Question

Bonds valuation

You own a bond that pays 70$ in annual interest, with a 1 000$ par value. It matures in 15 years. Your required rate of return is 7%.

Ba: Calculate the value of the bond.

Bb: How does the value change if your required rate of return (i) increases to 9% or (ii) decreases to 5% ?

Bc: Explain the implications of your answers in part Bb as they relate to interest rate risk, premium bonds, and discount bonds.

Bd: Assume that the bond matures in 5 years instead of 15 years. Recompute your answers in part Bb.

B1: Calculate the value of a bond that will mature in 16 years and has a 1 000$ face value. The yearly coupon interest rate is 4,5%, and the investor’s required rate of return is 6%.

B2: Trico bonds have an annual coupon rate of 8% and a par value of 1 000$ and will mature in 20 years.

B2a: If you require a return of 7%, what price would you be willing to pay for the bond ?

B2b: What happens if you pay more for the bond?

B2c: What happens if you pay less for the bond?

Prices and yields

A six-year government bond makes annual coupon payments of 5% and offers a yield of 3% annually compounded. Suppose that one year later the bond still yields 3%.

P.1: What return has the bondholder earned over the 12-month period?

P.2: Now suppose that the bond yields 2% at the end of the year. What return did the bondholder earn in this case?

Equity valuation:

You are willing to make a 10 000 $ investment in equity. You have the three following alternatives for investing that money:

(i) Bank of America bonds with a par value of 1 000$, that pays 6,35% on its par value in interest, sells for 1 020 $ and matures in 5 years.

(ii) Southwest Bancorp preferred stock paying a dividend of 2,63$ and selling for 26,25$ on the market.

(iii) Emerson Electric common stock selling for 52$ on the market, with a par value of 5$. The stock recently paid a 1,6$ dividend and the firm's earnings per share has increased from 2,23$ to 3,30$ in the past 5 years. The firm expects to grow at the same rate for the foreseeable future.

Your required rates of return for these investments are 5% for the bond, 8% for the preferred stock, and 12% for the common stock. Using this information, answer the following questions:

Ea: Calculate the value of each investment based on your required rate of return.

Eb: Which investment would you select, and why?

Ec: Assume Emerson Electric's managers expect earnings to grow at 1% above the historical growth rate. How does this affect your answers to parts Ea and Eb?

Ed: What required rates of return would make you indifferent to all three options?

Dividends discount model:

The MBS Corporation’s dividends per share are expected to grow indefinitely by 5% per year.

DDa.       If this year-end dividend is $8 and the market capitalization rate is 10% per year, what must the current stock price be according to the DDM (Dividends Discounting Model)?

DDb.      If the expected earnings per share are 12$, what is the implied value of the ROE on future investment opportunities?

DDc.       How much is the market paying per share for growth opportunities (i.e., for an ROE on future investments that exceeds the market capitalization rate)?

The stock of Nogo Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue indefinitely.

DD1.       Assuming the current market price of the stock reflects its intrinsic value as computed using the constant-growth DDM (Dividends Discounting Model), what rate of return do Nogo’s investors require?

DD2.      By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested?

DD3.       If Nogo were to cut its dividend payout ratio to 25%, what would happen to its stock price? What if Nogo eliminated the dividend?

Answer 1

B]

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 = 7% (YTM of bonds = required return)

nper = 15 (Years remaining until maturity with 1 coupon payment each year)

pmt = 70 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,000.00

b]

(i)

Price of bond is calculated using PV function in Excel :

rate = 9% (YTM of bonds = required return)

nper = 15 (Years remaining until maturity with 1 coupon payment each year)

pmt = 70 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $838.79

(ii)

Price of bond is calculated using PV function in Excel :

rate = 5% (YTM of bonds = required return)

nper = 15 (Years remaining until maturity with 1 coupon payment each year)

pmt = 70 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,207.59

c]

The implications are that :

• A bond trades at a premium (above par) if the YTM is lower than the coupon rate
• A bond trades at a discount (below par) if the YTM is higher than the coupon rate
• Interest rate risk arises for bonds due to the changes in market interest rates, since bond price is affected by changing interest rates

d]

(i)

Price of bond is calculated using PV function in Excel :

rate = 9% (YTM of bonds = required return)

nper = 5 (Years remaining until maturity with 1 coupon payment each year)

pmt = 70 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $922.21

The change in bond price is less than the change for a 15-year bond

(ii)

Price of bond is calculated using PV function in Excel :

rate = 5% (YTM of bonds = required return)

nper = 5 (Years remaining until maturity with 1 coupon payment each year)

pmt = 70 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,086.59

The change in bond price is less than the change for a 15-year bond

The change in bond price is less than the change for a 15-year bond