CMA January 2025 Examination Solutions

Solution:

The correct answer is **(a) Bond prices to fall more than stock prices**. When market interest rates rise, the value of existing bonds with lower coupon rates falls to make their yield competitive with new, higher-rate bonds. The longer the maturity of the bond, the more sensitive its price is to interest rate changes. Stock prices also react to rising interest rates (which can increase a company's borrowing costs), but bonds, with their fixed cash flows, are generally more sensitive to this change.

Solution:

The correct answer is **(b) Increase the price of stock**. In a reverse stock split, a company reduces the number of its outstanding shares. For example, a 1-for-10 split would give an investor one new share for every ten shares they previously held. This directly increases the price per share, often to avoid being delisted from a stock exchange due to a low share price.

Solution:

The correct answer is **(c) Yield**. Yield is the income return on an investment, such as the interest or dividends received from holding a security. This is different from a capital gain, which is the profit from selling an asset for more than the purchase price.

Solution:

The correct answer is **(a) Operating leverage**. Operating leverage is a measure of how sensitive a company's operating income is to changes in sales. A higher degree of operating leverage means a firm has a high proportion of fixed costs relative to variable costs. Financial leverage, by contrast, relates to the use of debt financing and its impact on a firm's earnings per share.

Solution:

The correct answer is **(c) The homemade leverage**. According to the Modigliani and Miller (M&M) theory of dividend irrelevance, investors can replicate any dividend policy they desire by buying or selling shares. This ability to create "homemade dividends" makes a firm's dividend policy irrelevant to its value in a perfect capital market.

Solution:

The correct answer is **(c) The riskiness of projected cash flows depends upon how the firm is financed**. This statement is the essence of financial leverage. By taking on debt, a firm introduces fixed interest payments. While this can magnify returns during good times, it also increases the volatility and risk of cash flows available to equity holders, making them more risky.

Solution:

The correct answer is **(a) The company's net income will increase**. By issuing common stock and repaying debt, the company's interest expense will decrease. Since EBIT remains the same, a lower interest expense will lead to a higher earnings before tax (EBT), which means both taxable income and net income will increase. As a result, the company will also pay more in taxes, not less.

Solution:

The correct answer is **(b) Market risk**. Market risk, also known as systematic risk, is the risk inherent in the entire market or a market segment. It affects the entire economy and cannot be eliminated through diversification. Examples include inflation, interest rate changes, and recessions.

Solution:

We can find the required return using the Capital Asset Pricing Model (CAPM):

Given: $R_{f} = 6\%$, $R_{M} = 12\%$, and $\beta = 1.2$.

$R_{i} = 6\% + 1.2 \times (12\% - 6\%)$

$R_{i} = 6\% + 1.2 \times 6\% = 6\% + 7.2\% = 13.2\%$

The correct answer is **(d) 13.2%**.

Solution:

The relationship is reciprocal. If $1 \text{ USD} = 1.0279 \text{ EUR}$, then to find out how many dollars one euro buys, you simply take the inverse of the given rate.

The correct answer is **(a) 0.9729**.

Solution:

True. The formula for the future value interest factor is $FVIF = (1+i)^n$. The formula for the present value interest factor is $PVIF = \frac{1}{(1+i)^n}$. As such, they are reciprocals of each other.

Solution:

False. The capital structure that maximizes a firm's stock price is called the **optimal capital structure**. The target capital structure is the mix of debt and equity that a firm strives to maintain over time, which may not be the optimal one at all times.

Solution:

False. The amount to which a cash flow or series of cash flows will grow is called its **future value**. An annuity is a series of equal payments made at regular intervals, not the value those payments grow to.

Solution:

False. The tax advantage of debt, known as the **tax shield**, is only beneficial to a firm with a positive taxable income to offset. A firm that is losing money has no tax liability, so it cannot benefit from the tax deductibility of its interest payments.

Solution:

False. The right described is called a **preemptive right**, not a common right. Preemptive rights are often included in a company's charter to protect existing shareholders from the dilution of their ownership interest when new stock is issued.

Solution:

The correct matches are as follows:

• **(1) Operating cycle** matches with **(f) Working capital**. The operating cycle is a key metric in working capital management, measuring the time it takes for a company to convert raw materials into cash from sales.
• **(2) Financial leverage** matches with **(e) Capital structure**. Financial leverage is the degree to which a firm uses debt to finance its assets, which is a central component of a firm's capital structure.
• **(3) Private placement** matches with **(c) Capital market**. A private placement is a way to raise capital by issuing securities directly to a small number of investors, bypassing the public capital markets.
• **(4) Covenants** matches with **(d) Bond indenture**. Covenants are clauses in a bond indenture (the legal document for a bond) that specify the rights and restrictions of the bond issuer and holder.
• **(5) Trend analysis** matches with **(i) Growth**. Trend analysis involves comparing financial data over time to identify patterns and trends, which is often used to analyze a company's growth trajectory.

Solution:

To determine which project maximizes shareholder wealth, we calculate the expected gross profit for each project.

• **Project 1 Expected Profit:**

  $=(0 \times 0.3333) + (3,000,000 \times 0.3333) + (9,000,000 \times 0.3333)$

  $ = 0 + 999,900 + 2,999,700 \approx \text{Tk. } 4,000,000$

• **Project 2 Expected Profit:**

  $=(600,000 \times 0.50) + (900,000 \times 0.50)$

  $ = 300,000 + 450,000 = \text{Tk. } 750,000$

Since **Project 1** has a significantly higher expected gross profit (Tk. 4,000,000 vs. Tk. 750,000), it is the project that maximizes shareholder wealth.

Now, we determine which compensation contract the manager would prefer if Project 1 is chosen. We compare the expected compensation under each contract.

• **Contract 1 (Flat Fee):**

  The manager's compensation is a fixed Tk. 300,000, regardless of the outcome.

• **Contract 2 (10% of Profits):**

  $Expected\ Compensation = (0 \times 0.10 \times 0.3333) + (3,000,000 \times 0.10 \times 0.3333) + (9,000,000 \times 0.10 \times 0.3333)$

  $ = 0 + 99,990 + 299,970 \approx \text{Tk. } 400,000$

The manager would prefer the **10 percent of corporate profits** contract because the expected compensation (Tk. 400,000) is higher than the flat fee (Tk. 300,000). This aligns the manager's incentives with shareholder wealth maximization.

Solution:

First, let's find the market risk premium using the CAPM equation for the stock: $R_i = R_{f} + \beta \times (R_M - R_{f})$.

$11.6\% = 3.6\% + 1.08 \times (R_M - R_{f})$

$8.0\% = 1.08 \times (R_M - R_{f}) \implies R_M - R_{f} = 7.41\%$

i. Expected return for an equally invested portfolio:

Portfolio Return = ($w_{stock} \times R_{stock}$) + ($w_{rf} \times R_{rf}$)

$= (0.5 \times 11.6\%) + (0.5 \times 3.6\%) = 5.8\% + 1.8\% = 7.6\%$

ii. Portfolio weights for a beta of 0.50:

Portfolio Beta = ($w_{stock} \times \beta_{stock}$) + ($w_{rf} \times \beta_{rf}$)

Since the risk-free asset has a beta of 0, we get: $0.50 = (w_{stock} \times 1.08) + ((1 - w_{stock}) \times 0)$

$w_{stock} = \frac{0.50}{1.08} \approx 0.463$ or **46.3%**.

$w_{rf} = 1 - 0.463 = 0.537$ or **53.7%**.

iii. Portfolio beta for an expected return of 10.5%:

First, find the weights. $10.5\% = (w_{stock} \times 11.6\%) + ((1 - w_{stock}) \times 3.6\%)$

$10.5 = 11.6w_{stock} + 3.6 - 3.6w_{stock}$

$6.9 = 8w_{stock} \implies w_{stock} = \frac{6.9}{8} = 0.8625$

Now, calculate the beta. $\beta_{portfolio} = (0.8625 \times 1.08) + ((1 - 0.8625) \times 0) = 0.9315$

The portfolio's beta is **0.9315**.

iv. Portfolio weights for a beta of 2.16:

$2.16 = (w_{stock} \times 1.08) + ((1 - w_{stock}) \times 0)$

$w_{stock} = \frac{2.16}{1.08} = 2$ or **200%**.

$w_{rf} = 1 - 2 = -1$ or **-100%**.

Interpretation: A 200% weight in the stock and a -100% weight in the risk-free asset means the investor has **borrowed 100% of the portfolio value at the risk-free rate** to invest an amount equal to 200% of the portfolio value in the stock. This strategy is known as using financial leverage to increase portfolio returns and risk beyond the standard market exposure.

Solution:

We can use the multi-stage dividend discount model to solve for the dividend payment ($D_1$). The price of the stock is the sum of the present values of the dividends over the next two years, plus the present value of the stock price at the end of year 2 (which is the start of the constant growth phase).

Given: $P_0 = \$59$, $k_e = 11\%$, $g = 3.5\%$. $D_1 = D_2$.

where $P_2$ is the price at the end of year 2, calculated using the Gordon Growth Model ($P_t = \frac{D_{t+1}}{k_e-g}$):

Since $D_1 = D_2$, we can substitute into the main formula:

$59 = \frac{D_1}{1.11} + \frac{D_1}{1.2321} + \frac{D_1(1.035)}{0.075 \times 1.2321}$

$59 = 0.9009D_1 + 0.8116D_1 + \frac{1.035D_1}{0.0924}$

$59 = 1.7125D_1 + 11.1991D_1 = 12.9116D_1$

$D_1 = \frac{59}{12.9116} \approx \$4.57$

The next year's dividend payment ($D_1$) is approximately **\$4.57**.

Solution:

The value of a call option ($C$) using the Black-Scholes model is calculated as follows:

Given: Stock Price ($S$) = Tk. 33, Strike Price ($K$) = Tk. 33, Risk-free rate ($r_f$) = 10% = 0.10, Time to maturity ($t$) = 0.50 years.

We are also provided with the values for $N(d_1)$ and $N(d_2)$.

$N(d_1) = 0.63369$

$N(d_2) = 0.55155$

First, let's calculate the present value of the strike price:

$PV(K) = K \times e^{-r_f \times t} = 33 \times e^{-0.10 \times 0.50} = 33 \times e^{-0.05}$

Using a calculator, $e^{-0.05} \approx 0.9512$.

$PV(K) = 33 \times 0.9512 = \text{Tk. } 31.39$

Now, substitute the values into the Black-Scholes formula:

$C = (33 \times 0.63369) - (31.39 \times 0.55155)$

$C = 20.91177 - 17.31174 \approx \text{Tk. } 3.60$

The value of the call option is approximately **Tk. 3.60**.

Solution:

First, we calculate the initial investment and the annual cash flows over the project's life. The initial investment includes the machine cost and the initial working capital investment.

Initial Investment (Year 0):

= Cost of machine + Initial net working capital (NWC)

= $1,200,000 + 200,000 = \text{Tk. } 1,400,000$

Depreciation Expense:

Annual depreciation = $\frac{\text{Cost}}{\text{Life}} = \frac{1,200,000}{5} = \text{Tk. } 240,000$

Project Cash Flows:

Year	0	1	2	3	4	5
Initial Outlay	(1,400,000)
Revenues (25,000 units)		1,175,000	1,210,250	1,246,558	1,283,955	1,322,474
Variable Costs (25,000 units)		(425,000)	(442,000)	(459,680)	(478,067)	(497,190)
Fixed Costs		(235,000)	(235,000)	(235,000)	(235,000)	(235,000)
Depreciation		(240,000)	(240,000)	(240,000)	(240,000)	(240,000)
EBIT		275,000	293,250	311,878	330,888	350,284
Tax (21%)		(57,750)	(61,583)	(65,494)	(69,486)	(73,559)
Net Income		217,250	231,667	246,384	261,402	276,725
Add Back Depreciation		240,000	240,000	240,000	240,000	240,000
Annual NWC Change						200,000
Terminal Value
**Total Cash Flow**	(1,400,000)	457,250	471,667	486,384	501,402	716,725

Note: The NWC of Tk. 200,000 is recovered in year 5. We calculate the PV of all cash flows at the 11% discount rate.

$NPV = -1,400,000 + \frac{457,250}{1.11^1} + \frac{471,667}{1.11^2} + \frac{486,384}{1.11^3} + \frac{501,402}{1.11^4} + \frac{716,725}{1.11^5}$

$NPV = -1,400,000 + 411,937 + 381,644 + 355,510 + 330,899 + 425,142$

$NPV \approx \text{Tk. } 505,132$

The NPV of the investment is approximately **Tk. 505,132**.

Solution:

Operating cash flow (OCF) can be calculated as: $OCF = (P-v)Q - F - \text{Depreciation}) \times (1-T) + \text{Depreciation}$.

The sensitivity of OCF to changes in quantity sold ($Q$) is the derivative of the OCF with respect to $Q$.

This formula measures the change in OCF for every one-unit change in quantity sold. Given the values:

Price per unit ($P$) = Tk. 41

Variable cost per unit ($v$) = Tk. 24

Tax rate ($T$) = 23% or 0.23

Sensitivity = $(41 - 24) \times (1 - 0.23) = 17 \times 0.77 = \text{Tk. } 13.09$

The operating cash flow is sensitive to a change in quantity sold by **Tk. 13.09** per unit.

Solution:

We can solve for the debt-equity ratio using the WACC formula. The WACC is a weighted average of the costs of equity and debt, with weights determined by the firm's capital structure.

Let the debt-equity ratio be $\frac{D}{E} = x$. We know that $V = E+D$, so we can express the weights in terms of $x$.

$\frac{E}{V} = \frac{E}{E+D} = \frac{1}{1 + \frac{D}{E}} = \frac{1}{1+x}$

$\frac{D}{V} = \frac{D}{E+D} = \frac{\frac{D}{E}}{\frac{E}{E}+\frac{D}{E}} = \frac{x}{1+x}$

Substitute these into the WACC formula:

$0.091 = \left( \frac{1}{1+x} \right) \times 0.11 + \left( \frac{x}{1+x} \right) \times 0.064 \times (1 - 0.21)$

$0.091 = \frac{0.11}{1+x} + \frac{0.064 \times 0.79x}{1+x} = \frac{0.11 + 0.05056x}{1+x}$

Now, solve for $x$:

$0.091(1+x) = 0.11 + 0.05056x$

$0.091 + 0.091x = 0.11 + 0.05056x$

$0.091x - 0.05056x = 0.11 - 0.091$

$0.04044x = 0.019$

$x = \frac{0.019}{0.04044} \approx 0.4699$

The company's debt-equity ratio is approximately **0.47**.

Solution:

According to Modigliani and Miller's Proposition I without taxes, the value of a firm is independent of its capital structure. In a frictionless market, the total value of the levered firm should be equal to the total value of the unlevered firm ($V_L = V_U$). Let's calculate the market value of both firms.

• **Value of Unlevered Plc ($V_U$):**

  = Number of shares $\times$ price per share

  = $3.8 \text{ million} \times 71 = \text{Tk. } 269.8 \text{ million}$

• **Value of Levered Plc ($V_L$):**

  = Market value of equity + Market value of debt

  = $(1.9 \text{ million} \times 98) + 65 \text{ million}$

  = $186.2 \text{ million} + 65 \text{ million} = \text{Tk. } 251.2 \text{ million}$

Based on the M&M proposition, both firms should have the same value, Tk. 269.8 million. However, the market value of Levered Plc is only Tk. 251.2 million. This suggests that Levered's stock is undervalued by the market. Therefore, for an investor, Levered's stock is a better buy. An investor can earn a higher return by purchasing the undervalued Levered stock, as its price should eventually rise to reflect the true value of the firm.

Solution:

The most likely true statement is **(i) Company G will have a faster growth rate than Company D. Therefore, G's stock price should be greater than Tk. 25.**

Here's a breakdown of the reasoning:

• **Statement (i):** Company G retains two-thirds of its earnings for reinvestment, while Company D retains none. Assuming both firms can earn a return on retained earnings, G will have a positive growth rate, while D's growth rate will be zero. Since both stocks are equally risky, their required rate of return ($k_e$) must be the same. The value of a stock is the present value of all its future dividends. Since G's dividends are expected to grow (whereas D's are stable), G's stock price should be higher, assuming the return on reinvested earnings is greater than the required rate of return.
• **Statement (ii):** This is incorrect based on the Modigliani-Miller dividend irrelevance theory. In a perfect market, the total value to shareholders (dividends plus capital gains) should be the same for both firms, regardless of the dividend payout policy.
• **Statement (iii):** The analogy is flawed. While a higher dividend payout may seem like a faster "payback," the total return to an investor comes from both dividends and capital gains. A higher required return for D would imply it is riskier, but the problem states they are equally risky.
• **Statement (iv):** This is incorrect. According to the CAPM, since both companies are equally risky, their required rates of return must be identical. While G's expected growth rate is higher, its stock price adjusts so that its expected total return to the investor (dividend yield + capital gain) equals the required rate of return for that level of risk.

Solution:

i. Impact of different borrowing rates on NAL:

The NAL calculation relies on discounting cash flows at the appropriate after-tax cost of debt for each party. Because the lessor and lessee have different borrowing rates, they will have different after-tax discount rates. This means the present value of a dollar for the lessor is different from the present value of a dollar for the lessee. The lessee's discount rate is $9\% \times (1 - 0.21) = 7.11\%$, while the lessor's is $7\% \times (1 - 0.21) = 5.53\%$. This difference means the NPVs from each side of the transaction may not be perfectly symmetrical, and a lease payment that is a zero-NPV for one party may not be for the other.

ii. Lease payments for indifference:

The "indifference" lease payment is the one that makes the NPV of the cost of leasing equal to the NPV of the cost of owning for each party. Given the different discount rates, there is no single lease payment that makes both parties equally well-off. There is a range of payments that will make both parties better off, which we will calculate in part (iii). The question is flawed in its assumption of a single indifference point.

iii. Lease payments for positive NPV for both parties:

We need to find a range of lease payments that result in a positive NPV for both the tax-exempt lessee and the tax-paying lessor.

**Lessee's Perspective (no taxes):**

Since the lessee pays no taxes, there is no depreciation tax shield. The cost of owning is simply the initial cost of the asset. The cost of leasing is the present value of the lease payments discounted at the pre-tax borrowing rate.

PV cost of owning = Initial cost = Tk. 640,000

PV cost of leasing = $L \times \left[1 + \frac{1}{(1.09)} + \frac{1}{(1.09)^2} \right] = L \times [1 + 0.9174 + 0.8417] = L \times 2.7591$

For a positive NPV, the cost of leasing must be less than the cost of owning:

$2.7591L < 640,000 \implies L < \frac{640,000}{2.7591} = \text{Tk. } 231,952.45$

So, the lessee's upper bound for the lease payment is **Tk. 231,952.45**.

**Lessor's Perspective (21% tax bracket):**

The lessor's NPV is the present value of after-tax lease payments minus the initial cost of the asset plus the present value of the depreciation tax shield.

Annual depreciation tax shield = $\frac{640,000}{3} \times 0.21 = \text{Tk. } 44,800$

PV of dep. tax shield (discounted at 5.53%) = $44,800 \times \left[\frac{1}{1.0553} + \frac{1}{1.0553^2} + \frac{1}{1.0553^3}\right]$

$= 44,800 \times [0.9475 + 0.8978 + 0.8507] = 44,800 \times 2.696 = \text{Tk. } 120,707.2$

PV of after-tax lease payments = $L(1 - 0.21) \times \left[1 + \frac{1}{1.0553} + \frac{1}{1.0553^2}\right] = L \times 0.79 \times [1 + 0.9475 + 0.8978] = L \times 0.79 \times 2.8453 = 2.2478L$

For a positive NPV for the lessor: $2.2478L - 640,000 + 120,707.2 > 0$

$2.2478L > 519,292.8 \implies L > \frac{519,292.8}{2.2478} = \text{Tk. } 231,027.5$

So, the lessor's lower bound for the lease payment is **Tk. 231,027.5**.

The range of lease payments where both parties benefit is between **Tk. 231,027.5 and Tk. 231,952.45**.

Solution:

International capital budgeting involves unique financial complications that are not present in domestic projects. These complications include:

• **Foreign Exchange Risk:** Fluctuations in exchange rates can significantly impact the value of a project's cash flows when they are converted back to the home currency.
• **Political Risk:** This includes the risk of political instability, expropriation of assets, restrictions on capital repatriation, or changes in tax laws by the host government.
• **Different Tax Laws:** The tax rates and regulations in the host country may differ from the home country, requiring careful analysis to determine the net after-tax cash flows.

Two common procedures for estimating NPV for an international project are:

• **1. Home Currency Approach:** This method involves converting all cash flows from the foreign currency to the home currency using projected future exchange rates. The converted cash flows are then discounted at the home country's required rate of return.
• **2. Foreign Currency Approach:** In this method, the cash flows are estimated in the foreign currency and discounted at a rate appropriate for that currency (which includes the foreign country's inflation and risk premium). The final NPV, calculated in the foreign currency, is then converted back to the home currency using the current spot exchange rate.

Solution:

i. Net Working Capital (NWC):

NWC is the difference between current assets and current liabilities.

• Current Assets = Tk. 14 million
• Current Liabilities = Accounts Payable + Accruals = $3 \text{ million} + 1 \text{ million} = \text{Tk. } 4 \text{ million}$

$NWC = \text{Current Assets} - \text{Current Liabilities} = 14 \text{ million} - 4 \text{ million} = \text{Tk. } 10 \text{ million}$

The company's net working capital was **Tk. 10 million**.

ii. Free Cash Flow (FCF):

Free Cash Flow is the cash flow from operations after accounting for capital expenditures and changes in net working capital. The formula is: $FCF = \text{EBIT}(1 - T) + \text{Depreciation} - \text{Capital Expenditures} - \text{Change in NWC}$.

• **After-tax EBIT:** $5 \text{ million} \times (1 - 0.40) = \text{Tk. } 3 \text{ million}$
• **Depreciation:** Tk. 1 million
• **Capital Expenditures (CapEx):** CapEx = Current Net Plant & Equipment - Prior Net Plant & Equipment + Depreciation.

  $CapEx = 15 \text{ million} - 12 \text{ million} + 1 \text{ million} = \text{Tk. } 4 \text{ million}$

• **Change in NWC:** The problem states NWC remained constant, so the change is zero.

$FCF = 3 \text{ million} + 1 \text{ million} - 4 \text{ million} - 0 = \text{Tk. } 0$

The company's free cash flow for the year was **Tk. 0**.

Solution:

The savings from stretching accounts payable come from the released funds that can be used for other purposes or to reduce borrowing. This amount is calculated as the increase in accounts payable from the new policy, multiplied by the cost of the resource investment.

• **Current Accounts Payable Period:** 10 days
• **New Accounts Payable Period:** $10 + 20 = 30$ days
• **Daily Purchases:** $\frac{\text{Annual Purchases}}{\text{Days in year}} = \frac{14,000,000}{360} = \text{Tk. } 38,888.89$
• **Current Accounts Payable:** $38,888.89 \times 10 = \text{Tk. } 388,888.90$
• **New Accounts Payable:** $38,888.89 \times 30 = \text{Tk. } 1,166,666.70$
• **Funds Released:** New Accounts Payable - Current Accounts Payable

  $= 1,166,666.70 - 388,888.90 = \text{Tk. } 777,777.80$

• **Annual Savings:** Released Funds $\times$ Cost of Investment

  $= 777,777.80 \times 0.12 = \text{Tk. } 93,333.34$

The firm can realize an annual savings of approximately **Tk. 93,333** from this plan.

Solution:

The Mexican peso will **depreciate** against the U.S. dollar. This is because higher inflation in Mexico will erode the purchasing power of the peso relative to the dollar. To maintain the same purchasing power, it will take more pesos to buy one dollar, thus the peso's value will decline.

The relationship being relied on here is the **Purchasing Power Parity (PPP)** theory. The PPP theory states that the exchange rate between two currencies should adjust to reflect the inflation differential between the two countries. The currency of the country with the higher inflation rate is expected to depreciate against the currency of the country with the lower inflation rate.