Question

1.You are considering an investment in the bonds of the Front Range Electric Company. The bonds pay interest quarterly, will mature in 15 years, and have a coupon rate of 4.50% on a face value of $1,000. Currently, the bonds are selling for $950.

a.If your required return is 4.80% for bonds in this risk class, what is the highest price you would be willing to pay? (Use the PV function.)

b.What is the current yield of these bonds?

c.What is the yield to maturity on these bonds if you purchase them at the current price? (Use the RATE function.)

d.If you hold the bonds for one year, and interest rates do not change, what total rate of return will you earn, assuming that you pay the market price? Why is this different from the current yield and YTM?

e.If the bonds can be called in three years with a call premium of 4% of the face value, what is the yield to call? (Use the RATE function.)

f.Now assume that the settlement date for your purchase is 7/30/2017, the maturity date is 7/30/2032, and the first call date is 7/30/2020. Using PRICE and YIELD recalculate your answers to parts a, c, and d.

g.If market interest rates remain unchanged, do you think it is likely that the bond will be called in three years? Why or why not?

h.Create a chart that shows the relationship of the bond’s price to your required return. Use a range of 0% to 15% in calculating the prices.

Only answers for E, F, G, H.

Answer 1

a]

Price of bond is calculated using PV function in Excel :

rate = 4.8%/4 (converting annual YTM of bonds into quarterly YTM)

nper = 15 * 4 (15 years remaining until maturity with 4 quarterly coupon payments each year)

pmt = 1000 * 4.5% / 4 (quarterly coupon payment = face value * coupon rate / 4)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $968.05.

A12 foc =PV(4.8%/4,15*4,1000*4.5%/4,1000) D E F G B C 12 (968.05)!

b]

Current yield = annual coupon payment / price of bond

Annual coupon payment = face value * coupon rate

Annual coupon payment = $1000 * 4.5% = $45.

Current yield = $45 / $950 = 4.74%.

c]

YTM is calculated using RATE function in Excel :

nper = 15 * 4 (15 years remaining until maturity with 4 quarterly coupon payments each year)

pmt = 1000 * 4.5% / 4 (quarterly coupon payment = face value * coupon rate / 4)

pv = -950 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 1000 (face value of bond receivable at maturity).

RATE is calculated to be 1.24%. This is the quarterly YTM. To get annual YTM, we multiply this by 4. Annual YTM = 4.98%.

d]

Price of bond after 1 year is calculated using PV function in Excel :

rate = 4.98%/4 (converting annual YTM of bonds into quarterly YTM)

nper = 14 * 4 (14 years remaining until maturity with 4 quarterly coupon payments each year)

pmt = 1000 * 4.5% / 4 (quarterly coupon payment = face value * coupon rate / 4)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $969.55.

A14 - fax =PV(4.8%/4,14*4,1000*4.5%/4,1000) D E F G B C 14 ($969.55)!

total rate of return = (price after 1 year - current price + annual coupon payment) / current price.

total rate of return = ($969.55 - $950 + $45) / $950

total rate of return = 6.79%.

This is different from current yield because this includes price appreciation of the bond. This is different from YTM because it is not is not held until maturity.

Answer 2

The bond is the debt instrument which is used to raise the debt capital in the firm. The investor will get the bond certificate and he is termed as bondholder who gets the periodical interest paid by the company.

The bond with a face value of $1,000 having coupon rate 4.5%, matures in eight years, and pays interest semi-annually is currently selling for $900.

a.

The present value of the bond is the current selling price of the bond more than or less than the par value of the bond at a specified discount rate and at a bond maturity period.

The following is the formula in excel to calculate the present value of the bond.

MS-Excel Formulas Financials PV (rate, nper, pmt, (fv), type)

Substitute the given values in the above formula as follows:

Therefore, the highest price to be paid is.

b.

Current yield is a bonds annual return based on coupon payments and present value of market price of the bond. The following is the formula to calculate the current yield.

Substitute the given value in the above formula as follows:

Therefore, the current yield is

c.

The yield to maturity is the rate of return on bonds. It is the internal rate of return gained by a bondholder at current market price.

The following is the formula in excel to calculate the yield to maturity.

MS-Excel Formulas Financials Rate (nper, pmt, pv, (fv), type)

Substitute the given values in the above formula as follows:

Therefore, the annual yield to maturity (YTM) is.

d.

Calculate the bond’s YTM if the bond is hold for one year as follows:

MS-Excel Formulas Financials Rate (nper, pmt, pv, (fv), type)

Therefore, the yield to maturity is.

e.

Calculate the bond’s YTM as follows:

MS-Excel Formulas Financials Rate (nper, pmt, pv, (fv), type)

Therefore, the yield to call is .