Valuation of Fixed Income Question on Practice paper CFA

CFA Level I FRA
#1
  1. Stellar Corp. recently issued $100 par value deferred coupon bonds, which
    will make no coupon payments in the next four years. Regular annual coupon payments at a rate of 8% will then be made until the bonds mature at the end of 10 years. If the bonds are currently priced at $87.00, their yield to maturity is closest to:
  2. A 6.0%.
  3. B 8.0%.
  4. C 10.1%.

A is correct. The yield to maturity ® is computed by solving for r in the following equation: 87.00=8/(1+r)5 +8/(1+r)6 +8/(1+r)7 +8/(1+r)8 +8/(1+r)9 +
108/(1 + r)10which gives a yield to maturity of 6.0%.

I have 2 doubt about the answer.

  1. why the FV value is not 100 ? why is it 108 ?
  2. and from the equation, I use my calculator type in FV=108 PV=-87 N=6 PMT=8
    and I get CPT I/Y = 12.157 Why the answer give me 6%

Hope you could clarify my doubt. Much appreciated.

#2

  1. The Future Value (FV) at Year 10 should have the Face Value 100 + Coupon 8 = 108 (when the bond matures)

  2. Your workings assume you are calculating the YTM of a 6 year bond.

You can use the [CF] worksheet

CFo = -87
C01 = 0
F01 = 4
C02 = 8
F02 = 5
C03 = 108
F03 = 1

[IRR] [CPT]

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#3

Thank you. That has been very clear to me!

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#4

how would you calculate using a financial calulator?

#5

See fino_abama’s explanation above!! :+1:

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#6

You could use the TVM worksheet and s2000magician’s method (try b first) as follows:

P/Y=C/Y=1
N 6 I 8 PMT 8 FV 100 CPT PV 100 (this is the value at time 4; NB: coupon=YTM so 100 par!!)
2nd CLR TVM
N 4 I 8 FV -100 CPT PV -73.502

Since the price of 73.502 < 87, our discount rate of 8% is too high. Therefore, pick 6%

Just to confirm that 6% is the YTM
P/Y=C/Y=1
N 6 I 6 PMT 8 FV 100 CPT PV -109.83 (value at time 4)
2nd CLR TVM
N4 I 6 FV -109.8346 CPT PV 86.99932

The CF worksheet approach is waaaaaaaay faster!!! :bulb:

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