Question

The Sisyphean Company has a bond outstanding with a face value of $1,000

that reaches maturity in nine

years. The bond certificate indicates that the stated coupon rate for this bond is 8.5?%

and that the coupon payments are to be made semiannually.Assuming that this bond trades for $1,163?,

then the YTM for this bond is closest? to:

A. 4.9?%

B. 7.34?%

C. 8.56?%

D. 6.11?%

Answer 1

Face Value = $1,000
Current Price = $1,163

Annual Coupon Rate = 8.50%
Semiannual Coupon Rate = 4.25%
Semiannual Coupon = 4.25% * $1,000
Semiannual Coupon = $42.50

Time to Maturity = 9 years
Semiannual Period to Maturity = 18

Let Semiannual YTM be i%

$1,163 = $42.50 * PVIFA(i%, 18) + $1,000 * PVIF(i%, 18)

Using financial calculator:
N = 18
PV = -1163
PMT = 42.50
FV = 1000

I = 3.059%

Semiannual YTM = 3.059%
Annual YTM = 2 * 3.059%
Annual YTM = 6.118% or 6.12%

So, YTM on this bond is closet to 6.11%