CMA May 2024 Examination Solutions

Solution:

The correct answer is **(c) EBIT-EPS**. The EBIT-EPS analysis is used to determine the impact of different financing options (financial leverage) on a firm's earnings per share. It shows how changes in earnings before interest and taxes (EBIT) affect earnings per share (EPS), highlighting the magnifying effect of financial leverage.

Solution:

The correct answer is **(e) Payables velocity**. Payables velocity is a measure of how quickly a company pays its suppliers, which is a key indicator of its operational performance and working capital management. The other options are capital structure or solvency ratios.

Solution:

The correct answer is **(d) To analyze variance between standard costs and actual costs**. The financial manager's control function involves ensuring that the company's financial activities are in line with its plans and objectives. Analyzing variances between standard and actual costs is a key part of this function, as it helps identify and correct deviations from the budget.

Solution:

The present value of a perpetual annuity (or perpetuity) is calculated as the annual payment divided by the interest rate.

Given: Annual Payment (A) = Tk. 1,000, Interest Rate (r) = 8% = 0.08

$PV = \frac{1,000}{0.08} = \text{Tk. } 12,500$

The correct answer is **(e) Tk. 12,500**.

Solution:

The correct answer is **(a) The expected return**. The expected return is a statistical measure of the returns on a portfolio or investment. It is calculated as the weighted average of the returns of each possible outcome, with the weights being their respective probabilities.

Solution:

According to Walter's model of dividend policy, the optimum payout ratio depends on the relationship between the firm's internal rate of return ($r$) and the cost of equity ($k_e$).

• If $r > k_e$ (growth firm), the firm should retain all earnings and the optimal payout ratio is **zero**.
• If $r < k_e$ (declining firm), the firm should distribute all earnings and the optimal payout ratio is **100%**.
• If $r = k_e$ (normal firm), the dividend policy is irrelevant and any payout ratio is optimal.

In this problem, $r = 15\%$ and $k_e = 12\%$. Since $r > k_e$, the firm is a growth firm, and it should reinvest all its earnings to maximize value. Therefore, the optimal dividend payout ratio is **(d) Zero**.

Solution:

The correct answer is **(b) Current assets**. Gross working capital refers to a firm's total current assets, which include cash, accounts receivable, inventory, and other short-term assets. Net working capital is the difference between current assets and current liabilities.

Solution:

The correct answer is **(c) The higher the yield**. Under normal conditions, the yield curve is upward-sloping. This is because investors demand a higher yield for taking on the additional risk associated with longer-term investments, such as liquidity risk and interest rate risk.

Solution:

The correct answer is **(d) Calculates the interest rate that equates outflows with subsequent inflows**. The Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of all cash flows from a project or investment equals zero. It is the rate that makes the present value of future inflows exactly equal to the initial investment outflow.

Solution:

The correct answer is **(e) The foreign exchange rate**. This is the standard term used to define the rate at which one currency will be exchanged for another.

Solution:

True. The relationship is inverse; a higher required rate of return (discount rate) leads to a lower present value for future cash inflows, thereby decreasing the project's net present value (NPV).

Solution:

False. The discount rate to be used in evaluating lease financing versus debt financing is the firm's **after-tax cost of debt**. This is because both leasing and borrowing are debt-like financing methods, and their cash flows should be discounted at the relevant after-tax debt rate.

Solution:

True. Earnings are either paid out as dividends or retained by the firm for reinvestment. They are two sides of the same coin, so increasing one automatically decreases the other.

Solution:

False. The expected return on a risk-free security is the **risk-free rate of return ($R_f$)**, which is greater than zero to compensate for inflation and the time value of money.

Solution:

False. The book value of a firm is equal to its **total assets minus its total liabilities**, which is the total equity. The common stock equity account is only a part of the total equity, which also includes retained earnings and additional paid-in capital.

Solution:

The correct matches are as follows:

• **(1) Coefficient of variation** matches with **(b) Risk per unit of expected return**. The coefficient of variation measures the risk per unit of return.
• **(2) Solvency** matches with **(e) Interest coverage**. Solvency is a measure of a firm's ability to meet its long-term obligations, and interest coverage is a key indicator of this.
• **(3) Derivative security** matches with **(g) Warrant**. A warrant is a type of derivative security that gives the holder the right to buy a firm's common stock at a predetermined price.
• **(4) Spontaneous financing** matches with **(i) Accrued expenses**. Spontaneous financing arises from a firm's day-to-day operations, such as accounts payable and accrued expenses, which grow naturally with the firm's sales.
• **(5) Capital budgeting** matches with **(j) Incremental cash flows**. Capital budgeting is the process of evaluating investment projects, and it focuses on the incremental cash flows that the project will generate.

Solution:

For a not-for-profit business, the primary goal is not profit maximization, but rather the maximization of the value of services provided to the community. As a financial manager of a not-for-profit hospital, your goals would include:

• **Cost Minimization:** Since the objective is to provide a service, you would strive to minimize costs to maximize the number of services provided with the available funds.
• **Operating Efficiency:** Maximizing operating efficiency is crucial to ensure that resources are used effectively to deliver the best possible care. This includes managing cash flow, accounts payable, and accounts receivable efficiently.
• **Liquidity Management:** Ensuring the hospital has enough cash to meet its short-term obligations is vital for its continued operation.
• **Fundraising and Resource Allocation:** You would need to manage funds from donations, grants, and other sources effectively. This includes allocating funds to the most critical and impactful projects, such as purchasing new equipment or expanding services.
• **Risk Management:** You would need to manage financial risks, such as interest rate risk and credit risk, to protect the hospital's financial stability.

Ultimately, the financial goals of a not-for-profit firm are to ensure long-term sustainability and to maximize the quality and quantity of services delivered to the community it serves.

Solution:

We will use the Present Value of an Ordinary Annuity formula:

Given: PV = Tk. 2,000,000, n = 25 years.

i. Defendants' offer:

PMT = Tk. 156,000

$2,000,000 = 156,000 \times \left[ \frac{1 - (1+i)^{-25}}{i} \right]$

$\frac{2,000,000}{156,000} = 12.8205 = \left[ \frac{1 - (1+i)^{-25}}{i} \right]$

Using a financial calculator or trial and error, we find that the interest rate that results in a present value factor of 12.8205 for 25 periods is approximately **6%**.

ii. Amina's counteroffer:

PMT = Tk. 255,000

$2,000,000 = 255,000 \times \left[ \frac{1 - (1+i)^{-25}}{i} \right]$

$\frac{2,000,000}{255,000} = 7.8431 = \left[ \frac{1 - (1+i)^{-25}}{i} \right]$

Using a financial calculator or trial and error, we find that the interest rate that results in a present value factor of 7.8431 for 25 periods is approximately **12%**.

iii. Annual payment at 9%:

We need to solve for PMT when PV = Tk. 2,000,000, n = 25, and i = 9% = 0.09.

First, calculate the PV factor: $\left[ \frac{1 - (1.09)^{-25}}{0.09} \right] = \left[ \frac{1 - 0.11604}{0.09} \right] = \left[ \frac{0.88396}{0.09} \right] = 9.8218$

$2,000,000 = PMT \times 9.8218$

$PMT = \frac{2,000,000}{9.8218} = \text{Tk. } 203,636.56$

An annual payment of **Tk. 203,637** would be acceptable to Amina.

Solution:

i. Shareholder value maximization vs. social responsibility:

Shareholder value maximization is not necessarily inconsistent with social responsibility, especially in the long run. In fact, they can be mutually reinforcing. While social responsibility may involve a short-term cost, it can lead to long-term benefits that increase shareholder value. For example:

• **Enhanced Reputation:** Socially responsible actions can improve a company's public image and brand reputation, leading to increased customer loyalty and a wider customer base.
• **Reduced Risk:** Adhering to environmental and social standards can reduce regulatory and legal risks, saving the company from potential fines and litigation costs.
• **Attracting Talent:** A socially responsible company is often more attractive to talented employees who want to work for an organization with a positive impact, leading to higher productivity and lower employee turnover.

Therefore, while some immediate social initiatives may seem costly, their long-term effects on brand loyalty, risk reduction, and talent acquisition can lead to sustainable growth and, ultimately, greater shareholder value.

ii. Non-financial objectives:

Non-financial objectives are goals that an organization sets that are not directly related to monetary outcomes, but are crucial for long-term success. Two examples are:

• **Customer Satisfaction:** This objective focuses on meeting and exceeding customer expectations. It can be measured through surveys, feedback, and repeat business. High customer satisfaction often leads to increased sales, brand loyalty, and positive word-of-mouth marketing, which indirectly contributes to financial success.
• **Employee Development and Morale:** This objective involves investing in employee training, creating a positive work environment, and ensuring fair compensation. A motivated and skilled workforce is more productive, innovative, and loyal. This reduces turnover costs and enhances the quality of products and services, which ultimately boosts the firm's financial performance.

Solution:

To determine a suitable range of valuations for Mayfly, we will use the Price-to-Earnings (P/E) ratio valuation method. The formula is: **Value of Equity = Expected Earnings $\times$ P/E Ratio**.

First, we need to calculate the average earnings for Mayfly over the past five years to smooth out any fluctuations.

Average Earnings = $\frac{50,000 + 72,000 + 68,000 + 71,000 + 75,000}{5} = \frac{336,000}{5} = \text{Tk. } 67,200$

Now, we can use the P/E ratios of the comparable companies to establish a valuation range.

• **Wasp (Lower End):** Wasp has a poor profit record and a P/E of 7. This can be used to set a conservative, lower bound for Mayfly's valuation.

  Value = $67,200 \times 7 = \text{Tk. } 470,400$

• **Industry Average (Mid-Range):** The industry average P/E is 10. This provides a central estimate for a company with typical growth prospects.

  Value = $67,200 \times 10 = \text{Tk. } 672,000$

• **Bumblebee (Upper End):** Bumblebee has very good growth prospects and a P/E of 15. Since the latest earnings for Mayfly (Tk. 75,000) show a good trend, a valuation closer to this P/E ratio may be justified. We can use this to set an aggressive, upper bound for the valuation.

  Value = $67,200 \times 15 = \text{Tk. } 1,008,000$

Based on this analysis, a suitable range of valuations for the shares of Mayfly would be from **Tk. 470,400 to Tk. 1,008,000**. The final negotiated price would depend on the specific growth prospects and other non-financial factors of Mayfly.

Solution:

i. Net Investment (Initial Outlay):

The net investment includes the cost of the new asset, the initial increase in net working capital, and the cash flow from the sale of the old asset (including any tax implications).

• **Cost of New Unit:** Tk. 700,000 (unit) + Tk. 50,000 (installation) = Tk. 750,000
• **Initial Working Capital Increase:** Tk. 40,000
• **Cash Flow from Sale of Old Unit:**

  Sale Price = Tk. 275,000

  Book Value = Tk. 250,000

  Taxable Gain = Sale Price - Book Value = $275,000 - 250,000 = \text{Tk. } 25,000$

  Tax on Gain = $25,000 \times 0.40 = \text{Tk. } 10,000$

  Net Cash from Sale = Sale Price - Tax on Gain = $275,000 - 10,000 = \text{Tk. } 265,000$

**Net Investment** = Cost of New Unit + Initial NWC - Net Cash from Sale of Old Unit

= $750,000 + 40,000 - 265,000 = \text{Tk. } 525,000$

ii. Annual Net Cash Flows:

The annual net cash flow is the sum of the incremental after-tax operating income, the incremental tax shield from depreciation, and the changes in working capital.

• **Incremental Revenues:** Tk. 100,000
• **Incremental Cost Savings:** Tk. 20,000
• **Incremental Depreciation:**

  New Dep. = $\frac{750,000}{5} = \text{Tk. } 150,000$

  Old Dep. = Tk. 50,000

  Incremental Dep. = $150,000 - 50,000 = \text{Tk. } 100,000$

Particulars	Amount (Tk.)
Incremental Revenues	100,000
Incremental Cost Savings	20,000
Incremental Depreciation	(100,000)
Incremental EBIT	20,000
Tax (40%)	(8,000)
Incremental EAT	12,000
Add back Incremental Dep.	100,000
Annual Cash Flow from Operations	112,000

We must also account for the change in net working capital (NWC).

• **Annual NWC Increase (Years 1-4):** Tk. 10,000

  Annual net cash flow (Y1-4) = $112,000 - 10,000 = \text{Tk. } 102,000$

• **Terminal Cash Flow (Year 5):**

  Annual Cash Flow from Operations = Tk. 112,000

  Salvage Value (after-tax) = Salvage Value - Tax on Gain

  Book Value = Tk. 0. Taxable Gain = $70,000 - 0 = \text{Tk. } 70,000$.

  Tax on Gain = $70,000 \times 0.40 = \text{Tk. } 28,000$

  After-tax Salvage Value = $70,000 - 28,000 = \text{Tk. } 42,000$

  Recovery of Total NWC = Initial NWC + Total Annual Increases = $40,000 + (4 \times 10,000) = \text{Tk. } 80,000$

  Terminal Cash Flow (Y5) = Annual CF + After-tax Salvage + NWC Recovery

  = $112,000 + 42,000 + 80,000 = \text{Tk. } 234,000$

The annual net cash flow for Years 1-4 is **Tk. 102,000**. The net cash flow for Year 5 is **Tk. 234,000**.

Solution:

i. Firm's Market Value Capital Structure:

We need to calculate the market value of the firm's common stock and debt.

• **Market Value of Equity (E):**

  Shares outstanding = 8.7 million

  Price per share = Tk. 37

  $E = 8,700,000 \times 37 = \text{Tk. } 321,900,000$

• **Market Value of Debt (D):**

  Bonds outstanding = 230,000

  Price per bond = $104\% \times 1,000 = \text{Tk. } 1,040$

  $D = 230,000 \times 1,040 = \text{Tk. } 239,200,000$

• **Total Firm Value (V):**

  $V = E + D = 321,900,000 + 239,200,000 = \text{Tk. } 561,100,000$

• **Capital Structure Weights:**

  Weight of Equity ($W_E$) = $\frac{E}{V} = \frac{321,900,000}{561,100,000} = 0.5737$ or $57.37\%$

  Weight of Debt ($W_D$) = $\frac{D}{V} = \frac{239,200,000}{561,100,000} = 0.4263$ or $42.63\%$

ii. Discount Rate for a New Project (WACC):

We need to calculate the firm's Weighted Average Cost of Capital (WACC), which is the appropriate discount rate for a typical project.

• **Cost of Equity ($R_E$):** Using the Capital Asset Pricing Model (CAPM).

  $R_E = R_f + \beta \times (\text{Market Risk Premium})$

  $R_E = 3.5\% + 1.20 \times 7\% = 3.5\% + 8.4\% = 11.9\%$

• **Cost of Debt ($R_D$):** We need to find the Yield to Maturity (YTM) of the bonds.

  Bond Price (PV) = Tk. 1,040

  Par Value (FV) = Tk. 1,000

  Coupon (PMT) = $1,000 \times 6.4\% = \text{Tk. } 64$ annually, or $\frac{64}{2} = \text{Tk. } 32$ semiannually.

  Periods (N) = $20 \text{ years} \times 2 = 40$ semiannual periods.

  Using a financial calculator, the semiannual yield is approximately 3.01%. The annual YTM is $3.01\% \times 2 = 6.02\%$.

  After-tax cost of debt = $R_D(1-T_C) = 6.02\% \times (1 - 0.35) = 6.02\% \times 0.65 = 3.91\%$

• **WACC Calculation:**

  $WACC = (W_E \times R_E) + (W_D \times R_D(1-T_C))$

  $WACC = (0.5737 \times 11.9\%) + (0.4263 \times 3.91\%)$

  $WACC = 6.827\% + 1.667\% = 8.494\%$

The firm should use a discount rate of approximately **8.49%** to evaluate a new project with similar risk.

Solution:

i. Current value of the firm:

The current value of the firm is the present value of the expected future value plus the value of the current dividend. Since the payout policy is 100%, the entire Tk. 85,000 of net income will be paid out as a dividend.

$V_0 = \frac{\text{Future Value} + \text{Dividend}}{\text{Discount Factor}}$

$V_0 = \frac{1,725,000 + 85,000}{1 + 0.12} = \frac{1,810,000}{1.12} = \text{Tk. } 1,616,071.43$

The current value of the firm is **Tk. 1,616,071.43**.

ii. Ex-dividend price:

The current dividend per share (D) is: $D = \frac{85,000}{25,000} = \text{Tk. } 3.40$

The current price per share is: $P_0 = \frac{1,616,071.43}{25,000} = \text{Tk. } 64.64$

The ex-dividend price is the current price minus the dividend per share: $P_{ex} = P_0 - D = 64.64 - 3.40 = \text{Tk. } 61.24$

The ex-dividend price of the stock is **Tk. 61.24**.

iii. Comment on the board's claim:

According to the Modigliani and Miller (M&M) theory of dividend irrelevance (assuming no taxes or transaction costs), a firm's dividend policy has no effect on its value or stock price. The board members' claim that a low dividend is depressing the price is **incorrect** under this theory. The value of the firm is determined by its earning power and its assets, not by how it divides its cash flow between dividends and retained earnings.

If Lily sells new shares to finance a higher dividend, the value of the firm remains constant, but the number of shares increases.

Proposed new dividend per share = Tk. 4.60

Total dividend payout = $4.60 \times 25,000 = \text{Tk. } 115,000$

Required new capital = Total dividend - Net income = $115,000 - 85,000 = \text{Tk. } 30,000$

The new shares will sell at the ex-dividend price. The ex-dividend price is the value of the firm one year from now divided by the number of shares. The total value of the firm is the same. The firm's expected value is still Tk. 1,725,000, and the initial value is Tk. 1,616,071.43. The price of the stock one year from now (ex-dividend) will be the same as if the old policy was followed. The price per share is:

$P_1 = \frac{V_1}{\text{Number of shares}} = \frac{1,725,000}{25,000} = \text{Tk. } 69$

The current price of the stock ($P_0$) under the new policy would be the present value of the future price and dividend: $P_0 = \frac{P_1 + D_1}{1+k_e} = \frac{69 + 4.60}{1.12} = \frac{73.60}{1.12} = \text{Tk. } 65.71$

This is higher than the original current price, which seems to contradict M&M. The key is that the number of shares changes. Let $N_1$ be the number of new shares to be sold.

Total dividend = $D \times (\text{Initial Shares}) = 4.60 \times 25,000 = \text{Tk. } 115,000$

New shares sold = $\frac{\text{Funds required}}{\text{Price per new share}}$

The new shares will sell at the ex-dividend price, which we need to find. The price of the stock after the dividend is paid will be the value of the firm minus the dividend, divided by the number of shares.

Let's use a simpler M&M approach. The value of the firm is constant. The total value of the firm's equity before the dividend is paid is Tk. 1,616,071.43.

Total funds available for dividend = Retained earnings + New equity from shares = $85,000 + \text{New Shares Sold} \times P_{new}$

Since $P_{new}$ is the ex-dividend price, which we are looking for. Let $P_{new} = P_{ex}$.

Total dividend = $4.60 \times 25,000 = \text{Tk. } 115,000$

Required funds = $115,000 - 85,000 = \text{Tk. } 30,000$

The value of the firm's assets after paying the dividend is $V_0 - \text{Total Dividend} = 1,616,071.43 - 115,000 = \text{Tk. } 1,501,071.43$

The ex-dividend price is the value of the firm's assets per share after the dividend is paid.

The number of new shares is: $N_{new} = \frac{\text{Required Funds}}{P_{ex}}$

Total shares after new issue: $25,000 + N_{new}$

The price per share after the dividend is paid is: $P_{ex} = \frac{V_0 - 115,000}{25,000 + N_{new}}$

This creates a circular reference. Let's use the M&M formula for a new share issue:

Value of the firm after the dividend: $V_L = V_U - D_1 + F_S$

The price of the new shares will be the ex-dividend price of the existing shares.

Value of Firm at t=1 (Unlevered) = Tk. 1,725,000.

Value of Firm at t=0 = $\frac{1,725,000}{1.12} + \frac{85,000}{1.12} = \text{Tk. } 1,616,071.43$ (already calculated).

The dividend is being paid from both internal and external funds. The value of the stock will not change. The price per share will still be Tk. 64.64, and the ex-dividend price will still be Tk. 61.24. The new shares will sell at the ex-dividend price of **Tk. 61.24**.

Number of new shares = $\frac{\text{Required new capital}}{\text{Price of new shares}} = \frac{30,000}{61.24} = 490$ shares.

Approximately **490 new shares** will be sold.

Solution:

We will compare the Net Present Value of the cost of leasing (NPV of Lease) to the Net Present Value of the cost of owning (NPV of Buy). The appropriate discount rate is the after-tax cost of debt, which is $9\% \times (1 - 0.35) = 5.85\%$.

i. Lease vs. Buy Decision:

Let's calculate the NPV of the cost for both options.

PV of Leasing:

Lease payments are Tk. 830,000 at the beginning of each year. The after-tax cost is $830,000 \times (1 - 0.35) = \text{Tk. } 539,500$.

Year	After-tax Lease Payment	PV Factor (5.85%)	PV of Cost
0	539,500	1.0000	539,500.00
1	539,500	0.9447	509,697.15
2	539,500	0.8925	481,593.75
3	539,500	0.8432	454,954.40
**Total PV Cost of Leasing**	**Tk. 1,985,745.30**

Note: The PV cost is the total of the discounted after-tax payments. Since payments are at the beginning of the year, Year 0 payment is not discounted.

PV of Buying:

This is the initial outlay minus the present value of the tax shield from depreciation and interest payments.

Initial Cost = Tk. 2,800,000

Annual Depreciation = $\frac{2,800,000}{4} = \text{Tk. } 700,000$

Depreciation Tax Shield = $700,000 \times 0.35 = \text{Tk. } 245,000$ per year.

Year	Beginning Balance	Interest (9%)	Principal	Total Payment	Interest Tax Shield (35%)	Depreciation Tax Shield (35%)	PV Factor (5.85%)	PV of Inflows
1	2,800,000	252,000	700,000	952,000	88,200	245,000	0.9447	314,640
2	2,100,000	189,000	700,000	889,000	66,150	245,000	0.8925	277,411
3	1,400,000	126,000	700,000	826,000	44,100	245,000	0.8432	243,962
4	700,000	63,000	700,000	763,000	22,050	245,000	0.7966	212,859

PV of all tax shields = $314,640 + 277,411 + 243,962 + 212,859 = \text{Tk. } 1,048,872$

PV cost of buying = Initial Cost - PV of Tax Shields

= $2,800,000 - 1,048,872 = \text{Tk. } 1,751,128$

**Decision:** Since the PV cost of buying (**Tk. 1,751,128**) is less than the PV cost of leasing (**Tk. 1,985,745.30**), Wolfson should **purchase** the machine with bank financing.

ii. Annual Lease Payment for Indifference:

For Wolfson to be indifferent, the PV cost of leasing must equal the PV cost of buying.

PV Cost of Buying = Tk. 1,751,128

Let $L$ be the annual lease payment. The PV cost of leasing is the present value of the after-tax lease payments. The payments are an annuity due.

PV factor for 4-year annuity due at 5.85% = $1 + \frac{1 - (1.0585)^{-3}}{0.0585} = 1 + \frac{1 - 0.8432}{0.0585} = 1 + \frac{0.1568}{0.0585} = 1 + 2.6803 = 3.6803$

$1,751,128 = L \times 0.65 \times 3.6803$

$1,751,128 = L \times 2.3922$

$L = \frac{1,751,128}{2.3922} = \text{Tk. } 732,019.23$

The annual lease payment that would make Wolfson indifferent is **Tk. 732,019.23**.

Solution:

While the Founder's point about investing idle cash for returns is valid, there are three primary motives for a firm to hold cash that outweigh the opportunity cost of lost investment income. These are often referred to as the "cash holding motives":

• **Transactions Motive:** A firm needs to hold cash to meet its day-to-day operational needs. This includes paying for raw materials, wages, rent, and utility bills. These outflows rarely match the timing of cash inflows from sales. Holding a certain amount of cash ensures that the company can meet these obligations smoothly and avoid disrupting its business operations.
• **Precautionary Motive:** This refers to holding cash as a buffer against unexpected events or emergencies. For a growing technology company, this could be anything from a sudden decline in sales, a major equipment failure, or an unforeseen market downturn. Having a precautionary cash balance allows the firm to handle these shocks without having to resort to costly emergency financing or selling off assets.
• **Speculative Motive:** This motive involves holding cash to take advantage of future investment opportunities. For a technology company, this could mean holding cash to quickly acquire a competitor, invest in new R&D, or purchase a new patent at a favorable price. By holding cash, the firm is prepared to seize these opportunities as they arise, potentially leading to higher returns than those from a typical investment in securities.

Solution:

A **forward premium** occurs when a currency's forward exchange rate is higher than its spot exchange rate. This means that the market expects the currency to appreciate against the other currency in the future. In other words, you have to pay more for the currency in the forward market than you would in the spot market.

A **forward discount** occurs when a currency's forward exchange rate is lower than its spot exchange rate. This means the market expects the currency to depreciate against the other currency in the future. You can get the currency at a cheaper rate in the forward market compared to the spot market.

Example:

Assume the following exchange rates:

• Spot Rate: Tk. 110.00 / US\$
• One-year Forward Rate: Tk. 112.50 / US\$

In this case, the US dollar is selling at a forward **premium** because its forward rate (Tk. 112.50) is higher than its spot rate (Tk. 110.00). The premium for the US dollar is Tk. 2.50. Conversely, the Bangladeshi Taka (Tk.) is selling at a forward **discount** because it is expected to depreciate against the US dollar.

Solution:

i. Funds to be released:

Released funds are equal to the total float, which is the amount of funds in transit that cannot be used by the company. The float is calculated as the daily check volume multiplied by the number of days of collection delay.

Number of outlets = 41

Daily receipts per outlet = Tk. 5,000

Days of collection float = 6 days

Total Daily Receipts = $41 \times 5,000 = \text{Tk. } 205,000$

Released Funds (Float) = Total Daily Receipts $\times$ Days of Float

$= 205,000 \times 6 = \text{Tk. } 1,230,000$

The amount of funds that will be released is **Tk. 1,230,000**.

ii. Net released funds:

The net released funds account for the compensating balances required by the local banks to offset the loss of float.

Total increase in compensating balances = Number of outlets $\times$ Compensating balance per outlet

= $41 \times 15,000 = \text{Tk. } 615,000$

Net Released Funds = Gross Released Funds - Compensating Balances

= $1,230,000 - 615,000 = \text{Tk. } 615,000$

The net amount of funds released is **Tk. 615,000**.

iii. Worthwhileness of the arrangement:

We need to compare the benefits of the released funds to the costs of the electronic transfer system.

Annual Benefit from Released Funds = Net Released Funds $\times$ Interest Rate

= $615,000 \times 0.10 = \text{Tk. } 61,500$

Annual Cost of Electronic Transfers = Cost per transfer $\times$ Transfers per store $\times$ Number of stores

= $7 \times 250 \times 41 = \text{Tk. } 71,750$

Since the annual benefit (**Tk. 61,500**) is **less than** the annual cost (**Tk. 71,750**), the proposed electronic funds transfer arrangement is **not worthwhile**.

Solution:

i. Should credit be extended (No defaults)?

We compare the cost of extending credit to the present value of the benefits. The benefits come from the current period's profit and the future profit from repeat customers.

Number of units = 125

Variable Cost per unit ($C$) = Tk. 11,400

Credit Price per unit ($P$) = Tk. 13,000

Required Return per period ($r$) = 1.9% = 0.019

Profit per unit = $P - C = 13,000 - 11,400 = \text{Tk. } 1,600$

Future value of repeat customers = $\frac{\text{Profit}}{\text{Required Return}}$

Number of repeat customers = $125 \times 0.30 = 37.5$ units. We can't have half a unit, so we'll use 37.5 in the calculation.

PV of profit from repeat customers = $\frac{37.5 \times (13,000 - 11,400)}{0.019} = \frac{37.5 \times 1,600}{0.019} = \frac{60,000}{0.019} = \text{Tk. } 3,157,894.74$

Total PV of benefits = PV of current profit + PV of future profit from repeat customers

= $125 \times (13,000 - 11,400) + \text{PV of repeat customers}$

= $125 \times 1,600 + 3,157,894.74$

= $200,000 + 3,157,894.74 = \text{Tk. } 3,357,894.74$

Cost of extending credit = Variable cost of current order = $125 \times 11,400 = \text{Tk. } 1,425,000$

Net Present Value (NPV) = PV of benefits - Cost of extending credit

$NPV = 3,357,894.74 - 1,425,000 = \text{Tk. } 1,932,894.74$

Since the NPV is positive, credit should be extended. Yes, credit should be extended.

ii. Should the orders be filled (with a 15% default rate)?

We need to adjust the calculation to account for the probability of default.

Probability of collection = $1 - 0.15 = 0.85$

Expected PV of benefits = (PV of current profit $\times$ probability of collection) + (PV of future profit $\times$ probability of collection)

Expected number of repeat customers = $125 \times (1-0.15) \times 0.30 = 125 \times 0.85 \times 0.30 = 31.875$ units.

Expected PV of future profit = $\frac{31.875 \times 1,600}{0.019} = \frac{51,000}{0.019} = \text{Tk. } 2,684,210.53$

Expected PV of current profit (sales) = $125 \times 13,000 \times 0.85 = \text{Tk. } 1,381,250$

Expected PV of total benefits = $1,381,250 + 2,684,210.53 = \text{Tk. } 4,065,460.53$

Cost of extending credit = Variable cost of current order = $125 \times 11,400 = \text{Tk. } 1,425,000$

Expected NPV = Expected PV of total benefits - Cost of extending credit

$Expected NPV = 4,065,460.53 - 1,425,000 = \text{Tk. } 2,640,460.53$

Since the expected NPV is positive, the orders **should be filled** despite the 15% probability of default.