Question

An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 8% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell, and each then had a new YTM of 6%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places. Enter all amounts as positive numbers.

	Price @ 8%	Price @ 6%	Percentage Change
10-year, 10% annual coupon	$	$	%
10-year zero
5-year zero
30-year zero
$100 perpetuity

Answer 1

The price of the bond is calculated using the PV function in excel.

= PV(Rate, Nper, PMT, FV, Type)

where, Rate = Yield-to-maturity

Nper = number of periods or years

PMT = Coupon amount

FV = Par value of the bond at maturity

i) For Bond A - 10-year, 10% annual coupon bond

Nper = 10 years

Par-Value = $1000

Coupon rate = 10%

Coupon payment = Coupon rate*Par-value = 10%*1000 = 100

Case A) YTM = Rate = 8%

Price of the bond = PV(8%,10,100,1000,0) = $1,134.20

Case B) YTM = Rate = 6%

Price of the bond = PV(6%,10,100,1000,0) = $1,294.40

Percentage change = (1294.40- 1134.20)/1134.20 = 14.12%

ii) For Bond B - 10-year, zero coupon bond

Nper = 10 years

Par-Value = $1000

Coupon rate = 0%

Coupon payment = Coupon rate*Par-value = 0%*1000 = 0

Case A) YTM = Rate = 8%

Price of the bond = PV(8%,10,0,1000,0) = $463.19

Case B) YTM = Rate = 6%

Price of the bond = PV(6%,10,0,1000,0) = $558.39

Percentage change = (558.39- 463.19)/463.19= 20.55%

iii) For Bond C - 5-year, zero coupon bond

Nper = 5 years

Par-Value = $1000

Coupon rate = 0%

Coupon payment = Coupon rate*Par-value = 0%*1000 = 0

Case A) YTM = Rate = 8%

Price of the bond = PV(8%,5,0,1000,0) = $680.58

Case B) YTM = Rate = 6%

Price of the bond = PV(6%,5,0,1000,0) = $747.26

Percentage change = (747.26- 680.58)/680.58= 9.80%

iv) For Bond D - 30-year, zero coupon bond

Nper = 30 years

Par-Value = $1000

Coupon rate = 0%

Coupon payment = Coupon rate*Par-value = 0%*1000 = 0

Case A) YTM = Rate = 8%

Price of the bond = PV(8%,30,0,1000,0) = $99.38

Case B) YTM = Rate = 6%

Price of the bond = PV(6%,30,0,1000,0) = $174.11

Percentage change = (174.11- 99.38)/99.38= 75.20%

v) For Bond E - $100 perpetuity

Present value of perpetual cash flow = Coupon Amount/YTM of the bond

Case A) YTM = Rate = 8%

Price of the bond = 100/0.08 = 1,250

Case B) YTM = Rate = 6%

Price of the bond = 100/0.06 = $1,666.67

Percentage change = (1666.67- 1250)/1250 = 33.33%