SU (SelviaUtama): Corporate Finance: Essay Quiz Payback, Cost of Capital, NPV 02

Marie Design Company can purchase a piece of equipment for RM 3,600. The asset has a two – year life, will produce a cash flow of RM 600 in the first year and RM 4,200 in the second year. The interest rate is 15%. Calculate the projects payback assuming steady cash flows. Also calculate the project’s IRR. Should the project be taken? Check your answer by computing the project’s NPV.

Answer:

To evaluate whether Marie Design Company should proceed with the equipment purchase, we will calculate the project's payback period, Internal Rate of Return (IRR), and Net Present Value (NPV).

Project Details

Initial Cost: RM 3,600
Cash Flow Year 1: RM 600
Cash Flow Year 2: RM 4,200
Interest Rate (Discount Rate): 15%

1. Payback Period Calculation

The payback period is the time it takes for the project to recover its initial investment from its cash inflows.

Cash Flows:

Year 0: -RM 3,600 (initial investment)
Year 1: +RM 600
Year 2: +RM 4,200

Cumulative Cash Flow:

End of Year 1: -RM 3,600 + RM 600 = -RM 3,000
End of Year 2: -RM 3,000 + RM 4,200 = RM 1,200

The payback occurs between Year 1 and Year 2. To find the exact point:

Payback Period = 1 + \frac{3, 000}{4, 200} \approx 1 + 0.7143 \approx 1.71 years

2. IRR Calculation

The IRR is the discount rate that makes the NPV of the cash flows equal to zero. We can use the cash flows to set up the equation:

0 = - 3, 600 + \frac{600}{(1 + I R R)^{1}} + \frac{4, 200}{(1 + I R R)^{2}}

This equation typically requires numerical methods or financial calculators to solve. However, we can estimate IRR using trial and error or software tools.Using a financial calculator or Excel:

Enter cash flows: -3,600 in Year 0, +600 in Year 1, and +4,200 in Year 2.
The calculated IRR is approximately 33.52%.

3. NPV Calculation

To compute NPV at a discount rate of 15%, we use the formula:

N P V = \sum_{t = 0}^{n} \frac{C F_{t}}{(1 + r)^{t}}

Where

C F_{t}

is the cash flow at time

t

and

r

is the discount rate.

Cash Flows:

Year 0: -RM 3,600
Year 1: RM 600
Year 2: RM 4,200

NPV Calculation:

N P V = - 3, 600 + \frac{600}{(1 + 0.15)^{1}} + \frac{4, 200}{(1 + 0.15)^{2}}

Calculating each term:

For Year 0: $- 3, 600$
For Year 1:

\frac{600}{1.15} = R M 521.74

For Year 2:

\frac{4, 200}{(1.15)^{2}} = \frac{4, 200}{1.3225} = R M 3, 174.60

Now summing these values:

N P V = - 3, 600 + R M 521.74 + R M 3, 174.60 = - R M 903.66

Based on our calculations: Payback Period: Approximately 1.71 years IRR: Approximately 33.52% NPV: Approximately -RM 903.66 Since the NPV is negative (-RM 903.66), this indicates that the project would not generate sufficient returns to justify the investment at a discount rate of 15%. Although the IRR exceeds the required return of 15%, the negative NPV suggests that the project should not be taken, as it does not create value for Marie Design Company when considering the cost of capital.

Perak Pewter has a cost of debt of 7%, a cost of equity of 11%, and a cost of preferred stock of 8 %. The firm has 104,000 shares of common stock outstanding at a market price of RM20 a share. There are 40,000 shares of preferred stock outstanding at a market price of RM34 a share. The bond issue has a total face value of RM500,000 and sells at 102% of face value. The tax rate is 34%. What is the weighted average cost of capital for Perak Pewter?

Answer:

To calculate the Weighted Average Cost of Capital (WACC) for Perak Pewter, we will consider the costs of debt, equity, and preferred stock, as well as their respective market values.

Given Data

Cost of Debt (Kd): 7%
Cost of Equity (Ke): 11%
Cost of Preferred Stock (Kp): 8%
Common Stock Outstanding: 104,000 shares at RM 20 each
Preferred Stock Outstanding: 40,000 shares at RM 34 each
Total Face Value of Bonds: RM 500,000 (selling at 102% of face value)
Tax Rate: 34%

Step 1: Calculate Market Values

Market Value of Common Equity (E): $E = Number of Shares \times Market Price per Share = 104, 000 \times 20 = R M 2, 080, 000$
Market Value of Preferred Equity (P): $P = Number of Preferred Shares \times Market Price per Share = 40, 000 \times 34 = R M 1, 360, 000$
Market Value of Debt (D):
- The bonds are selling at 102% of face value:
$D = Face Value \times Selling Price Percentage = 500, 000 \times 1.02 = R M 510, 000$

Step 2: Calculate Total Market Value (V)

The total market value

V

is the sum of the market values of equity, preferred stock, and debt:

V = E + P + D = R M 2, 080, 000 + R M 1, 360, 000 + R M 510, 000 = R M 3, 950, 000

Step 3: Calculate Proportions

Now we calculate the proportions of each component in the capital structure:

Weight of Equity (We): $W_{e} = \frac{E}{V} = \frac{2, 080, 000}{3, 950, 000} \approx 0.5263$
Weight of Preferred Stock (Wp): $W_{p} = \frac{P}{V} = \frac{1, 360, 000}{3, 950, 000} \approx 0.3444$
Weight of Debt (Wd): $W_{d} = \frac{D}{V} = \frac{510, 000}{3, 950, 000} \approx 0.1293$

Step 4: Calculate After-Tax Cost of Debt

The after-tax cost of debt is calculated as follows:

K_{d} (1 - T) = K_{d} (1 - 0.34) = 0.07 (1 - 0.34) = 0.07 (0.66) = 0.0462

Step 5: Calculate WACC

Now we can calculate the WACC using the formula:

W A C C = W_{e} K_{e} + W_{p} K_{p} + W_{d} K_{d} (1 - T)

Substituting in our values:

W A C C = (0.5263) (0.11) + (0.3444) (0.08) + (0.1293) (0.0462)

Calculating each term:

Equity component: $0.5263 \times 0.11 = 0.0579$
Preferred stock component: $0.3444 \times 0.08 = 0.0276$
Debt component: $0.1293 \times 0.0462 = 0.0060$

Adding these components together:

W A C C = 0.0579 + 0.0276 + 0.0060 = 0.0915

What securities have offered the highest average annual returns over the last several decades? Can we conclude that return and risk are related in real life? What are the lessons learned from capital market history? What evidence is there to suggest these lessons are correct?

Answer:

Highest Average Annual Returns Over Several Decades

Securities offering the highest average annual returns over the last several decades include:

Small Cap Stocks:
- Historically, small-cap stocks have provided the highest average annual returns, although they come with significant risks. According to historical records, investing in small caps can result in substantial gains, but it also involves considerable volatility and potential losses
Growth Stocks:
- Growth stocks, particularly those in emerging industries, have historically shown strong growth trajectories, leading to high returns. These stocks carry higher risks associated with rapid expansion and competitive pressures

Relationship Between Return and Risk

Yes, there is a relationship between return and risk in real-life scenarios. The concept known as the risk-return tradeoff underscores this principle:

Reward for Bearing Risk:
- Studies from capital market history consistently indicate that there is a direct correlation between the amount of risk taken and the potential rewards achieved. Higher-risk investments offer potentially higher returns, while lower-risk investments tend to provide lower returns
Evidence Supporting the Risk-Return Tradeoff:
- Historical data demonstrates that small-cap stocks, despite having the highest average returns, also exhibit extreme variability in performance. Conversely, stable investments like long-term government bonds offer consistent but relatively lower returns
Examples Illustrating the Risk-Return Tradeoff:
- Consider an example where an investor buys a stock initially priced at RM 35 and receives a dividend of RM 1.25 while selling it for RM 40 after one year. The total dollar return would be RM 10 + RM 1.25 = RM 11.25 or approximately 32% return. This illustrates how higher returns are often linked to higher risks, including fluctuations in stock prices

Lessons Learned from Capital Market History

Several key lessons emerge from studying capital market history:

Importance of Understanding Historical Trends:
- Studying historical trends provides insights into long-term drivers of nominal and real interest rates, helping investors navigate complex financial environments. For instance, understanding past interest rate behaviors aids in predicting future movements within certain bounds
Avoid Predictive Behavior Based on Past Patterns:
- Business and stock market cycles are unpredictable and highly variable. Attempting to predict the length or turning points of these cycles can lead to poor investment decisions. Instead, focusing on long-term strategies is advisable
Regime Shifts Impact Investment Environments:
- Changes in economic conditions ("regime shifts") alter investment landscapes significantly. Investors must adapt their strategies according to changing market conditions rather than relying solely on historical precedents
Value of Diversification:
- Investing across different asset classes reduces reliance on individual security performances. This diversification mitigates risks associated with concentrated holdings, aligning with broader principles observed in capital market histories
Behavioral Biases Influence Decision-Making Processes:
- Behavioral biases among investors skew perceptions regarding short-term metrics versus long-term outcomes. Recognizing these biases helps in avoiding impulsive decisions driven by immediate gratifications instead of strategic planning aligned with historical norms

Evidence Supporting These Lessons

Numerous pieces of evidence support these lessons:

Longitudinal Analysis Shows Variable Cycle Lengths:
- Statistical analysis spanning centuries confirms that business and stock market cycles vary widely in duration, ranging from approximately 2.5 to 6.9 years most frequently
Real-Life Examples Highlight Volatility Risks:
- During times like the global financial crisis of 2008, even seemingly robust investments experienced sharp declines. Conversely, periods like post-crisis recovery saw dramatic rebounds, underscoring dynamic nature of financial markets
Empirical Research Validates Risk-Reward Correlation:
- Empirical studies consistently validate that higher-risk investments correlate with higher potential returns. For instance, historical averages reveal that large-cap stocks averaged around 12%, while small-cap stocks averaged nearly double that figure at around 16% over extended periods

By integrating these lessons into investment strategies, investors can better navigate complex financial landscapes informed by historical experiences and empirical evidence.

SU (SelviaUtama)

Corporate Finance: Essay Quiz Payback, Cost of Capital, NPV 02

Project Details

1. Payback Period Calculation

Cash Flows:

Cumulative Cash Flow:

2. IRR Calculation

3. NPV Calculation

Cash Flows:

NPV Calculation:

Given Data

Step 1: Calculate Market Values

Step 2: Calculate Total Market Value (V)

Step 3: Calculate Proportions

Step 4: Calculate After-Tax Cost of Debt

Step 5: Calculate WACC

Highest Average Annual Returns Over Several Decades

Relationship Between Return and Risk

Evidence Supporting These Lessons

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