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Ch 04 P16 Build a Model 3/6/2003

Rework Problem 4-9 using a spreadsheet. After completing questions a through d, answer the new question.4-9. A 10-year 12 percent semiannual coupon bond, with a par value of $1,000, may be called in 4

years at a call price of $1,060. The bond sells for $1,100. (Assume that the bond has just been

issued.)

Work parts a through d with a spreadsheet. You can also work these parts with a calculator to check your

spreadsheet answers if you aren't confidient of your spreadsheet solution. You must then go on to work the

remaining parts with the spreadsheet.

a. What is the bond's yield to maturity?

Basic Input Data:

Years to maturity: 10Periods per year: 2

Periods to maturity:

Coupon rate: 12%

Par value: $1,000

Periodic payment:

Current price $1,100

Call price: $1,060

Years till callable: 4

Periods till callable:

YTM = This is a nominal rate,not the effective rate. Nominal rates are generally

quoted.

Duration: Calculate the duration using the duration function

Use the Excel duration function to find the duration of

b. What is the bond's current yield?

Current yield = Ann. Coupon / Price

/

c. What is the bond's capital gain or loss yield?

Cap. Gain/loss yield = YTM - Current yield

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Note that this is an economic loss, not a loss for tax purposes.

d. What is the bond's yield to call?

Chapter 4. Ch 04 P16 Build a Model

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Here we can again use the Rate function, but with data related to the call.

YTC =

The YTC is much lower than the YTM because if the bond is called, the buyer will lose the difference between

the call price and the current price in just 4 years, and that loss will offset much of the interest imcome. Notetoo that the bond is likely to be called and replaced, hence that the YTC will probably be earned.

NOW ANSWER THE FOLLOWING NEW QUESTIONS:

e. How would the price of the bond be affected by changing interest rates? (Hint: Conduct a sensitivity analysis of

price to changes in the yield to maturity, which is also the going market interest rate for the bond. Assume

that the bond will be called if and only if the going rate of interest falls below the coupon rate. That is an

oversimplification, but assume it anyway for purposes of this problem.)

Nominal market rate, r: 12%

Value of bond if it's not called:

Value of bond if it's called: The bond would not be called unless r

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If you study the graph, you will see that the "not called" situation shows the greatest price sensitivity, the "called"the least sensitivity, and the "modified" falls somewhere in between. Actually, the modified situation, which is

representative of most actual bonds because most bonds are callable, shows that bondholders will not win big if

rates fall because then the bond will be called, but they do lose big if rates rise because then the bonds will not be

called. In terms of the graph, the sensitivity line is notsteep where we want it to be steep, to the left of the 12%

coupon rate, but it is steep where we do not want it to be steep, to the right of 12%. The clear conclusion is

that callable bonds are riskier than non-callable bonds, and their risk is asymmetric.