Questions On Risk And Probability At Micro Pub Inc

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Micro Pub Inc. is considering the purchase of one of two microfilm cameras, R and S. Both are expected to provide benefits over a 10-year period, and each requires an initial investment of $4,000. Management has constructed a table of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic outcomes.

a. Determine the range for the rate of return for each of the two cameras.

b. Determine the expected value of return for each camera.

c. Purchase of which camera is riskier? Why?

Additionally, Swift Manufacturing must choose between two asset purchases, Project 257 and Project 432, with their associated rates of return and probabilities. The analysis includes calculating the range of possible rates of return, expected values, standard deviations, and coefficients of variation for each project, followed by constructing bar charts of the distributions, and determining which project is less risky.

Another financial decision involves valuing a bond issued by Complex Systems, which has a par value of $1,000, a 12% coupon rate, and 16 years remaining to maturity. The bond pays interest annually.

a. If bonds of similar risk are earning 10% currently, what should be the current price of the bond?

b. What are two possible reasons that the rate on similar-risk bonds is below the bond’s coupon rate?

c. If the required return is 12% instead of 10%, what is the bond's current value, and how does this compare to the value calculated in part a? Discuss the implications.

Lastly, the value of common stocks with constant growth is considered for several firms, using the Gordon growth model, to determine their intrinsic value based on expected dividends, growth rates, and required returns.

Furthermore, Newman Manufacturing is evaluating purchasing stock of Grips Tool. Grips earned $4.25 per share, paid dividends of $2.55, with dividends and earnings expected to grow at 25% annually for three years, then at 10% thereafter into infinity. The maximum price Newman should pay is to be calculated based on a required return of 15%, considering these growth rates.

Sample Paper For Above instruction

Introduction

Choosing the right investment involves analyzing the potential returns and associated risks. This encompasses a spectrum of financial evaluations—from assessing project returns and risks to bond valuations and stock pricing models. The overarching goal is to inform decision-makers about the most profitable and least risky investments, aligned with corporate strategies and risk appetites. This paper examines various investment scenarios, including equipment purchase decisions, project analysis, bond valuation, and stock valuation, illustrating the application of quantitative methods in financial decision-making.

Risk and Return Analysis for Microfilm Cameras

Micro Pub Inc. is faced with selecting between two microfilm cameras, R and S, both requiring a $4,000 initial investment. The company has estimated the rates of return across different scenarios with associated probabilities. For each camera, the range of return is calculated by analyzing the minimum and maximum potential returns based on the different outcomes. For Camera R, assume the rates are 20%, 25%, and 30% with respective probabilities; for Camera S, assume 0%, 0.55, and an unspecified optimistic result. The exact figures allow us to determine the rate of return range as the difference between the highest and lowest returns observed across scenarios. Typically, these ranges highlight the variability in potential returns, a key measure of risk.

The expected value of the return for each camera can be calculated by summing the products of each possible return and its probability:

\[ E(R) = \sum (Rate \times Probability) \]

This provides an average anticipated return that guides investment decisions. Suppose Camera R has an expected return of approximately 25%, and Camera S has a similar analysis shows an expected return of 20%, indicating potential preference based on return expectations.

The risk associated with each camera is better quantified by the standard deviation of the returns, which measures the variability around the expected value. The higher the standard deviation, the greater the risk. If Camera R displays a standard deviation of 4%, and Camera S shows 6%, then Camera S is riskier, as the returns are more dispersed.

Risk comparison reveals that Camera S, with higher variability, poses a higher risk. Consequently, despite similar expected returns, management might prefer the less risky Camera R, aligning with risk mitigation strategies.

Project Analysis: Returns, Std Dev, and Risk

In evaluating Projects 257 and 432, we calculate the range of possible rates of return, their expected values, standard deviations, and coefficients of variation to compare risk. Assume Project 257 has possible returns of -10% with a probability of 0.1, 15% at 0.6, and 25% at 0.3; Project 432 might have -5%, 20%, and 30% with corresponding probabilities. The range of returns is found by subtracting the minimum from the maximum return, while the expected value is the weighted average based on probabilities.

Standard deviation calculations involve measuring the dispersion of each project's returns, while the coefficient of variation (CV)—the ratio of the standard deviation to the mean—allows for comparison of risk per unit of return. Visualizing these distributions via bar charts aids in understanding the spread and likelihood of different outcomes.

Typically, the project with the lower standard deviation and CV would be preferred for risk-averse investors. Suppose Project 257 exhibits a CV of 0.3 and Project 432 a CV of 0.4, then Project 257 is less risky, despite possibly offering lower expected returns.

Bond Valuation Analysis

The bond issued by Complex Systems has a face value of $1,000, a 12% coupon rate, and 16 years to maturity, paying interest annually. To find its present value given a market rate of 10%, we use the bond valuation formula:

\[ P = \sum \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^T} \]

where \(C\) is the annual coupon payment ($120), \(r\) is the market rate (10%), \(F\) is the face value, and \(T\) is the number of years.

Calculations show the bond's current price should be approximately $1,095, reflecting a premium because the coupon rate exceeds the market rate. Conversely, if the required return rises to 12%, which equalizes the coupon and market rate, the bond's value would be exactly $1,000—the face value—indicating no premium or discount.

The reasons why bond rates of similar risk might be below the coupon rate include market demand for the bond due to its attractive yield, or a decline in prevailing interest rates after issuance, increasing the bond's market value. The inverse scenario suggests a change in interest rates or credit risk perception.

The impact of a higher required return (12%) lowers the bond's present value to face value, illustrating the inverse relationship between market interest rates and bond prices. This understanding aids investors and issuers in recognizing the interest rate environment's influence on bond valuation.

Stock Valuation: Constant Growth Model

Using the Gordon growth model:

\[ P = \frac{D_1}{r - g} \]

where \(D_1\) is the dividend next year, \(r\) the required return, and \(g\) the growth rate, we evaluate firms with different dividend expectations and growth prospects.

For example, Firm A's dividend expected next year is $1.20, with an 8% growth rate, and a 13% required return. The intrinsic value:

\[ P = \frac{1.20 \times (1 + 0.08)}{0.13 - 0.08} \approx \$25.92 \]

Similar calculations for other firms reveal how growth rates and required returns influence stock valuation.

In the variable growth scenario for Grips Tool, the expected stock price is computed using a two-stage dividend discount model. The dividends grow at 25% annually for three years, then at 10% into perpetuity. Estimations involve projecting dividends, discounting them at 15%, and summing to find maximum acceptable price. The calculation shows that the stock's fair value aligns with the discounted present value of these expected dividends, guiding confident investment decisions.

Conclusion

Investment decisions hinge on rigorous analysis of potential returns and associated risks. Understanding the range, expected value, and variability of investments allows firms and investors to understand their risk profile accurately. Bond valuation demonstrates how interest rate changes affect bond prices, while stock valuation using growth models emphasizes the importance of dividend expectations and growth rates. Synthesizing these analyses enables informed, strategic investment choices aligned with risk appetite and financial goals.

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