Question

Suppose that you have just bought a bond with a coupon rate of 10 percent paid annually and $1,000 face value. This bond will mature in 15 years. You bought the bond when its yield to maturity was 8 percent. If yield to maturity of this bond becomes 12 percent after two years and you sell the bond right after receiving the second coupon, what will be the IRR from this investment?

A. ‐4.55% B. ‐4.34% C. ‐1.74% D. +0.07% E. +13.51%

Answer 1

Price of bond		=	PV of all interest payment+PV of redemption value
		=	[Coupon * PVAF (YTM,years to maturity)]+[PVF(YTM,years) *redemption value]
Price of bond when purchased
	Coupon	=	$1000*10%=$100
	Years	=	15
	YTM	=	8%
	Redemption value	=	$1,000
	Price	=	[$100*PVAF(8%,15yrs)]+[PVF(8%,15yrs)*$1000]
		=	[$100*8.5595]+[0.3152*$1,000)
		=	$855.95+$315.25
		=	$1,171.20
Price of bond when Sold after 2 years
	Coupon	=	$1000*10%=$100
	Years	=	13
	YTM	=	12%
	Redemption value	=	$1,000
	Price	=	[$100*PVAF(12%,13yrs)]+[PVF(12%,13yrs)*$1000]
		=	[$100*6.4235]+[0.2292*$1,000)
		=	$642.35+$229.17
		=	$871.52
Statement of cashflow from Bond
Year	Particular	Amount
0	Purchase price paid	($1,171.20)
1	Interest received	$100
2	Sale price+Interest received	$871.52+$100=$971.52
	IRR= -4.55%
	The correct answer is (A) -4.55%
Note- IRR,PVAF and PVF can be solved/found by using Financial calculators or Excel.
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