Question

Answer as most as possible I want to understand it all

1. Union Local School District has bonds outstanding with a coupon rate of 4.2 percent paid semiannually and 17 years to maturity. The yield to maturity on these bonds is 3.5 percent and the bonds have a par value of $5,000.

-What is the dollar price of each bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

2.  Fluss AB has 9.5 per cent coupon bonds making annual payments with a YTM of 7.1 per cent. The current yield on these bonds is 7.5 per cent. The par value of the bond is €1,000.
How many years do these bonds have left until they mature?

3.Laurel, Inc., and Hardy Corp. both have 7 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has four years to maturity, whereas the Hardy Corp. bond has 15 years to maturity.

a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?

b.  If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of these bonds be then?

4. Stand AG has bonds on the market with 17.5 years to maturity, a YTM of 6 per cent, and a current price of €930. The bonds make semiannual payments. The par value of the bond is €1,000.

-What must the coupon rate be on these bonds?

Answer 1

Answer to Question 1:

Par Value = $5,000

Annual Coupon Rate = 4.20%
Semiannual Coupon Rate = 2.10%
Semiannual Coupon = 2.10% * $5,000
Semiannual Coupon = $105

Time to Maturity = 17 years
Semiannual Period = 34

Annual YTM = 3.50%
Semiannual YTM = 1.75%

Current Price = $105 * PVIFA(1.75%, 34) + $5,000 * PVIF(1.75%, 34)
Current Price = $105 * (1 - (1/1.0175)^34) / 0.0175 + $5,000 / 1.0175^34
Current Price = $105 * 25.462378 + $5,000 * 0.554408
Current Price = $5,445.59

Answer to Question 2:

Par Value = €1,000

Annual Coupon Rate = 9.50%
Annual Coupon = 9.50% * €1,000
Annual Coupon = €95

Annual YTM = 7.10%

Current Yield = Annual Coupon / Current Price
0.0750 = €95 / Current Price
Current Price = €1,266.67

Let Time to Maturity be n years

€1,266.67 = €95 * PVIFA(7.10%, n) + €1,000 * PVIF(7.10%, n)

Using financial calculator:
I = 7.10%
PV = -1266.67
PMT = 95
FV = 1000

N = 22.68

Number of Years to Maturity = 22.68 years or 23 years