBIT = $15\% \times \text{Sales} = 0.15 \times 3,000,000 = \text{Tk. } 450,000$

Fixed Assets = Tk. 600,000

Debt-to-Assets Ratio = 50%. This means Debt = 50% of Total Assets and Equity = 50% of Total Assets.

Policy 1: Current Assets = 40% of Sales

Current Assets = $0.40 \times 3,000,000 = \text{Tk. } 1,200,000$

Total Assets = Fixed Assets + Current Assets = $600,000 + 1,200,000 = \text{Tk. } 1,800,000$

Total Debt = $0.50 \times 1,800,000 = \text{Tk. } 900,000$

Interest Expense = $10\% \times \text{Debt} = 0.10 \times 900,000 = \text{Tk. } 90,000$

Net Income = $(EBIT - \text{Interest}) \times (1-T) = (450,000 - 90,000) \times (1-0.40) = 360,000 \times 0.60 = \text{Tk. } 216,000$

Equity = $0.50 \times 1,800,000 = \text{Tk. } 900,000$

$ROE_1 = \frac{216,000}{900,000} = 0.24$ or $24\%$

Policy 2: Current Assets = 50% of Sales

Current Assets = $0.50 \times 3,000,000 = \text{Tk. } 1,500,000$

Total Assets = $600,000 + 1,500,000 = \text{Tk. } 2,100,000$

Total Debt = $0.50 \times 2,100,000 = \text{Tk. } 1,050,000$

Interest Expense = $0.10 \times 1,050,000 = \text{Tk. } 105,000$

Net Income = $(450,000 - 105,000) \times 0.60 = 345,000 \times 0.60 = \text{Tk. } 207,000$

Equity = $0.50 \times 2,100,000 = \text{Tk. } 1,050,000$

$ROE_2 = \frac{207,000}{1,050,000} \approx 0.1971$ or $19.71\%$

Policy 3: Current Assets = 60% of Sales

Current Assets = $0.60 \times 3,000,000 = \text{Tk. } 1,800,000$

Total Assets = $600,000 + 1,800,000 = \text{Tk. } 2,400,000$

Total Debt = $0.50 \times 2,400,000 = \text{Tk. } 1,200,000$

Interest Expense = $0.10 \times 1,200,000 = \text{Tk. } 120,000$

Net Income = $(450,000 - 120,000) \times 0.60 = 330,000 \times 0.60 = \text{Tk. } 198,000$

Equity = $0.50 \times 2,400,000 = \text{Tk. } 1,200,000$

$ROE_3 = \frac{198,000}{1,200,000} = 0.165$ or $16.5\%$

The expected return on equity for the three policies is **24%**, **19.71%**, and **16.5%**, respectively.

Solution:

We need to calculate the incremental profit from the proposed change and compare it to the additional cost. Since we are working with before-tax figures, taxes are not a factor in this calculation. We will assume 12 months in a year.

Original Policy:

Average Collection Period = 2.5 months

Bad-debt losses = $0.04 \times 12,000,000 = \text{Tk. } 480,000$

Proposed Policy:

Average Collection Period = 2 months

Bad-debt losses = $0.03 \times 12,000,000 = \text{Tk. } 360,000$

The incremental cash flow from the change is the savings from bad-debt losses and the interest savings from reducing the average collection period.

Savings from Bad-Debt Losses:

Original losses - New losses = $480,000 - 360,000 = \text{Tk. } 120,000$

Savings from Reduced Receivables Investment:

Reduction in receivables = (Original ACP - New ACP) $\times$ Sales per day

Sales per day = $\frac{12,000,000}{360} = \text{Tk. } 33,333.33$

Reduction = $(2.5 - 2) \text{ months} \times \frac{12,000,000}{12} = 0.5 \times 1,000,000 = \text{Tk. } 500,000$

The problem is ambiguous about whether to use 360 or 365 days. Let's use months as it seems more consistent with the input data. We will also assume the cash flows are calculated based on the sales amount rather than the variable cost.

Reduction in receivables = $(2.5 - 2) \times \frac{12,000,000}{12} = 0.5 \times 1,000,000 = \text{Tk. } 500,000$

Incremental cost = Tk. 180,000

Scenario 1: Opportunity Cost of Funds = 20%

Interest savings = $500,000 \times 0.20 = \text{Tk. } 100,000$

Total incremental profit = Savings from bad debt + Interest savings - Incremental cost

= $120,000 + 100,000 - 180,000 = \text{Tk. } 40,000$

Since the incremental profit is positive, the increased effort is **worthwhile**.

Scenario 2: Opportunity Cost of Funds = 10%

Interest savings = $500,000 \times 0.10 = \text{Tk. } 50,000$

Total incremental profit = $120,000 + 50,000 - 180,000 = \text{Tk. } -10,000$

Since the incremental profit is negative, the increased effort is **not worthwhile**.