Question

A company has the following bond outstanding. The bond is callable every year on May 1st, the anniversary date of the bond. The bond has a deferred call with three years left. The call premium on the first call date is one year's interest. The call premium will decline by 10 percent of the original call premium for 10 years. Eleven years from today, the call premium will be zero. Given the following information, what is the yield to worst for this bond?

Current date:		5/1/2016
Maturity date:		5/1/2036
Price (percent of par):		104.5
Coupon rate:		10.00%
Par value (percent of par):		100
Coupons per year:		2
Call date	Call premium
5/1/2019	$          100.00
5/1/2020	$            90.00
5/1/2021	$            80.00
5/1/2022	$            70.00
5/1/2023	$            60.00
5/1/2024	$            50.00
5/1/2025	$            40.00
5/1/2026	$            30.00
5/1/2027	$            20.00
5/1/2028	$            10.00

Answer 1

Yield to worst is the lower of yield to call (YTC) and yield to maturity (YTM).

YTM is calculated using RATE function in Excel with these inputs :

nper = 20*2 (20 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 10% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1000 * 104.5 / 100 (current bond price = face value * price as percent of par / 100. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 4.75%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 9.49%

А1 : x v f =RATE(20*2,1000*10%/2,-1000*104.5/100,1000)*2 в А 9.49%| 1

YTC for each call date is calculated using RATE function in Excel with these inputs :

nper = __* 2 (__ years to call date with 2 semiannual coupon payments each year)

pmt = 1000 * 10% / 2 (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -1000 * 104.5 / 100 (current bond price = face value * price as percent of par / 100. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 + __ (call price of the bond receivable on call date = face value + call premium. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be __%. This is the semiannual YTC. To calculate the annual YTC, we multiply by 2. Annual YTC is __%

Α Number of Call Call date years until premium call 5/1/2019 $100 11.10%l 5/1/2020 $90] 10.46% 5/1/2021) $80] 10.10% 5/1/2022 $70 9.87% 5/1/2023 $60) 9.72% 5/1/2024 8 $50 9.61% 5/1/2025 9 $40 9.53% 5/1/2026 101 $30 9.48% 5/1/2027 $20 9.44% 5/1/2028 121 $109.41% VOUW TILLHET 11

YTC А в Number Call Call date of years until call premium 4 43586 100 5 43952 4 90 6 44317 5 80 7 44682 16 70 8 45047 9 45413 50 10 45778 11 46143 10 12 46508 11 20 13 46874 12 10 TOON 60 I=RATE(B4*2,1000*10%/2,-1000*104.5/100,1000+C4)*2 =RATE(B5*2, 1000*10%/2,-1000*104.5/100,1000+C5)*2 =RATE(B6*2,1000*10%/2,-1000*104.5/100,1000+C6*2 I=RATE(B7*2.1000*10%/2.-1000*104.5/100, 1000+C7)*2 =RATE(B8*2, 1000*10%/2,-1000*104.5/100,1000+C8)*2 =RATE(B9*2,1000*10%/2,-1000*104.5/100, 1000+C9)*2 =RATE(B10*2, 1000*10%/2,-1000*104.5/100,1000+C10)*2 =RATE(B11*2, 1000*10%/2,-1000*104.5/100,1000+C11)*2 I=RATE(B12*2,1000*10%/2,-1000*104.5/100,1000+C12)*2 | ERATE(B13*2, 1000*10%/2,-1000*104.5/100,1000+C13)*2 140 30

The lowest YTC is 9.41%.

The YTM is 9.49%.

Yield to worst is the lower of yield to call (YTC) and yield to maturity (YTM).

The yield to worst is 9.41%