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# P1.T4.316. Tuckman's yield to maturity (YTM)

#### Fran

AIMs: Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing. Compute a bond's YTM given a bond structure and price. Explain the relationship between spot rates and YTM. Calculate the price of an annuity and a perpetuity.

Questions:

316.1. Assume the following 2-year spot rate curve and corresponding discount function (set of discount factors):

Which is nearest to the semiannually compounded yield to maturity (YTM) of a $100 par bond with two year maturity that pays a 4.0% semi-annual coupon ? a. 2.65% b. 2.94% c. 3.07% d. 3.11% 316.2. Assume the upward-sloping 2-year theoretical spot rate curve, and associated discount factors, below: Consider three bonds with identical par value of$100 and maturity of two years:
• Bond I is a zero-coupon bond
• Bond II pays a semi-annual 2.0% coupon
• Bond III pays a semi-annual 4.0% coupon
From lowest to highest, what is the order of their yields-to-maturity (YTM)?

a. YTM (I) < II < YTM (III)
b. I = II = III (same YTM)
c. III < II < I

316.3. Sarah won a lottery that gives her a choice between two payouts. Neglecting any liquidity or counterparty risk, she simply wants to select the option with the higher present value. Her choices are between an annuity and a perpetuity:

I. The annuity will pay her $1,000 every six months, six months from today, over the next ten years; i.e., equivalent to a 2.0% semiannual coupon on$100,000 notional.
II. A perpetuity will pay her $500 every six months but forever The yield curve happens to be conveniently flat at 8.0% at all maturities. The annuity does not pay anything beyond the final$1,000 "coupon" which is why we might refer to a "notional" rather than a "principal." Which of the following is correct?

a. The annuity has a higher present value regardless of the yield
b. The annuity has a higher present value at the current 8.0% yield but not necessarily at any yield
c. The perpetuity has a higher present value regardless of the yield
d. The perpetuity has a higher present value at the current 8.0% yield but not necessarily at any yield

#### Joseph V2

##### New Member
Subscriber
For Question 316.1, Is there any difference between Yield to maturity and Par Yields of a coupon bond? Because the bond cashflows need to be discounted with coupon rate to get the par value..Kindly confirm

Thanks

#### [email protected]

##### Member
Subscriber
Hi David,
Could the following answers be right?
316.1 c
316.2 a
316.3 b

Dayo

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Hello Dayo,

Thank you for using Bionic Turtle! The answers, along with detailed explanations and discussions, are provided in the link above. All of our paid customers have access to the answers to our daily questions. You can view all of our packages HERE if you would like to have full forum access. Purchasing one of our packages also gives you access to more materials to help in your studies

Nicole

Subscriber
316.1 c
316.2 a
316.3 b

#### flex

##### Member
hi All, hi @David Harper CFA FRM, when i solve Q316.1 using calculator (N = 4, PV = -101.7820, PMT = 2, FV = 100) or excel, there is I/Yr = 3.13 % result. this result mismatch the posted answers, and i'm confused that it exceed z(4) [sr interest rate]. this obstacle return me back to discussion at topic. thx

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
hi All, hi @David Harper CFA FRM, when i solve Q316.1 using calculator (N = 4, PV = -101.7820, PMT = 2, FV = 100) or excel, there is I/Yr = 3.13 % result. this result mismatch the posted answers, and i'm confused that it exceed z(4) [sr interest rate]. this obstacle return me back to discussion at topic. thx
Hello @flex

The answers and explanations are available to members who have purchased one of our study packages. We do not provide the answers here in the free section of the forum. You can view all of our study packages here: https://www.bionicturtle.com/shop-courses/. The purchase of a study package includes forum support for all of our practice questions.

Thank you,

Nicole

#### Brijesh Mishra

##### New Member
Hello @flex

The answers and explanations are available to members who have purchased one of our study packages. We do not provide the answers here in the free section of the forum. You can view all of our study packages here: https://www.bionicturtle.com/shop-courses/. The purchase of a study package includes forum support for all of our practice questions.

Thank you,

Nicole

Staff member
Subscriber