Question

Today you paid $4,600 for a bond with following characteristics: Face Value = $5,000. Coupon rate = 9% semi-annual. Maturity = 15 years. What is your YTM (Yield to Maturity)?

Immediately after receiving your 9th coupon payment, you sell the Bond to Adam for $5,800. What is your HPY? What is Adam’s yield to maturity?

Immediately after receiving 8coupon payments, Adam sells the bond to Brenda. Brenda’s YTM = 10%. What is Adam’s HPY?

Answer 1

Part A

Using a financial calculator

FV = 5000

PV = -4600

N = 30 ( 15 years semi-annual periods = 30 semi annual periods)

PMT = 225 (9%/2 = 4.5% coupon payment on face-value $5000)

cpt I/Y, we get I/Y = 5.02

Hence, the YTM = 5.02%*2 = 10.04%

Part B

Total number of coupons enjoyed = 9

Total amount received in coupons = 225*9 = 2025

Holding period yield = (Capital gains + Coupon income) / Initial purchase price

Holding period yield = (5800-4600+2025)/4600 = 0.7011

Holding period yield = 70.11%

For finding Adam's YTM, Using a financial calculator

FV = 5000

PV = -5800

N = 21 ( Total period remaining = 30-9 = 21 semi-annual periods)

PMT = 225 (9%/2 = 4.5% coupon payment on face-value $5000)

cpt I/Y, we get I/Y = 3.42

Hence, the Adam's YTM = 3.42%*2 = 6.84%

Part C

First, we need to find the bond price at which it was sold

Using a financial calculator

FV = 5000

I/Y = 5 (10%YTM/2 = 5% yield per period)

N = 13 ( Total period remaining = 30-9-8 = 13 semi-annual periods)

PMT = 225 (9%/2 = 4.5% coupon payment on face-value $5000)

cpt PV, we get PV = 4765.46

Total number of coupons enjoyed by Adam = 8

Total amount received in coupons = 225*8 = 1800

Adam's HPY = (Capital gains + Coupon income) / Initial purchase price

Adam's HPY = (4765.46-5800+1800)/5800= 0.1320

Adam's HPY = 13.20%