Week 3 Practice Problems

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University of Regina *

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BUSINESS 3

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Finance

Date

Jan 9, 2024

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docx

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3

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5-1. 1. Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of six months. one year. one month. a. Since six months is 6 1 24 4 of two years, using our rule 1 4 1 0.2 1.0466 the equivalent six-month rate is 4.66%. b. Since one year is half of two years 1 2 1.2 1.0954 , the equivalent one-year rate is 9.54%. c. Since one month is 1 24 of two years, using our rule 1 24 1 0.2 1.00763 , the equivalent one-month rate is 0.763%
5-10. 10. Excel Project and Excel Solution Your son has been accepted into university. This university guarantees that your son’s tuition will not increase for the four years that he attends. The first $10,000 tuition payment is due in six months. After that, the same payment is due every six months until you have made a total of eight payments. The university offers a bank account that allows you to withdraw money every six months and has a fixed APR of 4% (with semiannual compounding) guaranteed to remain the same over the next four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this account, leaving the account empty when the last payment is made? Timeline: 0 1 2 1 4 0 1 2 8 10,000 10,000 10,000 4% APR (semiannual) implies a semiannual discount rate of 4% 2% 2 . So, 8 10,000 1 PV 1 0.02 1.02 $73, 254.81 . 7-10. 10. DFB Inc. expects earnings this year of $5 per share, and it plans to pay a $3 dividend to shareholders. DFB will retain $2 per share of its earnings to reinvest in new projects with an expected return of 15% per year. Suppose DFB will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares. What growth rate of earnings would you forecast for DFB? If DFB’s equity cost of capital is 12%, what price would you estimate for DFB stock? Suppose DFB instead paid a dividend of $4 per share this year and retained only $1 per share in earnings. If DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should DFB raise its dividend? a. Eq. 7.12: g = retention rate × return on new investments = (2/5) × 15% = 6% b. P = 3 / (12% – 6%) = $50 c. g = (1/5) × 15% = 3%, P = 4 / (12% – 3%) = $44.44. No, projects are positive NPV (return exceeds cost of capital), so don’t raise the dividend as it will cause the stock price to drop in this case.
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