Bond Excel

5/22/2018 Bond Excel

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Chapter 06Inputs are in Blue

Answers are in Red

NOTE: Some functions used in these spreadsheets may require that

the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.

To install these, click on the Office button

then "Excel Options," "Add-Ins" and select"Go." Check "Analysis ToolPak" and

"Solver Add-In," then click "OK."

2012, The McGraw-Hill Companies


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Quiz 3

A bond with face value $1,000 has a current yield of 6% and a coupon rate of 8%.

What is the bonds price?

Face value 1,000.00$Current Yield 6%Coupon Rate 8%

Solution:

Bond price 1,333.33$ note: current yield =coupon payment/bond price



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Quiz 4

A 6-year Circular File bond pays interest of $80 annually and sells for $950.What are its coupon rate and yield to maturity?

Time 6.00 yearsInterest 80.00Price 950.00

Solution:

Coupon rate 8.00%

Using a financial calculator:

Yield to maturity 9.119%



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Quiz 5

A 6-year Circular File bond pays interest of $80 annually and sells for $950.If Circular File wants to issue a new 6-year bond at face value, what coupon rate must the bond offer?

Time 6.00 yearsInterest 80.00Price 950.00

Solution:

In order for the bond to sell at par, the coupon rate must equal the yield to maturity.


Yield to maturity 9.119%

Hence the coupon rate must be 9.119%



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Quiz 6

A bond has 8 years until maturity, a coupon rate of 8%, and sells for $1,100.

a. What is the current yield on the bond?

b. What is the yield to maturity?

Time 8.00 yearsCoupon rate 8%Price 1,100.00

Solution:

a. Current yield = 7.27% recall: current yield=coupon paym

put the kursor on the answer, klic

b. Using a financial calculator:

Yield to maturity = 6.3662%



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ent/bond price

k on fx to see the functionargument =Rnta (perioder; betalning; nuvrde; slutvrde; typ)



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Quiz 7

General Matters outstanding bond issue has a coupon rate of 10%, and it sells at

a yield to maturity of 9.25%. The firm wishes to issue additional bonds to the public at facevalue. What coupon rate must the new bonds offer in order to sell at face value?

Coupon rate 10%YTM 9.25%

Solution:

Coupon rate on the new bonds = 9.25%



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Quiz 8

Refer to Table 6.1 (below). What is the current yield of the 8.75% 2020 maturitybond? Why is this more than its yield to maturity?

Table 6.1

Maturity Coupon Bid Price Asked Price Asked Yield, %

2012 May 15 1.375 101:05 101:06 0.782013 May 15 3.625 106:31 107:01 1.232014 May 15 4.75 111:22 111:23 1.72020 May 15 8.75 144:17 144:19 3.442025 Aug 15 6.875 133:07 133:11 3.942030 May 15 6.25 128:25 128:27 4.122040 May 15 4.375 100:28 100:29 4.32

Coupon Rate 8.75%Asked Price 144.00 19.00

Solution:

Current yield 6.05%

The current yield exceeds the yield to maturity on the bond because the bond is selling at a

premium. At maturity the holder of the bond will receive only the $1,000 face value, reducingthe total return on investment



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Practice Problem 9

One bond has a coupon rate of 8%, another a coupon rate of 12%. Both bonds have 10-yearmaturities and sell at a yield to maturity of 10%. If their yields to maturity next year are still 10%,what is the rate of return on each bond? Does the higher coupon bond give a higher rate of return?

Coupon rate - bond 1 8.00%Coupon rate - bond 2 12.00%Maturity 10.00 yearsYTM 10.00%YTM next year 10.00%

Solution:


Bond 1:

Rate of return = 10.00%

Bond 2:


Both bonds provide the same rate of return.



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Practice Problem 10

A bond has 8 years until maturity, a coupon rate of 8%, and sells for $1,100.

a. If this bond has a yield to maturity of 8% 1 year from now, what will its price be?

b. What will be the rate of return on the bond?

c. If the inflation rate during the year is 3%, what is the real rate of return on the bond?

Time 8.00 yearsCoupon rate 8%Price 1,100.00YTM 8%Inflation 3%

Solution:

a. Bond Price = 1,000.00$

b. Bond Price 1,000.00$

Rate of return = -1.82%

c. Rate of return -1.82%Real return = -4.68%



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Practice Problem 11

A General Electric bond carries a coupon rate of 8%, has 9 years until maturity, and sells at ayield to maturity of 7%.

a. What interest payments do bondholders receive each year?

b. At what price does the bond sell? (Assume annual interest payments.)

c. What will happen to the bond price if the yield to maturity falls to 6%?

Face value 1,000.00$Time 9.00 years

Coupon rate 8%YTM 7%YTM falls to 6%

Solution:

a. Annual interest payments = 80.00$

b. Annual interest payments 80.00Bond price = 1,065.15$

c. Annual interest payments 80.00

Bond price if YTM falls to 6% = 1,136.03$



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Practice Problem 12

A 30-year maturity bond with face value of $1,000 makes annual coupon payments and has a

coupon rate of 8%. What is the bonds yield to maturity if the bond is selling for

a. 900.00$ ?

b. 1,000.00$ ?

c. 1,100.00$ ?

Face value 1,000.00$Time 30.00 yearsCoupon rate 8%

Solution:


a. Yield to maturity = 8.971%

b. Yield to maturity = 8.000%

c. Yield to maturity = 7.180%



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Practice Problem 13

A 30-year maturity bond with face value of $1,000 makes semi-annual coupon payments

and has a coupon rate of 8%. What is the bonds yield to maturity if the bond is selling for

a. 900.00$ ?

b. 1,000.00$ ?

c. 1,100.00$ ?


Solution:



b. Yield to maturity = 8.000%

c. Yield to maturity = 7.184%



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Practice Problem 14

Fill in the table below for the following zero-coupon bonds. The face value of each bondis $1,000.

PriceMaturity

(years)

Yield to

Maturity300.00$ 30.00 300.00$ 8%

10.00 10%

Face value 1,000.00$

Solution:

Price = $1,000/(1 + y)maturity

PriceMaturity

(years)

Yield to

Maturity300.00$ 30.00 4.095%300.00$ 15.64 8.000%385.54$ 10.00 10.000%



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Practice Problem 15

Perpetual Life Corp. has issued consol bonds with coupon payments of $60. (Consols pay interestforever and never mature. They are perpetuities.) If the required rate of return on these bonds at thetime they were issued was 6%, at what price were they sold to the public? If the required return

today is 10%, at what price do the consols sell?

Coupon Payments 60.00$Required rate of return

at the time of issue 6%Current required rate of return 10%

Solution:

PV of perpetuity = coupon payment/rate of return

Present value = 1,000.00$

If the required rate of return is 10%, the bond sells for:

Present value = 600.00$



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Practice Problem 16

Sure Tea Co. has issued 9% annual coupon bonds that are now selling at a yield to maturity of10% and current yield of 9.8375%. What is the remaining maturity of these bonds?

Face value 1,000.00$Time 30.00 yearsCoupon rate 9%Yield to maturity 10%Current yield 9.8375%

Solution:


Remaining maturity = 20.00 years



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Practice Problem 17

Large Industries bonds sell for $1,065.15. The bond life is 9 years, and the yield to maturity is7%. What must be the coupon rate on the bonds?

Face value 1,000.00$Bond price 1,065.15$Time 9.00 yearsYield to maturity 7%

Solution:


Coupon rate = 8.00%



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Practice Problem 18

a. Several years ago, Castles in the Sand, Inc., issued bonds at face value at a yield to maturityof 7%. Now, with 8 years left until the maturity of the bonds, the company has run into hardtimes and the yield to maturity on the bonds has increased to 15%. What has happened to the

price of the bond?

b. Suppose that investors believe that Castles can make good on the promised coupon payments,but that the company will go bankrupt when the bond matures and the principal comes due.The expectation is that investors will receive only 80% of face value at maturity. If they buy thebond today, what yield to maturity do they expect to receive?

Face value 1,000.00$Yield to maturity 7%Years left 8.00Yield to maturity increased to 15%Face value received by the investors 80%

Solution:

a. Price of bond = 641.01$

b. Price of bond 641.01$Using a financial calculator:

Yield to maturity = 12.87%



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Practice Problem 19

You buy an 8% coupon, 10-year maturity bond for $980. A year later, the bond price is $1,200.

a. What is the new yield to maturity on the bond?

b. What is your rate of return over the year?

Face value 1,000.00$Coupon rate 8%Time 10.00 yearsBond price 980.00Bond price a year later 1,200.00

Solution:



b. Rate of return = 30.61%



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Practice Problem 20

You buy an 8% coupon, 20-year maturity bond when its yield to maturity is 9%. A year later, theyield to maturity is 10%. What is your rate of return over the year?

Face value 1,000.00$Coupon rate 8%Time 20.00 years bond price at t0Yield to maturity 9% 908.71 krYield to maturity next y 10% bond price at t1

832.70 kr

Solution: total return on investment on bond(coupon payment + P1-P0)/ P0

Using a financial calculator: 0.4388%




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:



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Practice Problem 21

Consider three bonds with 8% coupon rates, all selling at face value. The short-term bond has amaturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond hasmaturity 30 years.

a. What will happen to the price of each bond if their yields increase to 9%?

b. What will happen to the price of each bond if their yields decrease to 7%?

Face value 1,000.00$Coupon rate 8%Short term bond maturity 4.00 years

Intermediate-term bond maturity 8.00 yearsLong-term bond maturity 30.00 yearsYield (a) 9%Yield (b) 7%

Solution:

a., b.

Yield 4 Years 8 Years 30 Years7% 1,033.87$ 1,059.71$ 1,124.09$8% 1,000.00$ 1,000.00$ 1,000.00$9% 967.60$ 944.65$ 897.26$

Price of Each Bond at Different Yields to

MaturityMaturity of Bond



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Practice Problem 22

A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $80 andis selling at face value. What will be the rate of return on the bond if its yield to maturity atthe end of the year is

a. 6% ?

b. 8% ?

c. 10% ?

Face value 1,000.00$Annual coupon 80.00$Time 2.00 years

Solution:

a. Rate of return = 9.89%

b. Rate of return = 8.00%

c. Rate of return = 6.18%



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Practice Problem 23

A bond that pays coupons annually is issued with a coupon rate of 4%, maturity of 30 years,and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases

the bond and holds it for 1 year if the bonds yield to maturity at the end of the year is 8%?

Face value 1,000.00$Coupon rate 4%Time 30.00 yearsYield to maturity 7%Yield to maturity by end of 1st year 8%

Solution:

Rate of return = -5.43%



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Practice Problem 24

A bonds credit rating provides a guide to its risk. Long-term bonds rated Aa currently offer yields to

maturity of 7.5%. A-rated bonds sell at yields of 7.8%. If a 10-year bond with a coupon rate of 7% is

downgraded by Moodys from Aa to A rating, what is the likely effect on the bond price?

Face value 1,000.00$Coupon rate 7%Time 10.00 yearsCurrent yield to maturity 7.5%Yield of A rated bonds 8%

Solution:The bonds yield to maturity will increase from 7.5% to 7.8% when the perceived default risk

Increases.

The bond price will fall:

Initial price = $965.68

New price = $945.83



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Practice Problem 25

Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus acoupon payment of $70 at the end of the year. What real rate of return will you earn if the inflationrate is

a. 2% ?

b. 4% ?

c. 6% ?

d. 8% ?

Face value 1,000.00$Annual coupon 70.00$Time 1.00 year

Solution:

a. Real rate of return = 4.902%

b. Real rate of return = 2.885%

c. Real rate of return = 0.9434%

d. Real rate of return = -0.926%



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Practice Problem 26

Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus acoupon payment of $70 at the end of the year and the inflation rate is

a. 2% ?

b. 4% ?

c. 6% ?

d. 8% ?

Now suppose that the bond is a TIPS (inflation-indexed) bond with a coupon rate of 4%.

What will the cash flow provided by the bond be for each of the four inflation rates? What will bethe real and nominal rates of return on the bond in each scenario?

Face value 1,000.00$Time 1.00 yearCoupon rate 4%

Solution:

The principal value of the bond will increase by the inflation rate, and since the couponis 4% of the principal, the coupon will also increase along with the general level ofprices. The total cash flow provided by the bond will be:

1,000 x (1 + inflation rate) + coupon rate x 1,000 x (1 + inflation rate)

Since the bond is purchased for face value, or $1,000, total dollar nominal return istherefore theincrease in the principal due to the inflation indexing, plus coupon income:

Income = ($1,000 x inflation rate) + [coupon rate x $1,000 x (1 + inflation rate)]

Finally: Nominal rate of return = income/$1,000

a. Nominal rate of return = 6.080%

Real rate of return = 4.00%

b. Nominal rate of return = 8.160%


c. Nominal rate of return = 10.240%


d. Nominal rate of return = 12.320%




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Practice Problem 27

Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus acoupon payment of $70 at the end of the year and the inflation rate is

a. 2% ?

b. 4% ?

c. 6% ?

d. 8% ?

Now suppose the TIPS bond in the previous problem is a 2-year maturity bond.

What will be the bondholders cash flows in each year in each of the inflation scenarios?


Solution:

Second-Year

Cash Flow

a. 40.80$ 1,082.02$

b. 41.60$ 1,124.86$c. 42.40$ 1,168.54$d. 43.20$ 1,213.06$

First-Year

Cash Flow



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Challenge Problem 28

Suppose interest rates increase from 8% to 9%. Which bond will suffer the greater percentagedecline in price: a 30-year bond paying annual coupons of 8% or a 30-year zero-coupon bond?

Face value 1,000.00$Interest rate 1 8.00%Interest rate 2 9.00%Time 30.00 yearsCoupon 8.00%

Solution:

Coupon bond

Initial price = 1,000.00$

New price = 897.26$Price decline % = 10.27%

Zero-coupon bond

Initial price = 99.38$New price = 75.37$Price decline % = 24.16%

Hence zero-coupon bond will suffer greater price decline.



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Consider two 30-year maturity bonds. Bond A has a coupon rate of 4%, while bond B has a couprate of 12%. Both bonds pay their coupons semiannually

a. Construct an Excel spreadsheet showing the prices of each of these bonds for yields to maturanging from 2% to 15% at intervals of 1%. Column A should show the yield to maturity(ranging from 2% to 15%), and columns B and C should compute the prices of the two

bonds (using Excels bond price function) at each interest rate.

b. In columns D and E, compute the percentage difference between the bond price and its valuwhen yield to maturity is 8%.

c. Plot the values in columns D and E as a function of the interest rate. Which bonds price isproportionally more sensitive to interest rate changes?

Face value 100.00$Coupon rate bond A 4.00%Coupon rate bond B 12.00%

Time 30.00 yearsYield to maturity 8.00% -144.96 kr

-119.69 krSolution: -100.00 kr

c.a., b.

Yield Price A Price B % Diff. (8%) A % Diff. (8%) B

2% 144.96 324.78 165% 124%3% 119.69 277.21 119% 91%4% 100.00 239.04 83% 65%5% 84.55 208.18 54% 43%

6% 72.32 183.03 32% 26%7% 62.58 162.36 14% 12%

8% 54.75 145.25 0% 0%9% 48.40 130.96 -12% -10%

10% 43.21 118.93 -21% -18%11% 38.93 108.72 -29% -25%12% 35.35 100.00 -35% -31%13% 32.35 92.48 -41% -36%

14% 29.80 85.96 -46% -41%15% 27.62 80.26 -50% -45%

The price of

-100%

-50%

0%

50%

100%

150%

200%

100.00

150.00

200.00

250.00

300.00

350.00

Price A

Price B



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here you can see the higher the yield to maturity (IRR), the lower the bond price.

-

50.00

0% 5% 10% 15% 20%



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on

rity

ond A is more sensitive to interest rate changes as reflected in the steeper curve.

% Diff. (8%) A % Diff. (8%) B



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In Figure 6.7, we saw a plot of theyield curveon stripped Treasury bondsand pointed out thatbonds of different maturities may sell at different yields to maturity. In principle, when we are valuinga stream of cash flows, each cash flow should be discounted by the yield appropriate to its particular

maturity. Suppose the yield curve on (zero-coupon) Treasury strips is as follows:

YTM1 year 4.00%2 5%35 5.50%610 6%

You wish to value a 10-year bond with a coupon rate of 10%, paid annually.

a. Set up an Excel spreadsheet to value each of the bonds annual cash flows using this table ofyields. Add up the present values of the bonds 10 cash flows to obtain the bond price.

b. What is the bonds yield to maturity? recall: Yield to maturity is internal rate of retur

Face value 1,000.00$Coupon rate 10.00%Time to maturity 10.00 years

Solution:

a., b.

Year YTMCash Flow

from Bond

PV of cash

flow1 4.00% 100.00 96.15384615

2 5.00% 100.00 90.702947853 5.50% 100.00 85.161366424 5.50% 100.00 80.721674335 5.50% 100.00 76.51343538

6 6.00% 100.00 70.496054047 6.00% 100.00 66.505711368 6.00% 100.00 62.741237139 6.00% 100.00 59.1898463510 6.00% 1,100.00 614.2342546

Bond price (PV) = 1302.420374

YTM (RATE) = 5.91%

Time to Maturity



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n (IRR, overall interest rate) earned by an investor who buys the bond today at the market price.

stripped Treasury bonds:every coupon payment can be seen as azero coupon bond with time to maturity of the coupon payment.


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Bond Excel