Answer the following questions dealing with bonds a. What is the major determina

Question

Answer the following questions dealing with bonds

a. What is the major determinant of bond prices? Explain your answer (2)

b. The ABC bond carries a 6.5% semi-annual coupon rate and matures in 23 years. If the market yield on these bonds is 8%, calculate the price of the bond. (3)

c. If interest rates (yields) do not change in the marketplace, explain what happens to the price on a discounted bond as time goes by.   Explain why that occurs. (2)

d. If John purchased the bond at $1,050, what would his yield to maturity be if the stated rate is 6% (compounded semi-annually) and maturity 10 years? (3)

Explanation / Answer

a. The major determinant of bond prices is the interest rates.

To understand how and why, please assume a bond paying 5% coupon. If the market interest rate is 4%, the bond would be attractive to investors and they would be willing to pay a higher price.

Alternatively if the interest rate in the market is, say, 7%, the bond would be unattractive. The bond price would have to be lowered to give an attractive yield to investors

b.Assuming the par value of the bond is $1,000

Coupon rate = 6.5% semi-annually

Coupon = $1000 * 6.5%/2

= $32.50

Thus, coupon of $32.50 would be received per half year till 23*2 =46 half years and the par value of the bond,i.e., $1,000 would be received at the end of 46 half years

Price of the bond thus would be = $ 32.50 * PVIFA (8%/2, 46 half years) + $1000 PVF (8%/2, 46)

= $32.50 * 20.88 + $1,000 * 0.1646

= $678.75 + $ 164.62

= $843.37

c) In case the interest rates/yields do not change in the market place, the price of the bond approaches par value as time approaches expiration.

This is because the price of the bond is the present value of coupon payments and par value. As more coupons are received, the dependence on par value increases.

d) Let y be the yield of the bond. Coupon received per half year = 6%/2 * 1000 = $30

Using relationship mentioned in (b) and (c) above,

Price of bond = PV of coupon payments + PV of maturity/par value

$1,050 = $30 * PVIFA (y%/2, 10*2) + $1000 * PVF (y%/2,10*2)

Using trial and error, y = 1.58%

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