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Chapter 15: Problem 17

An all-equity firm is considering the following projects $$\begin{array}{|ccc|} \hline \text { Project } & \text { Beta } & \text { Expected Return } \\ \hline \mathrm{W} & .70 & 11 \% \\ \mathrm{X} & .95 & 13 \\ \mathrm{Y} & 1.05 & 14 \\ \mathrm{Z} & 1.60 & 16 \\ \hline \end{array}$$ The T-bill rate is 5 percent, and the expected return on the market is 12 percent. a. Which projects have a higher expected return than the firm's 12 percent cost of capital? b. Which projects should be accepted? c. Which projects would be incorrectly accepted or rejected if the firm's overall cost of capital were used as a hurdle rate?

Short Answer

Expert verified
Projects X, Y, and Z have a higher expected return than the firm's 12 percent cost of capital. Projects X and Y should be accepted as their expected returns are higher than their required returns based on their risk levels. Using the firm's overall cost of capital as a hurdle rate would result in the incorrect acceptance of Project Z, as its expected return is higher than the firm's cost of capital but lower than its required return.

Step by step solution

01

Calculate required return for each project using CAPM

We will first use the CAPM formula \(R_i = R_f + \beta_i (R_m - R_f)\) for each project, where \(R_i\) is the expected return for project i, \(R_f\) is the risk-free rate (5 percent), \(\beta_i\) is the beta value for project i, and \(R_m\) is the expected return on the market (12 percent). This will give the required return for each project: Project W - \(R_W = 0.05 + 0.7(0.12 - 0.05) = 0.099\) Project X - \(R_X = 0.05 + 0.95(0.12 - 0.05) = 0.1165\) Project Y - \(R_Y = 0.05 + 1.05(0.12 - 0.05) = 0.1235\) Project Z - \(R_Z = 0.05 + 1.6 (0.12 - 0.05) = 0.162\) a.
02

Identify projects with an expected return higher than the firm's cost of capital

Now, we will compare each project's expected return to the firm's cost of capital (12 percent). If the expected return is higher than 12 percent, the project has a higher expected return than the firm's cost of capital. Project W: 11% (lower than 12%) Project X: 13% (higher than 12%) Project Y: 14% (higher than 12%) Project Z: 16% (higher than 12%) Projects X, Y, and Z have a higher expected return than the firm's 12 percent cost of capital. b.
03

Determine which projects should be accepted

To determine which projects should be accepted, we need to compare their expected return to their required return calculated using the CAPM formula. Project W: Expected Return (11%) < Required return (9.9%) - Reject Project X: Expected Return (13%) > Required return (11.65%) - Accept Project Y: Expected Return (14%) > Required return (12.35%) - Accept Project Z: Expected Return (16%) < Required return (16.2%) - Reject Projects X and Y should be accepted as their expected returns are higher than their required returns. c.
04

Identify projects that would be incorrectly accepted or rejected using the overall cost of capital

If we were to use the firm's overall cost of capital of 12 percent as a hurdle rate, the following projects would be incorrectly accepted or rejected: Project W: Expected Return (11%) < Cost of capital (12%) - Reject (Correct decision) Project X: Expected Return (13%) > Cost of capital (12%) - Accept (Correct decision) Project Y: Expected Return (14%) > Cost of capital (12%) - Accept (Correct decision) Project Z: Expected Return (16%) > Cost of capital (12%) - Accept (Incorrect decision) Using the firm's overall cost of capital as a hurdle rate would result in the incorrect acceptance of Project Z, as its expected return is higher than the firm's cost of capital but lower than its required return.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cost of Capital
The 'cost of capital' is a critical concept for any business, reflecting the minimum return a company must earn to satisfy its investors or creditors. In corporate finance, the cost of capital represents the company's funding costs which can come from a mix of debt and equity. These costs are used in decision-making for financing new projects or operations.

Considering our exercise, the firm's cost of capital is given as 12%. This rate is used as a benchmark to assess whether a project should be considered as it includes the cost of both debt and equity. Each project's expected return should exceed this rate to be deemed as potentially viable and justify the risks associated with the investment. Thus, accurately calculating and understanding the cost of capital help companies evaluate their investment decisions prudently.
Expected Return
The 'expected return' is a significant figure in the world of finance, which estimates the potential gains from an investment. In other words, it is what investors anticipate earning from their investment, considering the levels of associated risk. The expected return is often calculated based on past performance and present market conditions.

In the context of our exercise, the expected return is given for each project. The Capital Asset Pricing Model (CAPM), is utilized to determine if the project's expected returns align with the risk undertaken, denoted by the beta. Using CAPM ensures that the returns are assessed relative to the market and a risk-free asset, allowing for a more robust evaluation of whether the project's potential gains meet or exceed the investor's requirements.
Project Evaluation
Project evaluation in corporate finance is a systematic approach to determine the worthiness of projects. This encompasses scrutinizing the expected benefits against the costs and risks. Commonly, different models are used, such as the CAPM, to evaluate projects in terms of their expected return and associated risk.

Through the lens of our exercise, project evaluation involves comparing expected and required returns using CAPM. This not only includes a comprehensive review of the financial returns but also accounts for market conditions and company specific risk profiles. The inclusion of the beta coefficient, a measure of systemic risk, provides additional clarity on risk-adjusted return potential. Decisions are then made to reject or accept projects based on these insights, aiming to maximize shareholder value while managing risk exposure effectively.

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Most popular questions from this chapter

Calculating cost of Equity Stock in Parrothead Industrics has a beta of 1.10 The market risk premium is 8 percent, and T-bills are currently yiclding 5.5 percent. Parrothead's most recent dividend was \(\$ 2.20\) per share, and dividends are expected to grow at a 5 percent annual rate indefinitely. If the stock sells for \(\$ 32\) per share, what is your best estimate of Parrothead's cost of equity?

Calculating cost of Debt Legend, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 12 years to maturity that is quoted at 107 percent of face value. The issue makes semiannual payments and has an embedded cost of 10 percent annually. What is Legend's pretax cost of debt? If the tax rate is 35 percent, what is the aftertax cost of debt?

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WACC Sniffles, Inc., has a target debt-cquity ratio of .90. Its WACC is 13 percent, and the tax rate is 35 percent. a. If Sniffles' cost of equity is 18 percent, what is its pretax cost of debt? b. If instead you know that the aftertax cost of debt is 7.5 percent, what is the cost of equity?

Estimating the DCF Growth Rate Suppose Massey Lid. just issued a dividend of \(\$ .68\) per share on its common stock. The company paid dividends of \(\$ .40, \$ .45, \$ .52,\) and \(\$ .60\) per share in the last four years. If the stock currently sells for \(\$ 12,\) what is your best estimate of the company's cost of equity capital?
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