10, a) A security pays $100 in one year and $100 in two years. The one-year disc
ID: 2818355 • Letter: 1
Question
10, a) A security pays $100 in one year and $100 in two years. The one-year discount rate is 4%, the two- year is 4.92%, what is its price? b) what is the "common" discount rate-ie., the same discount rate is applied to both years-such that it produces the price you calculate in a)? This is known as the security's "yield-to-maturity" (or "yield") 11, a) A security pays $100 in one year and $233 in two years. The one-year discount rate is 4%, the two- year is 4.92%. what is its price? b) What is the security's "yield-to-maturity? 12. A five-year annuity pays $22.94. At a price of $100, what is its yield? 13. what is the percentage price change of the security in #10 if: a) the one-year discount rate increases by 1% the two-year discount rate increases by 1%) both discount rates increase by 1%? the yield-to-maturity increases by 1%? b) d) 14, what is the percentage price change of the security in #11 if the yield-to-maturity increases by 1%? 15, what is the percentage price change of the annuity in #12 if the yield-to-maturity increases by 1%? IV 16. A five-year bond with a 4% coupon and face value of 100, what is its price at a yield-to-maturity of: a) b) c) d) 3% 4% 5% Calculate the percentage price changes from a) to b) and from b) to c). 17. Perform the same calculations as in #16 but change the maturity to 20 years.Explanation / Answer
Question 10:
a. Current price = Cash flow/(1+r1) +Cash flow/(1+r2)^2
Current price = 100/(1+0.04) + 100/(1+0.0492)^2 = 100/1.04 + 100/1.0492^2
Current price = $186.995
Current price = $187 (rounded)
b. Let the common discount rate = r
100/(1+r) + 100/(1+r)^2 = 187
(100*(1+r) + 100)/(1+r)^2 = 187
100 + 100r + 100 = 187*(1+r)^2
100r + 200 = 187*(1+ r^2 + 2r)
100r + 200 = 187 +187r^2 + 374 r
187r^2 + 274 r -13 =0
By trial and error, we calculate r = 0.046 or 4.60%
Common discount rate = Yield to maturity = 4.60%
Note: We have answered one full question with all vub-parts. Only one full question will be answered at a time. Kindly post the others separately for experts to asnwer
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.