Coates’s Decision

On January 1, 2017, Dave Coates, a 23-year-old mathematics teacher at Xavier High School, received a tax refund of $1,100. Because Dave didn’t need this money for his current living expenses, he decided to make a long-term investment. After surveying a number of alternative investments costing no more than $1,100, Dave isolated two that seemed most suitable to his needs.

Each of the investments cost $1,050 and was expected to provide income over a 10-year period. Investment A provided a relatively certain stream of income. Dave was a little less certain of the income provided by investment B. From his search for suitable alternatives, Dave found that the appropriate discount rate for a relatively certain investment was 4%. Because he felt a bit uncomfortable with an investment like B, he estimated that such an investment would have to provide a return at least 4% higher than investment A. Although Dave planned to reinvest funds returned from the investments in other vehicles providing similar returns, he wished to keep the extra $50 ($1,100 − $1,050) invested for the full 10 years in a savings account paying 3% interest compounded annually.

As he makes his investment decision, Dave has asked for your help in answering the questions that follow the expected return data for these investments.

Expected Returns | ||

End of Year | A | B |

2017 | $ 50 | $ 0 |

2018 | $ 50 | $ 150 |

2019 | $ 50 | $ 150 |

2020 | $ 50 | $ 150 |

2021 | $ 50 | $ 200 |

2022 | $ 50 | $ 250 |

2023 | $ 50 | $ 200 |

2024 | $ 50 | $ 150 |

2025 | $ 50 | $ 100 |

2026 | $ 1050 | $ 50 |

Questions

- Assuming that investments A and B are equally risky and using the 4% discount rate, apply the present value technique to assess the acceptability of each investment and to determine the preferred investment. Explain your findings.
- Recognizing that investment B is more risky than investment A, reassess the two alternatives, adding the 4% risk premium to the 4% discount rate for investment A and therefore applying a 8% discount rate to investment B. Compare your findings relative to acceptability and preference to those found for question a.
- From your findings in questions a and b, indicate whether the IRR for investment A is above or below 4% and whether that for investment B is above or below 8%. Explain.
- Use the present value technique to estimate the IRR on each investment. Compare your findings and contrast them with your response to question c.
- From the information given, which, if either, of the two investments would you recommend that Dave make? Explain your answer.
- Indicate to Dave how much money the extra $50 will have grown to by the end of 2026, assuming he makes no withdrawals from the savings account.

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