Question

1) a year ago you purchased a $1000 face value bond for $989. A year later you sold the bond for $981 after receiving a coupon payment for $53. What was your rate of capital gain?

2) A banker must earn at least a 4.8% return after expected inflation on short term loans. The inflation rate for the past 6 months has averaged 5.1%. The expected inflation rate for the next twelve months is 7.8%. Nominal interest rates for short term loans were 8.2% last month. What is the minimum nominal interest rate that he should charge for a one year loan?

3) A $5000 face value bond maturing in 4 years has a coupon rate of 4.1 percent. What is the coupon payment?

4) A $1080 face value bond is selling in the market place for $926. It matures in 3 years. If keep to maturity, what is the bond's yield to maturity?

Answer 1

	1)	Purchase Price	$989
		Selling Price	$981
		CapitalGain=981-989=	($8)
		Rate of Capital gain=(-8)/989=	-0.00809
		CapitalGain in percentage	-0.81%
		There is Capital Loss of 0.81%
		Dividend received is dividend income
	2)	Inflation Rate for last 6 months=5.1%	0.051
		Expected inflation rate=7.8%	0.078
		Nominal Rate of interest=8.2%	0.082
		Required RealReturn=4.8%	0.048
		(1+In)=(1+r)*(1+If)
		In=Nominal Interest
		r=Real return=0.048
		If=Inflation rate=0.078
		1+In=1.048*1.078=	1.1297
		In=Nominal Interest rate=1.1297-1=	0.1297
		Minimum Nominal interest for one year loan	12.97%
	3)	Face Value of the bond	$5,000
		Coupon Rate	4.10%
		Annual Coupon Payment=5000*0.041=	$205.00
	4)
	Pv	Current Market Value	$926
	Nper	Number of years	3
	Fv	Amount tobe received at maturity	$1,080
		Yield to maturity	5.26%	(Using RATE function of excelwith Nper=3, Pv=-926, Fv=1080)
		This can also be calculated by using following formula:
		FV=PV*((1+i)^N)
		FV=Future value=$1080
		PV=Present Value=$926
		N=Number of years=3
		i=yield tomaturity
		(1+i)^3=1080/926=	1.166307
		1+i=1.166307^(1/3)=	1.052618
		i=yield tomaturity=	0.052618
		Yield to Maturity =	5.26%