Question

Your father has just retired and does not know what to do with his retirement bonus. One of his friends told him that bonds might be a good option to invest since they are less risky. His friend suggest your father two bonds, however he cannot choose one to invest in. Thus, he asks your opinion.

Bond 1: Issued by U.S. Treasury today. It is a zero coupon Treasury Bill, one year to maturity and 10,000 par value. The yield to maturity on this bill is 7%.

Bond 2: Issued by Galveston Galleries Inc. The 30 year bond was issued ten years ago at a face value of $1,000, paying a coupon rate of 8%. It is paying semi-annual coupon payments. The bonds of companies that were similar to Galveston at the time its bond was issued are now yielding 10%.

a)Calculate the price of Bond 1.
b)CalculatethepriceofBond2.
c) If Bond 1 is selling for $9,000 and Bond 2 is selling for $950 today then decidewhich one your father should choose to invest. Briefly discuss your answer.
d) Assume that one year passed and the yield to maturity for Bond 2 becomes 9%calculate the new price of Bond 2.

e) If your father buys Bond 2 from the price you calculated in part (b) and sells it a year later from the price you calculated in part (d) then calculate the coupon yield and capital gains yield.
f) Assume your father did not sell Bond 2 and hold it one more year so another year passes and the price of Bond 2 becomes $1,101.45. Calculate yield to maturity on this bond. Please make only two iterations. Where you start and in which direction you change the yield to maturity in the second iteration are important for getting full credit on this question.
g) Assume your father bought Bond 2 two years ago and still holds it. Today he reads an article on the newspaper and learns that the credit rating of Galveston Galleries Inc. has decreased from AAA to AA. Briefly discuss how this information will affect the yield to maturity and price of Bond 2.

Answer 1

a]

Price of zero-coupon bond = face value / (1 + YTM)^{years to maturity}

Price of Bond 1 = $10,000 / (1 + 7%)¹

Price of Bond 1 = $9,345.79

b]

Price of a coupon bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of Bond 2 is calculated using PV function in Excel :

rate = 10%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 20 * 2 (20 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $828.41

The price of Bond 2 is $828.41

c]

Bond 1 should be invested in because the value the bond is higher than the market price. Bond 2 should not be invested in because the value of the bond is lower than the market price.

d]

Price of a coupon bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of Bond 2 is calculated using PV function in Excel :

rate = 9%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 19 * 2 (19 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $909.75

The price of Bond 2 is $909.75