Question

A 20-year, zero-coupon bond was recently being quoted at 29.853% of par. Find the current yield and the promised yield of this issue, given that the bond has a par value of $1,000. Then, using semiannual compounding, determine how much an investor would have to pay for this bond if it were priced to yield 8.230%. The current yield on this bond is %. (Round to the nearest whole percent.) The promised yield of this issue is %. (Round to two decimal places.) Using semiannual compounding, the amount an investor would have to pay for this bond if it were priced to yield 4.115% is $ . (Round to the nearest cent.)

Answer 1

Zero Coupon bond will not pay any coupon till maturity. We can receive Maturity value at the end of matuirty.

Current Yield = Coupon Amount / Current Price

= $ 0 / $ 298.53

= 0%

Promised Yield:

Yield is ret from Zero coupon bond. The Rate at which PV of Cash Inflows are equal to Current Price.

Period	CF	PVF @ 3%	Disc CF	[email protected]%	Disc CF
1-40	$             -	23.1148	$          -	21.3551	$          -
40	$ 1,000.00	0.3066	$ 306.56	0.2526	$ 252.57
PV of Cash Inflows	$ 306.56		$ 252.57
Bond Price	$ 298.53		$ 298.53
NPV	$      8.03		$ -45.96

Yield per anum = [ Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 0.5% inc in disc Rate ] * 0.5% ] * 2

= [ 3% + [ 8.03 / 53.98 ] * 0.5% ] * 2

= [ 3% + 0.074% ] * 2

= 3.074% * 2

= 6.15%

Part C:

Value of Bond = PV of CFs from it.

Period	CF	PVF @ 4.115%	Disc CF
1-40	$             -	19.4585	$          -
40	$ 1,000.00	0.1993	$ 199.28
Price	$ 199.28

Pls comment, if any further assistance is required.