Question

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%

Answer 1

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