Question

1. ABC, Inc. has issued a 21-year bond with a par value of $1,000, coupon rate of 7.42%. The yield to maturity (YTM) is 3.03%. Assume semi-annual payments. What is today's price of this bond?Note: Enter your answer rounded off to two decimal points. Do not enter $ or comma in the answer box.

2.A 5% semiannual coupon bond maturing in 5 years with a par value of $100 is trading at $95. Calculate the yield to maturity.

3.Suppose you paid $1,027.58 for a corporate bond that has a 4.13% coupon rate. What is the current yield? Assume that the par value of the bond is $1,000.Note: Convert your answer to percentage and round off to two decimal points. Do not enter % in the answer box.

Answer 1

Answer to Question 1:

Par Value = $1,000

Annual Coupon Rate = 7.42%
Semiannual Coupon Rate = 3.71%
Semiannual Coupon = 3.71% * $1,000
Semiannual Coupon = $37.10

Time to Maturity = 21 years
Semiannual Period = 42

Annual YTM = 3.03%
Semiannual YTM = 1.515%

Price of Bond = $37.10 * PVIFA(1.515%, 42) + $1,000 * PVIF(1.515%, 42)
Price of Bond = $37.10 * (1 - (1/1.01515)^42) / 0.01515 + $1,000 / 1.01515^42
Price of Bond = $1,678.38

Answer to Question 2:

Par Value = $100
Current Price = $95

Annual Coupon Rate = 5.00%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $100
Semiannual Coupon = $2.50

Time to Maturity = 5 years
Semiannual Period = 10

Let Semiannual YTM be i%

$95 = $2.50 * PVIFA(i%, 10) + $100 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -95
PMT = 2.50
FV = 100

I = 3.09%

Semiannual YTM = 3.09%
Annual YTM = 2 * 3.09%
Annual YTM = 6.18%

Answer to Question 3:

Par Value = $1,000
Current Price = $1,027.58

Annual Coupon Rate = 4.13%
Annual Coupon = 4.13% * $1,000
Annual Coupon = $41.30

Current Yield = Annual Coupon / Current Price
Current Yield = $41.30 / $1,027.58
Current Yield = 0.0402 or 4.02%