Question

a.Heath Foods’s bonds have 10 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 9%. They pay interest annually and have a 10% coupon rate. What is their current yield?

b.Suppose Hillard Manufacturing sold an issue of bonds with a 12-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments.

1. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 5%. At what price would the bonds sell?
2. Suppose that 2 years after the initial offering, the going interest rate had risen to 11%. At what price would the bonds sell?
3. Suppose that 2 years after the issue date (as in part a) interest rates fell to 5%. Suppose further that the interest rate remained at 5% for the next 10 years. What would happen to the price of the bonds over time?

Answer 1

Answer (a):

Time to maturity = 10 Years

Annual coupon = 1000 * 10% = $100

Yield to maturity = 9%

Price of bond = PV(rate, nper, pmt, fv, type) = PV(9%, 10, -100, -1000, 0) = $1064.18

Current yield of the bond = Annual coupon / Price = 1000/1064.18 = 9.40%

Current yield of the bond = 9.40%

Answer (b) (i):

Two years after the bonds were issued, if going rate of interest on bonds fell to 5%

Time to maturity in semiannual periods = (12- 2) * 2 = 20

Par value = $1000

Semiannual coupon = 1000 * 10%/2 = $50

Semiannual yield = 5%/2 = 2.5%

Price of the bond = PV(2.5%, 20, -50, -1000, 0) = $1389.73

Two years after the bonds were issued when going rate of interest fell to 5% price will be = $1,389.73

Answer (b) (ii):

Two years after the bonds were issued if  going interest rate had risen to 11%:

Semiannual yield = 11%/2 = 5.5%

Price of the bond = PV(5.5%, 20, -50, -1000, 0) = $940.25

Two years after the bonds were issued if  going interest rate had risen to 11% price will be = $940.25

Answer (b) (iii):

Bond referred to is the BOND in answer (a) above:

Suppose that 2 years after the issue date (as in part a) interest rates fell to 5%.

Time to maturity = 10 - 2 = 8 years

Yield to maturity = 5%

Price of bond = PV(rate, nper, pmt, fv, type) = PV(5%, 8, -100, -1000, 0) = $1323.16

If interest rate remains 5%, Price of Bond over time:

2 years after as calculated above price of bond = $1323.16

3 years after price of bond = PV(5%, 7, -100, -1000, 0) = $1,289.32

4 years after price of bond = PV(5%, 6, -100, -1000, 0) = $1,253.78

5 years after price of bond = PV(5%, 5, -100, -1000, 0) = $1,216.67

6 years after price of bond = PV(5%, 4, -100, -1000, 0) = $1,177.30

7 years after price of bond = PV(5%, 3, -100, -1000, 0) = $1,136.16

8 years after price of bond = PV(5%, 2, -100, -1000, 0) = $1,092.97

9 years after price of bond = PV(5%, 1, -100, -1000, 0) = $1,047.62

10 years after price of bond = Par value = $1,000

As we observe if interest rate remains 5%, price of bond will be $1,323.16 after two years and over time

the price will reduce (as given above) as maturity approaches and at maturity the price will be $1,000