Bond yield calculation

[Hilda_da_horsey]

A six‐year, 5% semiannual‐pay government bond is priced at 97 per 100 of par value. The annual yield‐to‐maturity (stated annual yield based on monthly compounding) is closest to:

a. 5.532%

b. 5.596%

c. 5.670%

Answer is c. 5.532% but I don’t get it. Can someone please help and see what am I missing? I got 5.74% (see below for my working). What am I not doing right? Thanks in advance!

Below are my workings:

I calculate the yield per semiannual period on the semiannual‐pay bond.

N = 12; PMT = $2.5; FV = $100; PV = −$97; CPT I / Y; I / Y = 2.798%

2.798% is multiplied by 2 to determine the stated annual yield (2.798% × 2 = 5.596%).

I then calculate the monthly compounding using (1 + 5.596%/12)^12 = 1.0574 (5.74%)

[Backwardation]

Step 1: Calculate Effective Semi-Annual-Yield (as you did) =2,798%

Step 2: Calculate a effective monthly rate = 1,02798^(1/6) -1 = 0,0046

Step 3: Calculate STATED rate = 0,0046 x 12 =0,05532

You should first calculate effective monthly yield and than make the stated yield out of it. Stated yield is always period yield x Number of Periods a Year.

[tau281290]

I believe the question asks for effective annual yield, using monthly compounding is not relevant. So you just have to do 1.02798^2 -1 = 5.67%.

[Hilda_da_horsey]

@Backwardation

Step 1: Calculate Effective Semi-Annual-Yield (as you did) =2,798%

Step 2: Calculate a effective monthly rate = 1,02798^(1/6) -1 = 0,0046

Step 3: Calculate STATED rate = 0,0046 x 12 =0,05532

You should first calculate effective monthly yield and than make the stated yield out of it. Stated yield is always period yield x Number of Periods a Year.

Thanks Backwardation, I think I get it, it’s asking for the STATED but I went for the compounded one.

[Hilda_da_horsey]

@tau281290

I believe the question asks for effective annual yield, using monthly compounding is not relevant. So you just have to do 1.02798^2 -1 = 5.67%.

Thanks tau281290,

Apologies but there’s a typo in my question, the answer is a. not c.

Backwardation got it right.

[breadmaker]

Even faster way to calc the rate: set P/Y=2 and C/Y=12 and leave all other inputs the same. Prepare to be amazed when you solve for I/Y!

[Hilda_da_horsey]

@breadmaker

Even faster way to calc the rate: set P/Y=2 and C/Y=12 and leave all other inputs the same. Prepare to be amazed when you solve for I/Y!

Thanks but I don’t quite follow, which buttons (commands features) are you referring to in the calculator? Could you please elaborate?

[breadmaker]

@Hilda\_da\_horsey

@breadmaker

Even faster way to calc the rate: set P/Y=2 and C/Y=12 and leave all other inputs the same. Prepare to be amazed when you solve for I/Y!

Thanks but I don’t quite follow, which buttons (commands features) are you referring to in the calculator? Could you please elaborate?

2nd I/Y displays P/Y (payments per year): hit 2 and enter. Hit the down arrow to display C/Y (compounding periods per year): hit 12 and enter. 2nd Quit then go about your TVM solve for I/Y.

[Hilda_da_horsey]

Woah! lightbulb moment. Thanks!

[olajideanuoluwa001]

Thank you breadmaker

[mhusnain]

Thank you all posting question as well as all your answers. I was very confused about the calucation of similar question from my notes. Happy thanksgiving ya’all.