 # value of a puttable bond

What is the issue price of a puttable note, with a par put after one year on a 2year annual pay 5% coupon note, given that the interest rate at present is 5.2% and in one year wil be 5.5% or 4.7%.

a) 99.895

b) 99.946

c) 100.27

This is a Q off schweser 2012 mock (afternoon Q 44) but i didn’t understand the answer which was B. Please can someone clarify how the answer is reached?

Thanks

Hi,

Not a problem.

Binomial Tree:

Node_0 (current):

Int = 5.2%

Node_t=1,5.5% (year 1, 5.5%)

Use Financial Calculator:

N =1; I/YR = 5.5%, PMT = 5, FV = 100.

Compute PV = 99.526 (In the money, put at 100)

Hence Price = 100 instead of 99.526

Value Node_t=1, 5.5% = Price + Coupon = 100+ 5 = 105

Next: Node_t=1, 4.7% (year 1 , 4.7%)

Again, Use financial caculator:

N =1; I/YR = 4.7%, PMT = 5, FV = 100.

Compute PV = 100.287 (Out of the money, put at 100)

Hence Price = 100.287

Value Node_t=1, 4.7% = Price + Coupon = 100.287 + 5 = 105.287

Next: Obtain avg value of the two nodes at t=1

Average value = (105 + 105.287)/2 = 105.14350

Next: Discount back to t=0 at 5.2%

Issue Price = 105.1435 / 1.052 = 99.946 Answer B

kyh, that’s way too complicated!! No need for calculator.

Just set up the tree and discount each value (price+coupon) by interest rate with 50% probability to each. Adjust price upwards if less than \$100. It takes 1 minute to do this.

Hi Dreary,

Yeap. Thanks. You’re right, since its just 1 year away we could just have 105/1.055 = 99.526 for example.

Yes, and then because that is less than \$100, bring it up to \$100 and add coupon.

Note that I have seen questions that say bond is puttable anytime from now, in which case the answer to the problem above is \$100, not 99.946.