Question

Determine the price of the following bonds. Please show your work.

a. Duration: 2 years Coupon Rate: 3% Face Value: $500 Discount Rate: 3.25% whats the Price: _______________

. This bond is selling at a : PREMIUM or DISCOUNT

b. Duration: 3 years Coupon Rate: 3% Face Value: $500 Discount Rate: 2.75%

whats the Price: __________________ ?

c This bond is selling at a : PREMIUM or DISCOUNT (pick one)

d. A $1,000, 10-year Treasury bond with a yearly coupon of $40 is selling for $900. The market interest rate is:

more than 4% OR less than than 4% (pick one)

e.. This bond is selling for premium or discount (pick one)

f A yield of 4.25% on a $1,000, 10-year Treasury bond with a 5% coupon implies that the bond is priced at a  premium or a  discount (select one)

Answer 1

a]

Price of a 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 is calculated using PV function in Excel :

rate = 3.25% (discount rate)

nper = 2 (Years remaining until maturity with 1 coupon payment each year)

pmt = 500 * 3% (annual coupon payment = face value * coupon rate)

fv = 500 (face value receivable on maturity)

PV is calculated to be $497.62

A1 X fo =PV(3.25%,2,500*3%,500) B C D E F A ($497.62)

This bond is selling at a discount as its price is lower than its face value.

b]

Price of a 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 is calculated using PV function in Excel :

rate = 2.75% (discount rate)

nper = 3 (Years remaining until maturity with 1 coupon payment each year)

pmt = 500 * 3% (annual coupon payment = face value * coupon rate)

fv = 500 (face value receivable on maturity)

PV is calculated to be $503.55

A1 X Fac =PV(2.75%,3,500*3%,500) B C D 1| ($503.55)!

c]

This bond is selling at a premium as its price is higher than its face value.

d]

YTM (market interest rate) is calculated using RATE function in Excel with these inputs :

nper = 10 (10 years to maturity with 1 annual coupon payment each year)

pmt = 40 (annual coupon payment. This is a positive figure as it is an inflow to the bondholder)

pv = -900 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 5.31%. This is the YTM.

A1 : x V fic =RATE(10,40,-900,1000) F 1| 5.31%

e]

This bond is selling at a discount as its price is lower than its face value.

f]

If a bond's YTM is lower than its coupon rate,the bond is a premium bond.

A yield of 4.25% on a 5% coupon bond implies that the bond is priced at a  premium