In: Finance
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.)
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%