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HW3sol - Solution to Problem Set 3 FINA 4200 Spring 2010 I...

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Solution to Problem Set 3 - FINA 4200 Spring 2010 I. Multiple Choices 1. a 2. b 3. a 4. b 5. e 6. d 7. e 8. d 9. e 10. b 11. a 12. c 13. b 14. b 15. a 16. a 17. a 18. d 19. c 20. d 21. d 22. a 23. b 24. a 25. a 26. c 27. c 28. d 29. c 30. d 31. e 32. d 33. a 34. b 35. b 36. b 37. b 38. a 39. c 40. e 41. e 42. a 43. b 44. d 45. c Explanations to multiple choice questions 11. 13.75% = 5% + (7%)b 8.75% = 7%b b = 1.25. 12. Step 1 Solve for risk-free rate r s = 15% = rRF + (10% - rRF)2.0 = rRF + 20% - 2rRF rRF = 5%. Step 2 Calculate new market return rM increases by 30%, so rM = 1.3(10%) = 13%. Step 3 Calculate new required return on stock rs = 5% + (13% - 5%)2 = 21%. Step 4 Calculate percentage change in return on stock % 40 = 15% 15% - 21% 15. Time Line: 0 12% 1 2 3 9 10 Years ├────────┼─────────┼─────────┼────── ··· ─────┼──────────┤ PMT = 100 100 100 100 100 PV = ? FV = 1,000 Numerical solution: V B = $100(PVIFA B 12%,10 ) + $1,000(PVIF 12%,10 ) = $100((1- 1/1.12 10 )/0.12) + $1,000(1/1.12 10 ) = $100(5.6502) + $1,000(0.3220) = $887.02. 1
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Thus, the value is significantly higher than the market price and the bond should be purchased. Financial calculator solution : Inputs: N = 10; I = 12; PMT = 100; FV = 1,000. Output: PV = -$887.00. 17. Statement a is correct; the other statements are false. A bond's price and YTM are negatively related. If a bond's YTM is greater than its coupon rate, it will sell at a discount. 19. Time Line: 0 4.5% 1 2 3 4 60 6-month | | | | | . . | Periods 50 50 50 50 50 PV = ? FV = 1,000 Numerical solution: V B = $50((1- 1/1.045 )/0.045) + $1,000(1/1.045 ) B 60 60 = $50(20.6380) + $1,000(0.071289) = $1,103.19° $1,103. Financial calculator solution: Inputs: N = 60; I = 4.5; PMT = 50; FV = 1,000. Output: PV = -$1,103.19; V B ° $1,103. B 20. Time Line: 0 5% 1 2 3 4 40 6-month | | | | | . . | Periods 40 40 40 40 40 PV = ? FV = 1,000 Numerical solution: V B = $40((1- 1/1.05 )/0.05) + $1,000(1/1.05 ) B 40 40 = $40(17.1591) + $1,000(0.1420) = $828.36 ° $828. Financial calculator solution: Inputs: N = 40; I = 5; PMT = 40; FV = 1,000. Output: PV = -$828.41; V B ° $828. B 21. Time Line: 0 28% 1 2 3 4 5 6 7 8 Years | | | | | | | | | Deferred PMTs earn 6% 80 80 80 80 80 80 80 80 6% 101.00 6% 107.06 V B = ? 6% 113.48 6% 120.29 FV Deferred PMTs + Interest = 441.83 FV Par = 1,000.00 2
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Numerical solution: Find the compounded value at Year 8 of the postponed interest payments FV Deferred interest = $80(1.06) 7 + $80(1.06) 6 + $80(1.06) 5 + $80(1.06) 4 = $441.83 payable at t = 8.
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