Question

Tardis Intertemporal 9.125% bonds mature March 7, 2028. The bond is callable March 7, 2019 at 10.625 call premium. The offer on the bond to settle March 7, 2015 is currently 100.00.

The Yield to Maturity is________%

and the Yield to Call is________ %

Answer 1

YTM :

YTM is the rate at which PV of Cash inflows are equal to Bond price when the bond is held till maturity. Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate

YTM = 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 @ 9 %	PV of Cash Flows	PVF/ PVAF @ 10 %	PV of Cash Flows
1-13	$                  91.25	7.4869	$      683.18	7.1034	$                     648.18
13	$             1,000.00	0.3262	$      326.18	0.2897	$                     289.66
PV of Cash Inflows			$ 1,009.36		$                     937.85
PV of Cash Oiutflows			$ 1,000.00		$                 1,000.00
NPV			$          9.36		$                     -62.15

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 9 % + [ 9.36 / 71.51 ] * 1%
= 9 % + [ 0.13 ] * 1%
= 9 % + [ 0.1309 % ]
= 9.13 %

Alternatively

When stock is trading at par, Then Coupon Rate and YTM will be same. I.e 9.125%

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

How to calculate PVAF using Excel?
+PV(Rate,NPER,-1)
Rate = Disc rate
NPER - No. of Periods

YTC:

The return a bondholder receives if the bond is held until the call date, which occurs sometime before it reaches maturity.

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 @11 %	PV of Cash Flows	PVF/ PVAF @12 %	PV of Cash Flows
1-4	$                  91.25	3.1024	$                        283.10	3.0373	$                     277.16
4	$             1,106.25	0.6587	$                        728.72	0.6355	$                     703.04
PV of Cash Inflows			$                    1,011.82		$                     980.20
PV of Cash Oiutflows			$                    1,000.00		$                 1,000.00
NPV			$                          11.82		$                     -19.80

YTC = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 11 % + [11.82 / 31.62 ] * 1%
= 11 % + [0.37 ] * 1%
= 11 % + [0.3738 % ]
= 11.37 %

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