Question

An investor purchases a just-issued 10-year, 9.500% semiannual coupon note at 97.805 percent of par value and sells it after 5 years. The bond’s yield to maturity is 9.850% at time of sale, and rises to 10.100% immediately after the purchase but before the first coupon is received. Assume all coupons are reinvested to maturity at the new yield to maturity. What is the realized rate of return (horizon yield) after 5 years?

	A.	9.770%
	B.	9.850%
	C.	9.973%
	D.	10.100%

Answer 1

Present value of bond = 978.05 (1000*97.805%)

Coupon = 1000*9.5%/2 = 47.5

Number of periods = 5* 2 = 10

New YTM = 10.10%/2 = 5.05%

First let's calculate sale price of bond after 5 years

Using financial calculator

[N = 10 ; I/Y = 5.05% ; PV = ? ; PMT = 47.5 ; FV = 1000]

Sale value of bond (PV) = $976.89

Value of $47.5 coupon payments after 5 years (given they are re invested at 5.05%)

[N = 10 ; I/Y = 5.05% ; PV = 0 ; PMT = 47.5 ; FV = ?]

So future value = 598.85

Total Future value =598.95 + 976.89 = $1575.74

Future value = present value*(1+r)^n

r = realized return

n = number of periods

1575.74 = 978.05*(1+r)^10

r = (1575.74 / 978.05)^(1/10)

r = 4.885%

Yearly rate = 4.885% * 2 = 9.770%

option A is correct