CMA September 2023 Examination Solutions

Comprehensive solutions for EF232, Intermediate Level II

Question 1: Multiple Choice Questions

Problem Statement: To determine the price of preferred stock:

a) divide the rate of return by the dividend amount

b) divide the dividend amount by the rate of return

c) divide the dividend amount by the rate of return minus the growth rate

d) divide the dividend amount by the growth rate

e) divide the dividend amount by one plus the rate of return

Solution:

The correct answer is **(b) divide the dividend amount by the rate of return**. Preferred stock typically pays a fixed dividend in perpetuity. Its price is therefore calculated as the present value of a perpetuity, which is the annual dividend divided by the required rate of return. This is similar to the formula for the value of a perpetual bond.

Problem Statement: The cost of retained earnings is equal to:

a) the return on new common stock

b) the return on preferred stock

c) the return on existing common stock

d) the weighted average cost of capital

e) zero

Solution:

The correct answer is **(c) the return on existing common stock**. The cost of retained earnings represents the opportunity cost to shareholders for forgoing dividends. If the earnings were paid out as dividends, shareholders could have invested that money in another asset with a similar risk profile, such as the company's existing common stock.

Problem Statement: The indifference point identifies:

a) equality of impact on EPS between two financing plans

b) equality of impact on EBIT between two financing plans

c) equality of impact on NAV between two financing plans

d) equality of impact on revenue between two financing plans

e) equality of impact on net profit between two financing plans

Solution:

The correct answer is **(a) equality of impact on EPS between two financing plans**. The indifference point, in the context of capital structure, is the level of EBIT (Earnings Before Interest and Taxes) at which the earnings per share (EPS) of two different financing alternatives (e.g., debt vs. equity) are exactly the same.

Problem Statement: The interest rate used to discount the cash flows associated with a bond is known as:

a) the required rate of return on the firm's equity

b) the prime rate

c) the coupon rate

d) the yield to maturity

e) he government T-bill rate

Solution:

The correct answer is **(d) the yield to maturity**. The yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. It is the internal rate of return (IRR) of a bond's cash flows and is the market's required rate of return for that specific bond. The coupon rate is the interest paid, not the rate used for discounting.

Problem Statement: All of the following influence the price of a stock for the firm going public by way of an IPO except:

a) anticipated public demand

b) an in-depth company analysis

c) future earnings potential of the company

d) the P/E ratio for similar firms in the industry

e) the previous share price

Solution:

The correct answer is **(e) the previous share price**. An Initial Public Offering (IPO) is when a company's stock is sold to the public for the first time. Since the company was previously private, there is no "previous share price" to consider. All other options are factors that would be carefully analyzed by investment banks and underwriters to determine the offering price.

Problem Statement: Given, risk-free rate of return = 5%, market return = 10%, cost of equity = 15%, value of beta is:

a) 1.9

b) 1.8

c) 2.0

d) 2.1

e) 2.2

Solution:

We can use the Capital Asset Pricing Model (CAPM) formula to solve for beta ($\beta$).

$k_e = R_f + \beta \times (R_M - R_f)$

Given: $k_e = 15\%$, $R_f = 5\%$, $R_M = 10\%$.

$0.15 = 0.05 + \beta \times (0.10 - 0.05)$

$0.15 - 0.05 = \beta \times 0.05$

$0.10 = \beta \times 0.05 \implies \beta = \frac{0.10}{0.05} = 2.0$

The value of beta is **(c) 2.0**.

Problem Statement: Under the net present value method:

a) the interest rate is determined that equates inflows and outflows

b) the time value of money is not taken into account

c) the basic discount rate is the internal rate of return

d) inflows are discounted back to determine if they exceed outflows

e) inflows are reinvested at the internal rate of return

Solution:

The correct answer is **(d) inflows are discounted back to determine if they exceed outflows**. The net present value (NPV) method calculates the difference between the present value of all cash inflows and the present value of all cash outflows. It is a fundamental capital budgeting technique that correctly incorporates the time value of money by using a discount rate to bring future cash flows to their present value.

Problem Statement: Projects that increase the overall risk level of the firm:

a) should be discounted at a rate higher than the cost of capital

b) should be discounted at the firm's cost of capital

c) should have a low standard deviation

d) should have a lower beta coefficient

e) should not be undertaken

Solution:

The correct answer is **(a) should be discounted at a rate higher than the cost of capital**. The cost of capital (WACC) is the appropriate discount rate for projects with an average risk level for the firm. A project that increases the firm's overall risk should be discounted at a higher rate to compensate investors for the additional risk. Using the firm's average cost of capital for a high-risk project would be incorrect and could lead to accepting a value-destroying project.

Problem Statement: Analyzing the performance of the firm through ratios over a number of years is referred to as:

a) financial analysis

b) trend analysis

c) vertical analysis

d) operational analysis

e) ratio analysis

Solution:

The correct answer is **(b) trend analysis**. Trend analysis involves examining a firm's financial data and ratios over multiple periods to identify patterns and changes in performance. This helps in understanding the company's financial health over time, unlike a static analysis of a single period.

Problem Statement: Fundamental factors influencing exchange rates include:

a) inflation, government policies, translation exposure

b) interest rates, government policies, and expropriation

c) balance of payments, spot rates, and expropriation

d) balance of trade, interest rates, taxation policy

e) government policies, balance of payments, inflation

Solution:

The correct answer is **(e) government policies, balance of payments, inflation**. These are the key macroeconomic factors that influence the supply and demand for a country's currency. Inflation and interest rate differentials are major drivers (Purchasing Power Parity and Interest Rate Parity), and government policies and the balance of payments (which includes the balance of trade) directly affect the demand for a currency.

Question 2: Modified True/False

Problem Statement: In valuing a security, we need to know the future cash flows and the discount rate.

Solution:

True. The intrinsic value of any security is the present value of its expected future cash flows, discounted at a rate that reflects the risk of those cash flows. Knowing the future cash flows and the appropriate discount rate are the two fundamental inputs for any valuation model.

Problem Statement: Capital budgeting is a responsibility of the Treasurer.

Solution:

True. The Treasurer is a key financial executive whose responsibilities typically include managing cash flows, obtaining financing, and making capital expenditure decisions, which fall under the scope of capital budgeting.

Problem Statement: Simple average cost of capital may be defined as the cost of raising an additional taka of capital.

Solution:

False. The cost of raising an additional taka of capital is the **marginal cost of capital (MCC)**. The simple average cost of capital is the average cost of all the firm's capital sources, weighted by their proportion in the firm's capital structure.

Problem Statement: Working capital management is mainly concerned with the management of the firm's capital assets.

Solution:

False. Working capital management is concerned with the management of a firm's **current assets and current liabilities**. The management of a firm's capital assets (long-term assets) is addressed by capital budgeting.

Problem Statement: A series of consecutive cash flows of equal amounts is known as a compound sum.

Solution:

False. A series of consecutive cash flows of equal amounts is known as an **annuity**. A compound sum refers to the future value of a single amount or a series of cash flows, which includes both the initial principal and the accumulated interest.

Question 3: Matching

Problem Statement: Match the items of column A with the most suitable items of column B.

Column AColumn B
1. Financial risk(a) the inability to meet debt obligations
2. Beta coefficient(b) dividend yield plus growth rate
3. Cost of equity(c) total assets minus total liabilities
4. Short-term credit(d) the historical volatility relative to the market's volatility
5. Net worth(e) earnings yield plus growth rate
(f) the inability to pay dividends
(g) suppliers
(h) the return relative to the market return
(i) bondholders
(j) total assets minus current liabilities

Solution:

The correct matches are as follows:

  • **(1) Financial risk** matches with **(a) the inability to meet debt obligations**. Financial risk is the risk to a firm's equity holders that the firm will not be able to pay its debt obligations.
  • **(2) Beta coefficient** matches with **(d) the historical volatility relative to the market's volatility**. Beta measures a security's systematic risk by comparing its historical returns to the market's historical returns.
  • **(3) Cost of equity** matches with **(b) dividend yield plus growth rate**. This is the formula for the cost of equity under the constant growth (Gordon Growth) model.
  • **(4) Short-term credit** matches with **(g) suppliers**. Trade credit from suppliers is a common and often spontaneous source of short-term financing for a firm.
  • **(5) Net worth** matches with **(c) total assets minus total liabilities**. Net worth is another term for a company's total equity, which is found by subtracting total liabilities from total assets.

Question 4: Agency Conflict, TVM & Portfolio Beta

Problem Statement: Shareholders generally look forward to acceleration of the growth rate of their business. They therefore, prefer management report on wealth maximization to profit maximization. Required: (i) Clarify the idea of profit maximization and wealth maximization with an example. (ii) Explain to a shareholder THREE (3) inherent disadvantages of using profit as a performance measure and THREE (3) advantages of using wealth maximization as a performance measure.

Solution:

i. Profit Maximization vs. Wealth Maximization:

Profit maximization is the objective of maximizing a firm's net income or earnings per share in the short term. It often focuses on quarterly or annual earnings and can lead to decisions that may not be in the firm's long-term best interest.

Wealth maximization is the long-term objective of maximizing the value of a firm's stock. It considers the timing of cash flows, the risk associated with those cash flows, and the impact of decisions on the firm's overall value. Wealth maximization is the preferred goal of modern financial management.

Example: Suppose a company has two projects. Project A has a higher expected profit in year one but is very risky. Project B has a lower profit in year one but is less risky and has a strong growth trajectory. A management focused on profit maximization might choose Project A, but a management focused on wealth maximization would likely choose Project B, as its lower risk and strong long-term growth would be more valuable to shareholders in the long run.

ii. Disadvantages of Profit and Advantages of Wealth Maximization:

  • **Disadvantages of Profit as a Performance Measure:**
    1. **Ignores risk:** Profit maximization does not account for the riskiness of the cash flows. A project with a high expected profit but also a high risk of failure might be chosen over a less profitable but more certain project.
    2. **Ignores timing of cash flows:** It does not consider the time value of money. A profit of Tk. 100,000 today is more valuable than a profit of Tk. 100,000 five years from now, but profit maximization treats them as equal.
    3. **Ambiguous definition of profit:** There are many different ways to measure profit (e.g., net income, EBIT), which can lead to ambiguity and manipulation.
  • **Advantages of Wealth Maximization as a Performance Measure:**
    1. **Considers risk:** Wealth maximization, as measured by stock price, inherently accounts for risk. Risky projects will be discounted at a higher rate, reducing their value to shareholders.
    2. **Considers the time value of money:** It uses discounting techniques to bring all future cash flows to their present value, making all decisions comparable in today's terms.
    3. **Focuses on long-term value:** By focusing on the stock price, it encourages management to make decisions that build sustainable, long-term value for the firm, which is aligned with shareholders' interests.

Problem Statement: ITC is a small technology company that develops financial technology (FinTech) applications for mobile devices. The company is selling one of its highly rated FinTech apps to a financial institution. The financial institution has proposed the following strategic payment options for ITC's consideration: Strategy 1: An immediate payment of Tk. 1.2 million followed by payments of Tk. 50,000 at the end of each quarter during the next five years. Strategy 2: Payment of Tk. 55,000 at the beginning of each month for the next five years. ITC's required rate of return is 25% per annum. Required: (i) Identify the type of cash flow pattern described under each option. (ii) Compute the present value of the cash flows for each strategy and advise ITC on the best payment option.

Solution:

i. Identification of cash flow patterns:

Strategy 1 is a combination of a lump-sum payment today and an **ordinary annuity** (a series of equal payments at the end of each period). The payments are quarterly.

Strategy 2 is an **annuity due** (a series of equal payments at the beginning of each period). The payments are monthly.

ii. Present value and advice:

We need to find the present value of each strategy. The required rate of return is 25% per annum.

  • **Strategy 1 (Quarterly):**

    Quarterly rate = $\frac{25\%}{4} = 6.25\% = 0.0625$

    Number of quarters = $5 \text{ years} \times 4 \text{ quarters/year} = 20 \text{ quarters}$

    PV of annuity = $PMT \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] = 50,000 \times \left[ \frac{1 - (1.0625)^{-20}}{0.0625} \right]$

    $= 50,000 \times 11.258 \approx \text{Tk. } 562,900$

    Total PV = Immediate Payment + PV of Annuity = $1,200,000 + 562,900 = \text{Tk. } 1,762,900$

  • **Strategy 2 (Monthly):**

    Monthly rate = $\frac{25\%}{12} \approx 2.0833\% = 0.020833$

    Number of months = $5 \text{ years} \times 12 \text{ months/year} = 60 \text{ months}$

    The formula for an annuity due is the ordinary annuity formula multiplied by $(1+i)$.

    PV of annuity due = $PMT \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] \times (1+i)$

    $= 55,000 \times \left[ \frac{1 - (1.020833)^{-60}}{0.020833} \right] \times (1.020833)$

    $= 55,000 \times [34.787] \times 1.020833 \approx \text{Tk. } 1,950,568$

Advice: ITC should choose **Strategy 2**. Its present value of approximately **Tk. 1,950,568** is significantly higher than the present value of Strategy 1 (**Tk. 1,762,900**), representing a greater value for the company today.

Problem Statement: ECRI Corporation is a holding company with four main subsidiaries. The percentage of its capital invested in each of the subsidiaries, and their respective betas, are as follows: Subsidiary, Percentage of Capital, Beta. Electric utility: 60%, 0.70. Cable company: 25%, 0.90. Real estate development: 10%, 1.30. International/special projects: 5%, 1.50. Required: (i) What is the holding company’s beta? (ii) If the risk-free rate is 6 percent and the market risk premium is 5 percent, what is the holding company’s required rate of return? (iii) ECRI is considering a change in its strategic focus; it will reduce its reliance on the electric utility subsidiary, so the percentage of its capital in this subsidiary will be reduced to 50 percent. At the same time, it will increase its reliance on the international/special projects division, so the percentage of its capital in that subsidiary will rise to 15 percent. What will the company’s required rate of return be after these changes?

Solution:

i. Holding company's beta:

The beta of a portfolio (or holding company) is the weighted average of the betas of its individual components.

$\beta_{portfolio} = \sum_{i=1}^n w_i \beta_i$

$\beta_{ECRI} = (0.60 \times 0.70) + (0.25 \times 0.90) + (0.10 \times 1.30) + (0.05 \times 1.50)$

$= 0.42 + 0.225 + 0.13 + 0.075 = 0.85$

The holding company's beta is **0.85**.

ii. Holding company's required rate of return:

Using the CAPM formula:

$k_e = R_f + \beta_{ECRI} \times (\text{Market Risk Premium})$

$k_e = 6\% + 0.85 \times 5\% = 6\% + 4.25\% = 10.25\%$

The holding company's required rate of return is **10.25%**.

iii. Required rate of return after strategic change:

We need to recalculate the portfolio beta with the new weights. The weights for the cable company and real estate development subsidiaries remain the same.

New weight for Electric utility = 50% = 0.50

New weight for International/special projects = 15% = 0.15

Weights for Cable company and Real estate = $1 - 0.50 - 0.15 = 0.35$.

We are not given a new breakdown for the remaining 35%. We can assume the proportions remain the same for the other two.

Original combined weight = $0.25+0.10 = 0.35$. So the proportions remain the same.

New weight of Cable = $0.25 \times \frac{0.35}{0.35} = 0.25$. New weight of Real estate = $0.10 \times \frac{0.35}{0.35} = 0.10$.

New portfolio beta = $(0.50 \times 0.70) + (0.25 \times 0.90) + (0.10 \times 1.30) + (0.15 \times 1.50)$

$= 0.35 + 0.225 + 0.13 + 0.225 = 0.93$

New required rate of return = $6\% + 0.93 \times 5\% = 6\% + 4.65\% = 10.65\%$

The company's new required rate of return will be **10.65%**.

Question 5: Capital Rationing, ARR & WACC

Problem Statement: In periods of difficult global financial environment, raising of capital is a challenge necessitating the need for prudent and best use of scarce capital for projects. Required: (i) Explain the term capital rationing. (ii) Distinguish between soft capital rationing and hard capital rationing giving an example each. (iii) Discuss the uses and limitations of capital rationing.

Solution:

i. Explanation of capital rationing:

Capital rationing is the practice of restricting the amount of new investments or projects a firm undertakes to a certain budget, even if there are more projects with a positive Net Present Value (NPV) that could be accepted. This is typically done when a firm has a limited amount of capital to invest.

ii. Soft vs. Hard capital rationing:

  • **Soft Capital Rationing:** This occurs when a firm's management voluntarily sets a limit on the amount of capital to be invested. This might be due to a desire to maintain a stable debt-to-equity ratio or to avoid taking on too many new projects at once to prevent overstretching management capacity.

    **Example:** A company's CEO decides to limit the capital budget for new projects to Tk. 10 million for the year, even though the company has access to more funds at a reasonable cost.

  • **Hard Capital Rationing:** This occurs when a firm is unable to raise additional capital, regardless of how many profitable projects it has. This can happen due to external factors, such as a credit crisis, economic recession, or if the firm has a poor credit rating.

    **Example:** A small, unprofitable startup is unable to secure a bank loan or attract new investors to fund a promising new project because of its poor financial history.

iii. Uses and limitations:

  • **Uses:** Capital rationing is used to enforce financial discipline, manage risk, and prevent over-expansion. It forces management to prioritize projects and choose only the most profitable ones, which can lead to a more efficient use of capital.
  • **Limitations:** The primary limitation is that it may lead to the rejection of profitable projects (those with a positive NPV), which can reduce the firm's long-term value and growth potential. It can also lead to suboptimal decisions, as managers may choose a portfolio of smaller projects that fit within the budget, rather than a single, larger, and more valuable project.

Problem Statement: Sakura Limited uses the Accounting Rate of Return (ARR) as the basis of evaluating projects for investment of its scarce financial resources. It uses its predetermined expected return on capital as the basis for the choice of investment projects. The company’s Finance team has provided the information below regarding various projects and their initial investments and net cash flows. The hurdle rate or target Accounting Rate of Return for Sakura is 25%. Project, A (Tk.), B (Tk.), C (Tk.). Initial Investment: 1,000,000, 1,600,000, 2,000,000. Net Cash flows: Year 1: 600,000, 700,000, 800,000. Year 2: 500,000, 600,000, 600,000. Year 3: 400,000, 500,000, 500,000. Year 4: 300,000, 500,000, 400,000. Year 5: --, 400,000, --. Required: (i) Calculate the Accounting Rate of Return for each project (Average Investment basis). (ii) Using the target return of 25% advice Sakura Limited which projects should be undertaken.

Solution:

i. Accounting Rate of Return (ARR) for each project:

The formula for ARR on an average investment basis is: $ARR = \frac{\text{Average Annual Net Profit}}{\text{Average Investment}}$. To find the net profit, we must subtract the annual depreciation from the net cash flows.

  • **Project A:**

    Total Net Cash Flows = $600,000+500,000+400,000+300,000 = \text{Tk. } 1,800,000$

    Average Annual Cash Flow = $\frac{1,800,000}{4} = \text{Tk. } 450,000$

    Depreciation = $\frac{\text{Initial Investment}}{\text{Life}} = \frac{1,000,000}{4} = \text{Tk. } 250,000$

    Average Annual Net Profit = $450,000 - 250,000 = \text{Tk. } 200,000$

    Average Investment = $\frac{\text{Initial Investment}}{2} = \frac{1,000,000}{2} = \text{Tk. } 500,000$

    $ARR_A = \frac{200,000}{500,000} = 0.40$ or $40\%$

  • **Project B:**

    Total Net Cash Flows = $700,000+600,000+500,000+500,000+400,000 = \text{Tk. } 2,700,000$

    Average Annual Cash Flow = $\frac{2,700,000}{5} = \text{Tk. } 540,000$

    Depreciation = $\frac{1,600,000}{5} = \text{Tk. } 320,000$

    Average Annual Net Profit = $540,000 - 320,000 = \text{Tk. } 220,000$

    Average Investment = $\frac{1,600,000}{2} = \text{Tk. } 800,000$

    $ARR_B = \frac{220,000}{800,000} = 0.275$ or $27.5\%$

  • **Project C:**

    Total Net Cash Flows = $800,000+600,000+500,000+400,000 = \text{Tk. } 2,300,000$

    Average Annual Cash Flow = $\frac{2,300,000}{4} = \text{Tk. } 575,000$

    Depreciation = $\frac{2,000,000}{4} = \text{Tk. } 500,000$

    Average Annual Net Profit = $575,000 - 500,000 = \text{Tk. } 75,000$

    Average Investment = $\frac{2,000,000}{2} = \text{Tk. } 1,000,000$

    $ARR_C = \frac{75,000}{1,000,000} = 0.075$ or $7.5\%$

ii. Advice to Sakura Limited:

Sakura Limited's target ARR is 25%. We should accept all projects whose ARR is equal to or greater than this hurdle rate.

  • Project A's ARR (40%) is > 25% -> **Accept**
  • Project B's ARR (27.5%) is > 25% -> **Accept**
  • Project C's ARR (7.5%) is < 25% -> **Reject**

Sakura Limited should undertake **Projects A and B**.

Problem Statement: Beach Limited is into the provision of online conference call facilities which has become popular due to Covid-19. The company has 10 million issued shares currently at Tk. 50 each, 3 million preference shares trading at Tk. 25 each and 5,000 bonds also trading at Tk. 600 each. Required: (i) Calculate the capital structure of the company. (ii) How much should the company earn annually to achieve a return of 25% per annum on capital employed for equity holders if dividend rate on preference shares per annum is 20% and coupon on the bonds is 18%? Interest paid on debt is tax deductible and corporate tax rate is 25%.

Solution:

i. Capital structure of the company:

We first calculate the market value of each component of the capital structure.

Market Value of Equity = $10,000,000 \times 50 = \text{Tk. } 500,000,000$

Market Value of Preference Shares = $3,000,000 \times 25 = \text{Tk. } 75,000,000$

Market Value of Bonds = $5,000 \times 600 = \text{Tk. } 3,000,000$

Total Market Value of Capital = $500,000,000 + 75,000,000 + 3,000,000 = \text{Tk. } 578,000,000$

The capital structure, in terms of market value weights, is as follows:

  • Weight of Equity: $\frac{500,000,000}{578,000,000} \approx 0.865$ or $86.5\%$
  • Weight of Preference Shares: $\frac{75,000,000}{578,000,000} \approx 0.130$ or $13.0\%$
  • Weight of Debt: $\frac{3,000,000}{578,000,000} \approx 0.005$ or $0.5\%$

The capital structure is approximately **86.5% equity, 13.0% preference shares, and 0.5% debt**.

ii. Annual earnings required:

We are asked to find the annual earnings required to achieve a **25% return on capital employed for equity holders**. This is different from a WACC calculation. We need to work backwards from the required return to find the required EBIT (Earnings Before Interest and Taxes).

Total Return on Equity = $0.25 \times 500,000,000 = \text{Tk. } 125,000,000$

After-tax earnings available to common shareholders (Net Income) must be Tk. 125,000,000.

First, we find the dividend payments on the preference shares and the interest payments on the bonds.

Preference dividend = $3,000,000 \times 25 \times 0.20 = \text{Tk. } 15,000,000$

Interest on bonds = $3,000,000 \times 0.18 = \text{Tk. } 540,000$

Total earnings after tax must cover the preference dividends and the required return for equity holders.

Earnings After Tax (EAT) = Return on Equity + Preference Dividend

$EAT = 125,000,000 + 15,000,000 = \text{Tk. } 140,000,000$

Since EAT = $(EBIT - \text{Interest}) \times (1-T)$, we can rearrange this to solve for EBIT.

$EBIT - \text{Interest} = \frac{EAT}{1-T} = \frac{140,000,000}{1-0.25} = \frac{140,000,000}{0.75} \approx \text{Tk. } 186,666,667$

$EBIT = 186,666,667 + \text{Interest} = 186,666,667 + 540,000 = \text{Tk. } 187,206,667$

The company should earn approximately **Tk. 187.21 million** annually.

Question 6: Public Listing, Leasing & Valuation

Problem Statement: The Dhaka Stock Exchange (DSE) market has recently been intensifying its public education for Bangladeshi companies to list on the stock market to raise the needed capital for expansion and growth. You have been approached by owners of RANGSgroup who have expressed interest in getting listed on the stock market but has limited knowledge on what they stand to benefit by listing their company on the market. Required: Explain FOUR (4) advantages RANGS group could derive from listing on DSE.

Solution:

Listing on a stock exchange like the DSE, also known as an Initial Public Offering (IPO), can provide several significant benefits to a company like RANGSgroup.

  • **Access to Capital:** An IPO provides the company with access to a much larger and more diverse pool of investors, allowing it to raise a significant amount of capital to fund expansion, research and development, or to pay off existing debt. This can be more cost-effective and flexible than relying on traditional bank loans.
  • **Enhanced Reputation and Credibility:** Being a publicly listed company on a major stock exchange like the DSE can significantly enhance a company's public image, reputation, and credibility. This can help attract new customers, partners, and talent, as well as facilitate future financing.
  • **Liquidity for Shareholders:** An IPO provides a liquid market for the shares of the company. This means that existing shareholders (such as the founders and early investors) can easily sell their shares and realize the value of their investment. This can be a key exit strategy and a powerful incentive for investors.
  • **Improved Employee Incentives:** Publicly listed companies can use stock-based compensation (e.g., stock options, employee stock purchase plans) to attract and retain top talent. These incentives can align the interests of employees with those of the shareholders, motivating them to work towards increasing the company's value.

Problem Statement: High electricity costs have made Farmer Corporation’s chicken-plucking machine economically worthless. Only two machines are available to replace it. The International Plucking Machine (IPM) model is available only on a lease basis. The lease payments will be Tk. 80,000 for five years, due at the beginning of each year. This machine will save Farmer Tk. 29,000 per year through reductions in electricity costs. As an alternative, Farmer can purchase a more energy-efficient machine from Basic Machine Corporation (BMC) for Tk. 365,000. This machine will save Tk. 32,000 per year in electricity costs. A local bank has offered to finance the machine with a Tk. 365,000 loan. The interest rate on the loan will be 10 percent on the remaining balance and will require five annual principal payments of Tk. 73,000. Farmer has a target debt-to-asset ratio of 67 percent. Farmer is in the 34 percent tax bracket. After five years, both machines will be worthless. The machines will be depreciated on a straight-line basis. Required: Should Farmer lease the IPM machine or purchase the more efficient BMC machine?

Solution:

We will compare the two options (Lease vs. Buy) by calculating the Net Present Value (NPV) of each. The discount rate for both options is the after-tax cost of debt.

Cost of Debt = 10%. Tax Rate = 34%.

After-tax cost of debt = $10\% \times (1 - 0.34) = 6.6\%$

Option 1: Lease the IPM machine

The cash flows for the lease option are the after-tax lease payments and the after-tax savings from the machine's operation.

After-tax lease payment (annuity due) = $80,000 \times (1-0.34) = \text{Tk. } 52,800$

After-tax savings = $29,000 \times (1-0.34) = \text{Tk. } 19,140$

NPV = PV of Savings - PV of Payments

The lease payments are an annuity due over 5 years.

PV of Payments = $52,800 + 52,800 \times \left[ \frac{1 - (1.066)^{-4}}{0.066} \right] = 52,800 + 52,800 \times 3.424 \approx \text{Tk. } 233,639$

The savings are an ordinary annuity over 5 years.

PV of Savings = $19,140 \times \left[ \frac{1 - (1.066)^{-5}}{0.066} \right] = 19,140 \times 4.198 \approx \text{Tk. } 80,359$

$NPV_{Lease} = 80,359 - 233,639 = \text{Tk. } -153,280$

The NPV of the lease option is approximately **Tk. (153,280)**.

Option 2: Purchase the BMC machine

Initial cost = Tk. (365,000)

Depreciation (straight-line) = $\frac{365,000}{5} = \text{Tk. } 73,000$ per year.

Depreciation tax shield = $73,000 \times 0.34 = \text{Tk. } 24,820$ per year.

After-tax savings = $32,000 \times (1 - 0.34) = \text{Tk. } 21,120$ per year.

NPV of Buying = $-365,000 + \sum_{t=1}^5 \frac{(\text{Savings} + \text{Dep. Tax Shield})}{(1.066)^t}$

$NPV_{Buy} = -365,000 + (21,120 + 24,820) \times \left[ \frac{1 - (1.066)^{-5}}{0.066} \right]$

$= -365,000 + 45,940 \times 4.198 \approx -365,000 + 192,866 = \text{Tk. } -172,134$

The NPV of the purchase option is approximately **Tk. (172,134)**.

Conclusion:

Both options result in a negative NPV, which means neither should be undertaken. However, if Farmer Corporation must replace the machine, the **lease option is marginally better** as it has a lower negative NPV ($-153,280$ vs. $-172,134$).

Problem Statement: Panama Limited is in advanced negotiation with shareholders of Zeal Limited to acquire 70% shares in that company. The following financial information is provided for Zeal Limited: Number of ordinary shares = 20 million, Net assets per share = Tk. 8, Earnings per share = Tk. 15, Price Earnings ratio (P/E) = 10 times. The Finance Director who performed a due diligence review recommended the following: 1. Fixed assets included in the net assets were overstated by Tk. 6 million. 2. A key customer who owes Tk. 4 million has gone bankrupt and debt considered irrecoverable. 3. A provision of Tk. 10 million is made for a tax liability. 4. Panama Limited's cost of capital is 16% and risk premium of 4% is added in the valuation of Zeal Limited to take care of additional operational risk. 5. The Finance manager provided a statement showing projected cash inflows for the next 5 years as follows: Year, (Tk.): 1: 125 million, 2: 60 million, 3: 150 million, 4: 200 million, 5: 110 million. Required: Advise shareholders of Panama Limited on how much to pay for 70% of the shares of Zeal Limited using the following valuation methods: (i) Price Earnings (P/E) ratio (ii) Balance sheet valuation basis (iii) Cash flow valuation

Solution:

We will calculate the value of 100% of Zeal Limited and then take 70% of that value to advise on the purchase price.

i. P/E Ratio Valuation:

Value = EPS $\times$ P/E Ratio $\times$ Number of Shares

Value = $15 \times 10 \times 20,000,000 = \text{Tk. } 3,000,000,000$

Purchase price for 70% = $3,000,000,000 \times 0.70 = \text{Tk. } 2,100,000,000$

Using the P/E ratio, the price to pay for 70% of the shares is **Tk. 2.1 billion**.

ii. Balance Sheet Valuation Basis:

First, we find the total net assets before any adjustments.

Book Value of Equity = Net assets per share $\times$ Number of shares = $8 \times 20,000,000 = \text{Tk. } 160,000,000$

Now, we apply the due diligence adjustments.

Value of Net Assets = Book Value of Equity - Overstated Fixed Assets - Irrecoverable Debt - Tax Provision

= $160,000,000 - 6,000,000 - 4,000,000 - 10,000,000 = \text{Tk. } 140,000,000$

Purchase price for 70% = $140,000,000 \times 0.70 = \text{Tk. } 98,000,000$

Using the balance sheet valuation, the price to pay for 70% of the shares is **Tk. 98 million**.

iii. Cash Flow Valuation:

We find the present value of the projected cash inflows. The discount rate is the company's cost of capital plus the additional risk premium.

Discount Rate = $16\% + 4\% = 20\%$

PV = $\frac{125}{(1.20)^1} + \frac{60}{(1.20)^2} + \frac{150}{(1.20)^3} + \frac{200}{(1.20)^4} + \frac{110}{(1.20)^5}$

$= 104.17 + 41.67 + 86.81 + 96.45 + 44.29 = \text{Tk. } 373.39 \text{ million}$

Purchase price for 70% = $373,390,000 \times 0.70 = \text{Tk. } 261,373,000$

Using the cash flow valuation, the price to pay for 70% of the shares is approximately **Tk. 261.37 million**.

Advice to Shareholders:

The three methods provide a wide range of values: Tk. 2.1 billion (P/E), Tk. 98 million (Balance Sheet), and Tk. 261.37 million (Cash Flow). The P/E and Cash Flow methods are typically more forward-looking and thus more relevant for an acquisition decision. The balance sheet method is more of a liquidation value. The P/E ratio of 10 times with an EPS of Tk. 15 may be too simplistic and not fully reflect the risks. The cash flow valuation, which accounts for the cost of capital and risk, provides the most robust valuation. Therefore, the shareholders should consider paying a price that is closer to the cash flow valuation, likely around **Tk. 261.37 million** for 70% of the shares.

Question 7: Dividend Policy, Credit Policy & Hedging

Problem Statement: A firm is in dilemma about two options of dividend policy (i) a stable dividend payment per share; (ii) a stable dividend-payout ratio. As a financial manager, which one would you recommend & why?

Solution:

As a financial manager, I would recommend a policy of **stable dividend payment per share**. This policy aims to maintain a constant or steadily increasing dividend over time, even if the firm's earnings fluctuate.

The primary reason for this recommendation is that a stable dividend payment provides a clear and positive signal to the market. Investors often view a stable dividend as an indication of a firm's financial health, management's confidence in future earnings, and a commitment to returning value to shareholders. This predictability can reduce investor uncertainty, attract a stable base of investors, and potentially lead to a higher and more stable stock price. While a stable payout ratio may sound logical, it can result in volatile dividend payments that confuse investors and can be a sign of financial instability. A stable dividend policy, on the other hand, prioritizes investor relations and market stability over a rigid link between dividends and short-term earnings.

Problem Statement: Best Electronics Limited is a wholesale distributor of household electrical products of major electronic brands. The company currently sells on credit to all its customers. Although the credit term is net 20 days, the receivables turnover days has been 15 days. The company’s annual credit sales revenue is Tk. 80 million, and its contribution margin ratio is 30%. Bad debt is 2% of sales revenue, and credit collection cost is Tk. 50,000 per annum. Management is considering extending the credit period to net 30 days. It is expected that the implementation of this proposal would attract new customers, and the annual revenue would increase by 20%. It is also expected that both the existing and the new customers will probably take the full 30 days credit. To mitigate the probable lengthening in the receivables turnover days, management proposes that the extension in the credit period be combined with the introduction of a cash discount policy of 2% on all payments made within the first 10 days of the credit period. It is expected that 30% of all customers will pay their accounts early to take the discount. Consequently, the receivables turnover days would increase to 24 days. While the bad debt will remain at 2% of sales revenue, the annual credit collection cost will increase to Tk. 65,000. The company’s cost of capital is 24%. Required: Evaluate the proposed change in the credit policy and recommend whether the proposed change should be implemented.

Solution:

We need to compare the incremental costs and benefits of the proposed credit policy change to determine if it is worthwhile.

Current Policy:

Sales = Tk. 80 million

Contribution Margin = $80,000,000 \times 0.30 = \text{Tk. } 24,000,000$

Bad Debt = $80,000,000 \times 0.02 = \text{Tk. } 1,600,000$

Collection Cost = Tk. 50,000

Receivables Investment = $\frac{80,000,000 \times (1-0.30)}{365} \times 15 = \text{Tk. } 2,301,370$

Cost of Investment = $2,301,370 \times 0.24 = \text{Tk. } 552,329$

Proposed Policy:

New Sales = $80,000,000 \times 1.20 = \text{Tk. } 96,000,000$

New Bad Debt = $96,000,000 \times 0.02 = \text{Tk. } 1,920,000$

New Collection Cost = Tk. 65,000

New Receivables Investment = $\frac{96,000,000 \times (1-0.30)}{365} \times 24 = \text{Tk. } 4,402,192$

New Cost of Investment = $4,402,192 \times 0.24 = \text{Tk. } 1,056,526$

Cash Discounts = $96,000,000 \times 0.30 \times 0.02 = \text{Tk. } 576,000$

Incremental Analysis:

Incremental Sales = $96,000,000 - 80,000,000 = \text{Tk. } 16,000,000$

Incremental Contribution Margin = $16,000,000 \times 0.30 = \text{Tk. } 4,800,000$

Incremental Bad Debt = $1,920,000 - 1,600,000 = \text{Tk. } 320,000$

Incremental Collection Cost = $65,000 - 50,000 = \text{Tk. } 15,000$

Incremental Cost of Receivables Investment = $1,056,526 - 552,329 = \text{Tk. } 504,197$

Incremental Cash Discounts = Tk. 576,000

Net Incremental Profit = Incremental CM - Incremental Bad Debt - Incremental Collection Cost - Incremental Cost of Receivables - Incremental Cash Discounts

= $4,800,000 - 320,000 - 15,000 - 504,197 - 576,000 = \text{Tk. } 3,384,803$

Recommendation: Since the net incremental profit is positive, the proposed change should be **implemented**.

Problem Statement: Home Decor Limited, a trading company based in Bangladesh, usually buys foreign currency to settle invoices for imports. The Treasury Manager is considering ways of hedging the company’s foreign currency risk exposures. After considering various options available to her, she has settled on both forwards and futures contract. Required: Explain advantages of currency forwards over currency futures contract.

Solution:

While both currency forwards and futures are used for hedging foreign exchange risk, a currency forward contract offers distinct advantages over a currency futures contract, particularly for a company like Home Decor Limited.

  • **Customization:** A forward contract is a private agreement between two parties. This allows the contract to be customized to the exact amount and maturity date needed by the company, matching the value of the import invoice. Futures contracts, in contrast, are standardized in terms of size and maturity, which may result in a company being over- or under-hedged.
  • **Flexibility in Delivery:** A forward contract can be settled by physical delivery of the currency or through cash settlement. Futures contracts, being standardized, usually involve a cash settlement. This flexibility is beneficial if the company needs to physically receive the foreign currency to pay for its imports.
  • **No Margin Requirements:** Futures contracts are traded on exchanges and require a daily margin to be maintained. This means a company might have to post additional collateral if the market moves against it, creating a cash flow strain. Forward contracts, being over-the-counter, do not have a daily margin requirement.
CMA May 2023 Exam Solutions

CMA May 2023 Examination Solutions

Comprehensive solutions for EF232, Intermediate Level II

Question 1: Multiple Choice Questions

Problem Statement: If a company's current ratio declined in a year during which its quick ratio improved, which of the following is the most likely explanation?

a) inventory is increasing

b) inventory is declining

c) no change in inventory

d) receivables are being collected more slowly than in the past

e) receivables are being collected more rapidly than in the past

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).

Problem Statement: What is the intrinsic value of a Tk. 1,000 face value, 8% coupon paying perpetual bond if an investor's required rate of return is 6%? (Assume annual interest payments and discounting)

a) Tk. 1,333.33

b) Tk. 1,000

c) Tk. 750

d) Tk. 75.47

e) cannot be determined

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**.

Problem Statement: All of the following influence capital budgeting cash flows EXCEPT:

a) accelerated depreciation

b) method of project financing used

c) salvage value

d) tax rate changes

e) opportunity cost

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.

Problem Statement: Combined leverage can be used to measure the relationship between:

a) EBIT and EPS

b) Sales and EPS

c) Sales and EBIT

d) Sales and Net profit

e) EBIT and Net profit

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).

Problem Statement: What is the book value of common equity per share for the following firm? The firm has 20,000 common shares authorized of which 15,000 are outstanding at a par value of Tk. 1. Additional paid-in-capital represents Tk. 300,000 and retained earnings are Tk. 300,000.

a) 1

b) 20

c) 21

d) 41

e) 40

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**.

Problem Statement: With continuous compounding at 8% for 20 years, what is the approximate future value of a Tk. 20,000 initial investment?

a) Tk. 52,000

b) Tk. 93,219

c) Tk. 96,650

d)Tk. 99,061

e)Tk. 915,240

Solution:

The formula for future value with continuous compounding is:

$FV = PV \times e^{rt}$

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**.

Problem Statement: Operating leverage is the function of which of the following factors?

a) Amount of variable cost.

b) Variable contribution margin.

c) Volume of purchases.

d) Amount of semi-variable cost.

e) Amount of fixed cost.

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.

Problem Statement: If credit term of $"1/10$ net 35" is offered, the approximate cost (using 365 days) of not taking the discount and paying at the end of the credit period would be:

a) 10.0%

b) 10.3%

c) 14.7%

d) 18.4%

e) 21.5%

Solution:

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

$\text{Approximate Cost} = \frac{\text{Discount \%}}{100 - \text{Discount \%}} \times \frac{365}{\text{Credit Period} - \text{Discount Period}}$

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%**.

Problem Statement: Firm's cost of capital is the average cost of:

a) All sources of finance.

b) All borrowings.

c) All share capital.

d) All internal funds.

e) All bonds &debentures.

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.

Problem Statement: Which of the following is a liquidity ratio?

a) Equity ratio.

b) Proprietary ratio.

c) Debt to equity ratio.

d) Capital gearing ratio.

e) Net working 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.

Question 2: Modified True/False

Problem Statement: The firm beta is directly influenced by financial leverage.

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.

Problem Statement: The receivable-turnover ratio helps management to managing inventory.

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.

Problem Statement: Financial structure refers to long term funds.

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).

Problem Statement: Firm with high operating leverage will have lower business risk.

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.

Problem Statement: According to Modigliani and Miller, the investor is indifferent between receiving dividends and having earnings retained by the firm.

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.

Question 3: Matching

Problem Statement: Match the items of column A with the most suitable items of column B.

Column AColumn B
1. Shareholder wealth(a) Market price per share
2. Profitability ratio(b) Net asset value per share
3. Capital structure(c) Profitability index
4. Money market(d) Profit margin
5. Risk-free rate(e) Current asset and current liability
(f) Debt and equity
(g) Commercial paper
(h) Mutual fund
(i) Treasury bill
(j) Treasury stock

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.

Question 4: Markets, TVM & Bond Valuation

Problem Statement: Financial markets provide platforms or medium through which holders of surplus funds invest their funds. Those with financial deficits could raise funds or capital, enabling both parties to achieve their objectives.

Required: Distinguish between money markets and capital markets giving an example of financial instruments traded in each type of market.

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.

Problem Statement: RD Foods Limited is borrowing Tk. 500,000 to finance a project involving an expansion of its existing factory. It has obtained an offer from City Bank. The terms of the loan facility are as follows: Annual interest rate: 22%, Duration: 2 years, Interest method: compound interest with quarterly compounding, Payment plan: equal installments at the end of each quarter. Required: (i) Compute the quarterly installment. (ii) Prepare a loan amortization schedule to show the periodic interest charges, installment payments, principal payments, and balance of the loan at the end of each quarter.

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).

$PV = PMT \times \left[ \frac{1 - (1+i)^{-n}}{i} \right]$

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:

QuarterBeginning BalanceInstallmentInterest (5.5%)Principal RepaymentEnding Balance
1500,000.0078,924.9727,500.0051,424.97448,575.03
2448,575.0378,924.9724,671.6354,253.34394,321.69
3394,321.6978,924.9721,687.6957,237.28337,084.41
4337,084.4178,924.9718,539.6460,385.33276,699.08
5276,699.0878,924.9715,218.4563,706.52212,992.56
6212,992.5678,924.9711,714.6067,210.37145,782.19
7145,782.1978,924.978,017.9870,906.9974,875.20
874,875.2078,924.974,118.1474,806.8368.37

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

Problem Statement: Fortune Limited has in issue 12% bonds with par value Tk. 150,000 and redemption value Tk. 165,000 with interest payable quarterly. The cost of debt on the bonds are 8% annually and 2% quarterly. The bonds are redeemable on 30 June 2023 and it is now 31 December 2019. Required: Calculate the market value of the bonds.

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.

$PV_{bond} = PMT \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] + \frac{FV}{(1+i)^n}$

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

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

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

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

Problem Statement: Mr. Enamul has decided to start saving for his retirement. Beginning on his twenty-first birthday, he plans to invest Tk. 2,000 each birthday into a savings investment earning a 7 percent compound annual rate of interest. He will continue this savings program for a total of 10 years and then stop making payments. But his savings will continue to compound at 7 percent for 35 more years, until Enamul retires at age 65. Mr. Rafeed plans to invest TK. 2,000 a year, on each birthday, at 7 percent, and will do so for a total of 35 years. However, he will not begin his contributions until his thirty-first birthday. How much will Enamul's and Rafeed's savings programs be worth at the retirement age of 65? Who is better off financially at retirement, and by how much?

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).

$FV_{annuity} = PMT \times \left[ \frac{(1+i)^n - 1}{i} \right]$

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

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

Question 5: Risk, Capital Budgeting & WACC

Problem Statement: If a company's beta were to double, would its expected return double?

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):

$R_{i} = R_{f} + \beta_i \times (R_{M} - R_{f})$

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.

Problem Statement: Metro Limited manufactures household utensils in Bangladesh and is considering investing in a new aluminum smelting and molding plant. This plant will have a useful life of 5 years but will cost Tk. 400,000 to acquire and install with a residual value of Tk. 20,000. The plant will produce 100,000 units per year. Other estimates are given below: Selling price: Tk. 30 per unit, Direct cost: Tk. 20 per unit. Fixed cost (including depreciation) is Tk. 160,000 per annum. Marketing and promotion cost not included in the above will be Tk. 20,000 and Tk. 32,000 for years 1 and 2, respectively. Additionally, investment in debtors and stocks will increase in year 1 by Tk. 30,000 and Tk. 40,000, respectively. Creditors will also increase by Tk. 20,000 in year 1. Thus, debtors, stocks, and creditors will be recouped at the end of the machine life. The cost of capital is 18%. Corporate tax is 25% and is paid in the year in which profits are made. Depreciation is tax deductible. Required: Compute the Net Present Value of this project and advise Metro Limited whether the plant should be acquired.

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):

ParticularsYear 1Year 2Year 3Year 4Year 5
Sales Revenue3,000,0003,000,0003,000,0003,000,0003,000,000
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)000
Depreciation(76,000)(76,000)(76,000)(76,000)(76,000)
**EBIT**820,000808,000840,000840,000840,000
Tax (25%)(205,000)(202,000)(210,000)(210,000)(210,000)
EBIT(1-T)615,000606,000630,000630,000630,000
Add back Depreciation76,00076,00076,00076,00076,000
Working Capital Recovery50,000
Salvage Value20,000
Tax on Salvage (assuming no gain/loss)(0)
**Total Cash Flow**691,000682,000706,000706,000776,000

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.

Problem Statement: A colleague has been taken ill. Your managing director has asked you to take over from the colleague and to provide urgently-needed estimates of the discount rate to be used in appraising a large new capital investment. You have been given your colleague's working notes, which you believe to be numerically accurate. Working notes: Estimates for the next five years (annual averages): Stock market total return on equity: 16%, Own company dividend yield: 7%, Own company share price rise: 14%, Standard deviation of total stock market return on equity: 10%, Systematic risk of own company return on equity: 14%, Growth rate of own company earnings: 12%, Growth rate of own company dividends: 11%, Growth rate of own company sales: 13%, Treasury bill yield: 12%. The company's gearing level (by market values) is 1:2 debt to equity, and after-tax earnings available to ordinary shareholders in the most recent year were Tk. 54,000,000, of which Tk. 21,400,000 was distributed as ordinary dividends. The company has 1 million issued ordinary shares which are currently trading on the Stock Exchange at Tk. 3.21. Corporate debt may be assumed to be risk-free. The company pays tax at 30% and personal taxation may be ignored. Required: Estimate the company's weighted average cost of capital using: (i) The dividend valuation model; (ii) The capital asset pricing model. State clearly any assumptions that you make. Under what circumstances these models would be expected to produce similar values for the weighted average cost of capital?

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%.

$k_e = \text{Dividend Yield} + \text{Growth Rate} = 7\% + 11\% = 18\%$

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.

Question 6: Capital Structure, Leasing & Rights Issue

Problem Statement: What are the trade-offs in the static trade-off theory of capital structure? How is the firm's optimal capital structure determined under the assumptions of this theory? Is it possible to determine the optimal capital structure in precise term in the real world? Why or Why not? Explain.

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.

Problem Statement: The Locke Corporation has just leased a metal-bending machine that calls for annual lease payments of Tk. 30,000 payable in advance. The lease period is six years, and the lease is classified as a capital lease for accounting purposes. The company's incremental borrowing rate is 11 percent, whereas the lessor's implicit interest rate is 12 percent. Amortization of the lease in the first year amounts to Tk. 16,332. On the basis of this information, compute the following: (i) The accounting lease liability that will be shown on the balance sheet immediately after the first lease payment. (ii) The annual lease expense (amortization plus interest) in the first year as it will appear on the accounting income statement. (The interest expense is based on the accounting value determined in Part (i).)

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:

$PV = PMT + PMT \times \left[ \frac{1 - (1+i)^{-(n-1)}}{i} \right]$

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**.

Problem Statement: The Board of Directors of City Bank Limited (CBL) decided through a Board resolution to raise additional capital through rights issue to meet the new capital requirement by Bangladesh Bank. CBL plans to issue 1 new share for every 3 shares held by existing shareholders at 10% discount to its existing market price. CBL currently has 6 million shares in issue at a book value of Tk. 2 per share. CBL maintains a dividend payout ratio of 50% and earnings per share currently is Tk. 1.6. Dividend growth is 5% per annum and this is expected into the foreseeable future. CBL's cost of equity is 15%. The issue cost is Tk. 600,000. Required: Calculate: (i) The market price per share (ii) The capitalization of CBL (iii) The rights issue price (iv) The theoretical ex-right price (v) The market capitalization after the rights issue

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**.

Question 7: Risk Management & Working Capital

Problem Statement: COVID-19 has led to volatility in the international money market. Although the international business has seen some improvement, progress has been very slow. As a result, the risk of losing part of an investment due to exchange rate and currency value fluctuations are very high.

Required: Explain how Interest Rate Swap and Currency Swap can be used to mitigate the effects of market volatility.

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.

Problem Statement: The Confidence Company is attempting to establish a current asset policy. Fixed assets are Tk. 600,000 and the firm plans to maintain a 50% debt-to-assets ratio. Confidence has no operating current liabilities. The interest rate is 10% on all debt. Three alternative current asset policies are under consideration: 40%, 50% and 60% of projected sales. The company expects to earn 15% before interest and taxes on sales of Tk. 3 million. Confidence's effective tax rate is 40%. Required: What is the expected return on equity under each asset policy?

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.

Problem Statement: Porras Pottery Products, Inc., spends Tk. 220,000 per annum on its collection department. The company has Tk.12 million in credit sales, its average collection period is 2.5 months, and the percentage of bad-debt losses is 4 percent. The company believes that, if it were to double its collection personnel, it could bring down the average collection period to 2 months and bad-debt losses to 3 percent. The added cost is Tk. 180,000, bringing total collection expenditures to Tk. 400,000 annually. Is the increased effort worthwhile if the before-tax opportunity cost of funds is 20 percent? If it is 10 percent?

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**.