In: Finance
Edward Lewis bought 10-year, 11.8 percent coupon bonds issued by the U.S. Treasury three years ago at $915.06. If he sells these bonds, for which he paid the face value of $1,000, at the current price of $811.17, what is his realized yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments. (Round intermediate calculations to 5 decimal places, e.g. 1.25145 and final answer to 2 decimal places, e.g. 15.25%.)
Realised rate of return |
there are 2 method to caluculate realised yield
1. IRR
2. Shortcut Formula
By IRR
PVAF (Present value annuity factor) : this is used when we receive same amount at same interval for a particular period. In our case we are receiving interest @ of 11.8% i.e 118(1000 * 11.8%)
PVAF = {[1/(1+r)]n -1} / r
r = yield percentage in our case(in IRR method we have to trial and error by taking 2 rates, so i have taken 9% and 10%)
for your reference i am calculating PVAF @ 9% = {[1/(1+r)]n -1} / r = {[1/(1+.09)]3 -1} / 0.09 = {[0.7722] -1} / 0.09
= -0.2278/ 0.09 = 2.5312
n = no of years or period = 3 in our question
PVF where we have to calculate present value of any one time payment, as in our case we will get 811.17 at maturity which is a one time payment and not recurring unlike interest of 118
PVF = [1/(1+r)]n
Year | Cash flow or interest per year(A) | @9% (B) | PV = (A) * (B) | PVF@10% (C) | PV = (A) * (C) |
1-3 | 118 | 2.5313(PVAF) | 298.69 | 2.4868(PVAF) | 293.44 |
3 | 811.17 | .7722(PVF) | 626.38 | .7513(PVF) | 609.43 |
925.07 | 902.87 | ||||
1000 | 1000 | ||||
74.93 | 97.13 |
IRR = 9 + {[74.93/(74.93+97.13)] * (10-9)}
IRR = 9 + {[74.93/(74.93+97.13)] * (1)}
IRR = 9 + {[74.93/(172.06)] * (1)}
IRR = 9 + {[.4354] * (1)}
IRR = 9 + 0.4354
IRR = 9.435% 9.45% (variance is because we took decimal upto 4 places in above calculations)
By YTM(Shortcut formula)
YTM (Yield to maturity)= C + (RV-PP/N)/ (RV+PP)/2
Given:
C= Annual Coupon = $118
RV=Redemption Value = $811.17
PP = Purchase Price = 915.06
N = No of years holding bond = 3 years
Solution:
YTM (Yield to maturity)= C + (RV-PP/N)/ (RV+PP)/2
YTM = [$118 + (811.17-915.06)/3]/[(811.17+915.06)/2]
YTM = [$118 + (-103.89)/3]/[(1726.23)/2]
YTM = [$118 -34.63]/863.11]
YTM = [$83.37/863.11]
YTM = .0965 or 9.65%(approx)