handout - sample bond problems

8/4/2019 Handout - Sample Bond Problems

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Sample Bond Problems(with answers)

Question #1

Cannon Corporation is selling a new issue of bonds to raise money to finance its new line of yogurt products. The

bonds will pay a coupon rate of 5% and will mature in 15 years. The face value of the bonds is $1,000 each; interest

is paid semi-annually.

The market rate of interest is currently 6% for similar bonds. What is the fair price for an investor to pay for one of

these bonds?

The current market price is $920 for each bond. If you paid this price, what would be your yield-to-maturity?

Answer to Question #1

Using 3% as the discount rate and 30 semi-annual periods:

$ 25 x 19.600 = 490.00

1,000 x 0.412 = 412.00Fair Value = $902.00

If you paid a price of $ 920 for each bond, you would earn a yield-to-maturity of 5.8% per year. (A reasonablerounding error is acceptable)

Question #2

You have a chance to buy a BB-rated Grandview, Inc. bond that has a face value of $1,000. The bond has a 7%

coupon rate of interest and matures in six years. Interest is paid semi-annually.

BB-rated bonds of similar maturity pay an interest rate of 8%. How much should you be willing to pay for the

Grandview bond?

If you were to pay the current market price of $940 for the bond, what would be your yield-to-maturity on the bond?


Using 4% as the discount rate and 12 semi-annual periods:

$ 35 x 9.385 = 328.48

1,000 x 0.625 = 625.00Fair Value = $953.48

Yield-to-maturity = 8.3% (a reasonable rounding error is acceptable)

Question #3

You have saved a little over $10,000, which you would like to invest in some high grade corporate bonds. You haveevaluated three different sets of bonds, all of which are rated AA. Assuming that all are equally risky, which of the

bonds should you buy? Answer by (1) comparing the fair price of the bonds to the market price and (2) solving forthe bonds’ yield-to-maturity. (We are assuming that current income and the maturity of the bonds will not affect

your decision.) The information for each bond is given below:

8/4/2019 Handout - Sample Bond Problems

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Sample Bond Problems –

Company A has just issued some new 10-year bonds which pay the current market rate of interest of 6% (i.e.,

the coupon rate is 6%). The current market price of the bonds totals $10,000. Interest is paid semi-annually.

Company B issued some bonds three years ago and pays a coupon rate of 8%. The bonds mature in 7 years andpays interest on an annual basis. The face value of the bonds that you are considering is $9,000 and the current

market price is $9,940.

Company C has issued some new zero-coupon bonds that mature in 10 years. You are considering buying

$18,000 face value of the bonds; the current price is $10,050.


Company A:

Using 3% as the semiannual discount rate and 20 semiannual periods:

$ 300 x 14.8775 = 4,463.2510,000 x 0.5537 = 5,537.00

Fair Value = $10,000.25

At a current market price of $10,000, the bonds are selling for their fair price. (The $0.25 difference is caused byrounding of the present value factors to four decimal places.)


Company B:

Using 6% as the annual discount rate and 7 annual periods:

$ 720 x 5.5824 = 4,019.339,000 x 0.6651 = 5,985.51

Fair Value = $10,004.84

Since the current price of the bonds is $9,940, the bonds are underpriced by $64.84.


Company C:

(Note: Since almost all bonds pay interest semiannually, the zero coupon bond is evaluated using semiannualperiods.) Using 3% as the semiannual discount rate and 20 semiannual periods:

$ 0 x 14.8775 = 0

18,000 x 0.5537 = 9,966.60Fair Value = $9,966.60

Since the current price of the bonds is $10,050, the bonds are overpriced by $83.40.


Conclusion:The only bonds that are underpriced (and the ones with the highest yield-to-maturity) are those of Company B, so

they are the most attractive.

handout - sample bond problems

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