# Yield To Call and Yield To Put

Can anyone explain via the use of an example (calculations as well) why the yield to call is greater than the YTM if it is trading at a discount and why the YTP is greater than the YTM if it is trading at a premium???

Suppose that you have a 10-year, semiannual pay, 6% coupon, \$1,000 par bond callable after 5 years at 104, trading at 98.

To calculate the YTM,

• n = 20
• PV = -980
• PMT = 30
• FV = 1,000
• Solve for i = 3.1361%, so YTM = 6.2723%

To calculate YTC,

• n = 10
• PV = -980
• PMT = 30
• FV = 1,040
• Solve for i = 3.5812%, so YTC = 7.1623%

You get more money sooner; that’s why the yield is higher.

(Note that if it’s trading at par, the YTC is also higher. If it’s trading at any price below 107.112, the YTC will be higher than the YTM.)

Suppose that you have a 10-year, semiannual pay, 6% coupon, \$1,000 par bond putable after 5 years at 96, trading at 102.

To calculate the YTM,

• n = 20
• PV = -1,020
• PMT = 30
• FV = 1,000
• Solve for i = 2.8672%, so YTM = 5.7344%

To calculate YTP,

• n = 10
• PV = -1,020
• PMT = 30
• FV = 960
• Solve for i = 2.4141%, so YTP = 4.8281%

You get less money sooner; that’s why the yield is lower.

(Note that if it’s trading at par, the YTP is also lower. If it’s trading at any price above 93.1593, the YTP will be lower than the YTM.)

Thanks s2000.

I didn’t really have a question with YTC and YTP, but looking at your explanation and solved problems, it really crystallizes the concept in my mind.

Fullset

My pleasure.

Awesome.

thanks s2000…appreciate it

You’re welcome.