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Exercises

Exercises. 2010 September 29-30. Exercise. A financial adviser has just given you the following advice : “ Long-term bonds are a great investment because their interest rate is over 10%”. Is the financial adviser necessarily right?. Sol.

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Exercises

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  1. Exercises 2010 September 29-30

  2. Exercise • A financialadviserhas just givenyou the followingadvice: “Long-termbonds are a greatinvestmentbecausetheir interest rate isover 10%”. • Is the financialadvisernecessarily right?

  3. Sol • If interest rates rise sharply in the future, long-term bonds may suffer such a sharp fall in price that their return might be quite low, possibly even negative.

  4. Exercise • Ifthereis a decline in interest rates, whichwouldyouratherbe holding, long-termbonds or short-termbonds? • Why?

  5. Sol • You would rather be holding long-term bonds because their price would increase more than the price of the short-term bonds, giving them a higher return

  6. Exercise • A lotteryclaimsisgrandprizeis $ 10 million, payableover 20 years at $ 500,000 per year. • If the first paymentismadeimmediately, whatisthisgrandprizereallyworth? • Use a discount rate of 6%

  7. Sol This is a simple present value problem. Using a financial calculator: • Compute PV: PV = $6,079,058.25

  8. Exercise • Consider a coupon bond thathas a $ 1,000 par value and a coupon rate of 10%. • The bond iscurrentlysellingfor $ 1,150 and haseightyearstomaturity. • Whatis the bond’s yieldtomaturity?

  9. Sol To calculate the bond’s yield to maturity using a financial calculator: • N 8; I 100; FV 1000; PV  1150 • Compute i 7.44

  10. Exercise • You are willingtopay $ 15,625 nowtopurchase a perpetuitythatwillpayyou $ 1,250 eachyear, forever, starting at the end ofthisyear. • Ifyourrequired rate ofreturndoesnotchange, howmuchwouldyoubewillingtopayifthiswhere a 20-year, annualpayment, ordinaryannuity, insteadof a perpetuity?

  11. Sol • 15,625 1,250/i • i 0.08 The answer to the final part, using a financial calculator: • N 20; i 8; P 1250; FV 0 • Compute PV : PV 12,272.69

  12. Exercise • Assume you just deposited $ 1,000 into a bank account. The currentreal interest rate is 2%, and inflationisexpectedtobe 6% over the nextyear. • Whatnominal rate wouldyourequirefrom the bankover the nextyear? • Howmuchmoneywillyouhave at the end ofoneyear?

  13. Exercise(Cont.) • Ifyou are savingtobuy a stereo thatcurrentlysellsfor $ 1,050, willyouhaveenoughtobuyit?

  14. Sol • The required nominal rate would be: iire • 2%  6%  8%. At this rate, you would expect to have $1,000  1.08, or $1,080 at the end of the year. Can you afford the stereo? In theory, the price of the stereo will increase with the rate of inflation. So, one year later, the stereo will cost $1,050  1.06, or $1,113. You will be short by $33.

  15. Exercise • Find the price of a 10% coupon bond with a face valueof $ 1,000, a 12.25% yieldtomaturity and eightyearstomaturity

  16. Sol • N = Yearstomaturity = 8 • FV = 1,000 • i = 12.25% • Coupon payments = 100 • PV = 889.20

  17. Exercise • A 10-year, 7% coupon bond with a face valueof $ 1,000 iscurrentlysellingfor $ 871.65. • Computeyour rate ofreturnifyou sell the bond nextyearfor $ 880.10

  18. Sol • R= (70 + 880.10 – 871.65) / 871.65 = • R= 0,09 = 9%

  19. Exercise • You have paid $980.30 for an 8% coupon bond with a face value of $1,000 that mature in five years. • You plan on holding the bond for one year. If you want to earn a 9% rate of return on this investment, what price must you sell the bond for?

  20. Sol • (80 + 980.30 – P t+1) / 980.30 = 9% • P t+1 = 988.53

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