Question

In: Finance

Christie DeLeon purchased a ten-year $1,000 bond with semiannual coupons for $962. The bond had a...

Christie DeLeon purchased a ten-year $1,000 bond with semiannual coupons for $962. The bond had a $1,200 redemption payment at maturity, a nominal coupon rate of 7% for the first five years, and a nominal coupon rate of q% for the final five years. Christie calculated that her annual effective yield for the ten-year period was 7.25%. Find q. (Round your answer to two decimal places.)

Solutions

Expert Solution

Effctive Yield = [(1+Semi Annual Rate)^2]-1

0.0725 = [(1+R)^2]-1

1.0725^1/2 = 1+R

Therefore, R = 1.035616-1 = 0.035616

Period Cash Flow Discounting Factor
[1/(1.035616^year)]
PV of Cash Flows
(cash flows*discounting factor)
1 35 0.965608874 33.7963106
2 35 0.932400498 32.63401744
3 35 0.900334195 31.51169684
4 35 0.869370689 30.42797412
5 35 0.839472052 29.38152183
6 35 0.810601664 28.37105822
7 35 0.78272416 27.3953456
8 35 0.755805395 26.45318882
9 35 0.729812397 25.54343388
10 35 0.704713327 24.66496644
11 0.680477442 0
12 0.657075057 0
13 0.634477506 0
14 0.61265711 0
15 0.591587143 0
16 0.571241795 0
17 0.551596147 0
18 0.532626134 0
19 0.514308522 0
20 0.496620873 0
20 1200 0.496620873 595.9450475
Price of the Bond =
Sum of PVs
886.1245613

Price of Bond without considering coupons for last 5 years = 886.12

PV of Coupons of last 5 years = 962-886.12 = $75.88

FV of $75.88 at the end of 5th year = PV*[(1+Interest Rate)^Number of Periods] = 75.88*[(1+0.035616)^10] = 75.88*1.419 = $107.67

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, PV = 107.67, i = Interest Rate = 0.035616, n = Number of Periods = 10

Therefore,

107.67 = P*[1-{(1+0.035616)^-10}]/0.035616

3.83477 = P*0.295287

Therefore, Coupon = Annuity = P = 3.83477/0.295287 = $12.9866

Therefore, Semi-Annual Rate = 12.9866/1000 = 0.0129866

Therefore, Nominal Annual Rate = Semi Annual Rate*2 = 0.0129866*2 = 0.0259732

Therefore, Q = 2.5973%


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