Question

In: Finance

A callable bond pays annual interest of $5, has a par value of$100, matures in...

A callable bond pays annual interest of $5, has a par value of $100, matures in 10 years but is callable in 4 years at a price of $110, and has a value today of $106. Calculate the yield to call.

Group of answer choices

  • 5.18%

  • 5.27%

  • 5.39%

  • 5.58%

Solutions

Expert Solution

YTC:
YTC is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till it is called.

YTC = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%

Year Cash Flow PVF/ PVAF @5 % PV of Cash Flows PVF/ PVAF @6 % PV of Cash Flows
1-4 $                    5.00 3.5460 $                          17.73 3.4651 $                       17.33
4 $                110.00 0.8227 $                          90.50 0.7921 $                       87.13
PV of Cash Inflows $                        108.23 $                     104.46
PV of Cash Oiutflows $                        106.00 $                     106.00
NPV $                            2.23 $                        -1.54

YTC = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 5 % + [2.23 / 3.77 ] * 1%
= 5 % + [0.59 ] * 1%
= 5 % + [0.5905 % ]
= 5.58 %

PVAF = Sum [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r - Disc rate per period
n - No. of Periods

How to calculate PVAF in Excel?
+PV(Rate,NPER,-1)
Rate - Disc Rate per period
NPER - No. of Periods

OPtion D is correct


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