2010_FIN300_Fall_Midterm_Solutions-1

# 2010_FIN300_Fall_Midterm_Solutions-1 - UNIVERSITY OF...

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Page 1 of 12 UNIVERSITY OF MICHIGAN ROSS SCHOOL OF BUSINESS BUS FIN 300 Financial Management Erica Li Midterm Examination Fall 2010 SOLUTIONS Quick Reference 1. A 2. C 3. B 4. B 5. D 6. D 7. E 8. D 9. C 10. C 11. A 12. E 13. E 14. C 15. D 16. B 17. A 18. B 19. D

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Page 2 of 12 Section I: Time Value of Money (4 Questions, 20 points). #1. You're trying to save to buy a new \$170,000 Ferrari. You have \$40,000 today that can be invested at your bank. The bank pays 5.3 percent interest compounded monthly on its accounts. How long will it be before you have enough to buy the car? A. 27.36 years B. 28.02 years C. 26.02 years D. 28.27 years E. None of the above Solution: A You want to have 40,000(1+r)^T = 170,000, so for r = 0.053/12, we have ln(170/40)/ln(1+0.053/12) = 328.32 months = 27.36 years. #2 . You have decided to fund a new program for charity. For the first 5 years, you will give \$100,000 each year. After that, you will provide \$500,000 every five years in perpetuity, with the first payment of \$500,000 coming in year 10. What is the present value of your gift if the interest rate is 7%? A. 410.02K B. 1652.10K C. 1295.60K D. 5092.76K E. None of the above Solution: C The PV of the annuity part is 410.02K. The PV of the perpetuity part is 500/0.402*1/1.07^5, or 885.58K, where the 0.402 is the interest rate that applies to a five-year step (= 1.07^5-1). The sum of the two is 1295.60K.
3 of 12 The following applies for #3-4. Cindy is planning her retirement and expenses in the future. The rate of interest that she can lend and borrow at the bank is 4 percent compounded annually. She would like to retire 25 years from now. She currently has \$250,000 in the bank. She intends to buy a car 3 years from now. She estimates it will cost \$55,000 then. She would like to buy her mother a house 15 years from now. She estimates it will cost \$500,000 then. Cindy wants to have a fixed pension of \$120,000 per year with the first payment being 26 years from now and the last being 40 years from now. #3. What is the constant amount she needs to save each year assuming the first time she puts away money is 1 year from now and the last time is 25 years from now? A. 35,506 B. 36,935 C. 52,938 D. 106,307 E. None of the above Solution: B. Let S be the amount she saves her year in years 1-25. PV(Expenditures) = 55/1.04^3 + 500/1.04^15 + 120/0.04*(1-1/1.04^15)*1/1.04^25 = 827.0103K PV(Savings) = S/0.04*(1-1/1.04^25) + 250 PV(Expenditures) must equal PV(Savings), so S = 36,935. #4. What is the constant amount she needs to save each year assuming the first time she puts away money is today and the last time is still 25 years from now ? A. 49,753 B. 34,713 C. 32,658 D. 99,913 E. None of the above Solution: B. Same as #1, except

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## 2010_FIN300_Fall_Midterm_Solutions-1 - UNIVERSITY OF...

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