Question

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

Answer 1

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)