Question 1

Consider a 35 year coupon bond with a face value of $1,000 that pays $80 annual coupons (beginning one year from today).Assume that you invest each coupon in a bank that pays 8% interest.By the maturity date of the bond,how much interest have you earned by investing the coupons? Express your answer as a proportion of all of the money that you have received from owning the bond by the maturity date.

Accepted Answer

Step 1 - Calculate the future value of the coupon payments.
FV = C × 11ea7fdb_fbff_012f_a768_e72889f0859e_TB2902_11 FV = 80 × 11ea7fdb_fbff_0130_a768_49713dc6fc06_TB2902_11 = $13,785.34
Using a financial calculator:
N = 35, I/Y = 8 PV = 0, PMT = -80, cpt FV = $13,785.34
Step 2 - Calculate how much interest is earned on the coupons.
13,785.34 - (35 × 80) = $10,985.34
Step 3 - Sum all of the funds from owning the bond.
1,000 + 13,785.34 = $14,785.34
Step 4 - Calculate interest earned as a proportion of all money received from owning the bond. 11ea7fdb_fbff_0131_a768_bb956eec6a60_TB2902_11 = 74.3%

Question 2

Assume that Microsoft bonds have just left the printer and have a stated coupon of $100 (a coupon rate of 10%)and a yield-to-maturity of 15%.The bonds mature in three years and the next coupon is due in one year.What is the fair price for the bond today?

Accepted Answer

P_bond = C × 11ea7fdb_fbfd_c991_a768_7753cc604f86_TB2902_11 + 11ea7fdb_fbfd_f0a2_a768_0f4f0e3077a6_TB2902_11 P_bond = 100 × 11ea7fdb_fbfd_f0a3_a768_294f9812d308_TB2902_11 + 11ea7fdb_fbfd_f0a4_a768_6bca1508224b_TB2902_11 = $885.84 Using a financial calculator: N = 3, I/Y = 15, PMT = -100, FV = -1,000, CPT PV = $885.84

Question 3

In September 2000 the Pullman Group arranged a bond issue for the estate of the late Marvin Gaye.The collateral on the bonds (and source of cash flow for interest and principal payments)consisted of future royalties from classic songs such as "What's Going On," and "I Heard It Though The Grapevine." The bond issue had a $1,000 face value and a coupon rate of 5%.If the bond matures in 26 years,pays semiannual coupons,and the yield to maturity is 6%,what will the bond sell for? Calculate your answer to two decimal points.

Accepted Answer

P_bond = 11ea7fdb_fbfc_b804_a768_13a8b28aecf7_TB2902_11 × 11ea7fdb_fbfc_df15_a768_dd5fa4fafc87_TB2902_11 + 11ea7fdb_fbfc_df16_a768_8196e62979d5_TB2902_11 P_bond = 25 × 11ea7fdb_fbfc_df17_a768_f96cfff65431_TB2902_11 + 11ea7fdb_fbfc_df18_a768_3326c5ef813f_TB2902_11 = $869.17 Using a financial calculator: N = 52, I/Y = 3, PMT = -25, FV = -1,000, CPT PV = $869.17

Question 4

Schlitz Brewery Inc.bonds are trading today for a price of $961.29.The bond currently has 10 years until maturity and has a yield to maturity of 5%.The bond pays annual coupons and the next coupon is due in one year.What is the coupon rate of the bond?

Accepted Answer

P_bond = C × 11ea7fdb_fbfd_7b67_a768_ff5039dd5284_TB2902_11 + 11ea7fdb_fbfd_7b68_a768_f924ef4c1715_TB2902_11 961.29 = C × 11ea7fdb_fbfd_7b69_a768_9f48f8156f01_TB2902_11 + 11ea7fdb_fbfd_a27a_a768_b11025ff5570_TB2902_11 = 347.38 = C × 11ea7fdb_fbfd_a27b_a768_1528b2dcef02_TB2902_11 C = 45 Using a financial calculator: N = 10, I/Y = 5, PV = -961.29, FV = -1,000, CPT PMT = $45 Coupon Rate = 11ea7fdb_fbfd_a27c_a768_972208efd3ea_TB2902_11 = 4.5%

Question 5

Consider a 30 year coupon bond with $75 annual coupons.The next coupon is due one year from today.Assume that the yield curve is flat and so all yields are 8%,and yields are expected to remain constant over the bond's life.At maturity,how much interest will a bond investor have earned on the re-invested coupons?

Accepted Answer

Step 1 - Calculate the future value of the coupon payments.
FV = C × 11ea7fdb_fbff_2842_a768_57663208153e_TB2902_11 FV = 75 × 11ea7fdb_fbff_2843_a768_e5cd39e673df_TB2902_11 = $8,496.24
Using a financial calculator:
N = 30, I/Y = 8 PV = 0, PMT = -75, cpt FV = $8,496.24
Step 2 - Calculate how much interest is earned on the coupons.
8,496.24 - (30 × 75) = $6,246.24

Question 6

The table below shows market prices for four zero coupon bonds with four different terms: one,two,three and four years.The bonds all have a face value of $1,000.Which line best represents the yield curve derived from the bond prices in the table? Use the letter labels at the end of each line.
Zero Coupon Bond Prices

Accepted Answer

Step 1 - Compute the yield for Year 1. k = 11ea7fdb_fbfc_90f1_a768_8de1fc648ad5_TB2902_11 - 1 970.8738 = 11ea7fdb_fbfc_90f2_a768_d3dbf3ef5007_TB2902_11 K₁ = 3% Step 2 - Compute the yield for Year 4. 822.7025 = 11ea7fdb_fbfc_b803_a768_c35197a3300b_TB2902_11 K₄ = 5% The curve is upward sloping. Line C starts at 3% and ends at 5%.

Question 7

The bonds of Vandalay Inc.pay annual coupons at the rate of 7%.They mature in 15 years with a face value of $1,000.What is their price if their yield is 6%?

Accepted Answer

P_bond = C × 11ea7fdb_fbfd_5453_a768_3d7a3b4c8a83_TB2902_11 + 11ea7fdb_fbfd_5454_a768_6f8bbbb9a204_TB2902_11 P_bond = 70 × 11ea7fdb_fbfd_5455_a768_6d43ccd819a6_TB2902_11 + 11ea7fdb_fbfd_5456_a768_27554724e80b_TB2902_11 = $1,097.12 Using a financial calculator: N = 15, I/Y = 6, PMT = -70, FV = -1,000, CPT PV = $1,097.12

Question 8

A 2-year T-Note has a face value of $1,000 and pays annual coupons of $75.The next coupon is due in one year.What is the correct price for the coupon bond today? Use the term structure of interest rates shown below to answer the question.

Accepted Answer

P_bond = 11ea7fdb_fbfe_65e2_a768_d51ea97ab1d3_TB2902_11 + 11ea7fdb_fbfe_8bf3_a768_6f334de3e9fa_TB2902_11 P_bond = 11ea7fdb_fbfe_8bf4_a768_7df1e0392033_TB2902_11 + 11ea7fdb_fbfe_8bf5_a768_c3f25a7ca604_TB2902_11 P_bond = 70.42 + 921.64 = $992.06

Question 9

Consider a 35 year coupon bond that pays $80 annual coupons (beginning one year from today).What is the future value of the coupons at maturity if you can invest them at 8%?

Accepted Answer

FV = C × 11ea7fdb_fbfe_da1d_a768_9b639d045039_TB2902_11 FV = 80 × 11ea7fdb_fbfe_da1e_a768_6110f80cb0e4_TB2902_11 = $13,785.34
Using a financial calculator:
N = 35, I/Y = 8 PV = 0, PMT = -80, cpt FV = $13,785.34

Question 10

Consider a 6-year corporate bond issued by Vandelay Industries.The bond has a face value of $1,000,and has an annual coupon rate of 6.8%.The yield to maturity of the bond is 8.2%.What is the fair price for the bond today?

Accepted Answer

P_bond = C × 11ea7fdb_fbfd_a27d_a768_ffed560f4773_TB2902_11 + 11ea7fdb_fbfd_c98e_a768_b749172254f5_TB2902_11 P_bond = 68 × 11ea7fdb_fbfd_c98f_a768_1106ffbe2f54_TB2902_11 + 11ea7fdb_fbfd_c990_a768_fdff335b1b82_TB2902_11 = $935.67 Using a financial calculator: N = 6, I/Y = 8.2, PMT = -68, FV = -1,000, CPT PV = $935.67

Question 11

The US Government has a 3-year 5% coupon bond with a face value of $1,000.The bond pays annual coupons and the first coupon is due in one year.Using the data on zero coupon US Government bond yields in the table,below,what is the price of the coupon bond?

Accepted Answer

P_bond = 11ea7fdb_fbfe_b307_a768_f30c65a324f4_TB2902_11 + 11ea7fdb_fbfe_b308_a768_73f1a5465d96_TB2902_11 + 11ea7fdb_fbfe_b309_a768_cf3fc9142923_TB2902_11 P_bond = 11ea7fdb_fbfe_b30a_a768_bba6deee3281_TB2902_11 + 11ea7fdb_fbfe_b30b_a768_73b4642a70cc_TB2902_11 + 11ea7fdb_fbfe_b30c_a768_e9e8b3249146_TB2902_11 P_bond = 46.25 + 45.00 + 918.79 = $1,010.04

Question 12

The Federal Government 2-year coupon bond has a face value of $1,000 and pays annual coupons of $33.The next coupon is due in one year.Currently,the one and two-year spot rates on Federal Government zero coupon bonds are 4% and 4.5%.What is the correct price for the coupon bond at time zero (immediately)?

Accepted Answer

P_bond = 11ea7fdb_fbfe_3ecd_a768_97086743a838_TB2902_11 + 11ea7fdb_fbfe_3ece_a768_57307a5f4e7b_TB2902_11 P_bond = 11ea7fdb_fbfe_65df_a768_1de4b1f8d84b_TB2902_11 + 11ea7fdb_fbfe_65e0_a768_97c7e9c1518a_TB2902_11 P_bond = 31.73 + 945.95 = $977.68

Question 13

Consider a Federal Government coupon bond with a $1,000 face value and a coupon rate of 1%.If the bond matures in 25 years,pays semi-annual coupons,and the yield to maturity is 5%,then what will the bond sell for?

Accepted Answer

P_bond = 11ea7fdb_fbfd_2d3e_a768_d1c0784d9142_TB2902_11 × 11ea7fdb_fbfd_2d3f_a768_352575557e69_TB2902_11 + 11ea7fdb_fbfd_2d40_a768_39cd6c392152_TB2902_11 P_bond = 5 × 11ea7fdb_fbfd_2d41_a768_85700f141303_TB2902_11 + 11ea7fdb_fbfd_5452_a768_410fa3f58bf8_TB2902_11 = $432.75 Using a financial calculator: N = 50, I/Y = 2.5, PMT = -5, FV = -1,000, CPT PV = $432.75

Question 14

You have just purchased a 15-year,$1,000 par value US Government bond for $909.20.The yield to maturity on the bond is 8.6%.What is the coupon rate?

Accepted Answer

P_bond = C × 11ea7fdb_fbfd_f0a5_a768_8f6a4eef8602_TB2902_11 + 11ea7fdb_fbfe_17b6_a768_f50174b22cda_TB2902_11 909.20 = C × 11ea7fdb_fbfe_17b7_a768_69244225c044_TB2902_11 + 11ea7fdb_fbfe_17b8_a768_e3d5d8956b00_TB2902_11 619.096 = C × (8.2546) C = 75, so coupon rate = 11ea7fdb_fbfe_17b9_a768_abcb0c598eea_TB2902_11 = 11ea7fdb_fbfe_17ba_a768_697bfae22bf8_TB2902_11 = 7.5% Using a financial calculator: N = 15, I/Y = 8.6, FV = 1,000, PV = -909.20, CPT PMT = 75 Coupon Rate = 11ea7fdb_fbfe_17bb_a768_11f08eb1cd34_TB2902_11 = 11ea7fdb_fbfe_3ecc_a768_d5ea29193fc5_TB2902_11 = 7.5%

Question 15

To raise funds for Gravina Island Bridge,the Government of Alaska issued bonds.The bonds,called "Nowhere Bonds" have a face value of $1,000,15 years to maturity and a 7% coupon rate (annual coupons with the first coupon due in one year).The bonds are priced at $771.82.What is the yield to maturity of the Nowhere Bonds?

Accepted Answer

P_bond = C × 11ea7fdb_fbff_4f58_a768_7bfd6fb5b764_TB2902_11 + 11ea7fdb_fbff_7669_a768_0b5bfc9463a1_TB2902_11 $771.82 = $70 × 11ea7fdb_fbff_766a_a768_3b2c4e82e6b9_TB2902_11 + 11ea7fdb_fbff_766b_a768_4b3584640b19_TB2902_11 k_d = 10% Using a financial calculator: N = 15, PMT = 70, PV = $-771.82, FV = 1,000, CPT I/Y = 10%

Question 16

You just purchased a Federal Government bond for $1,180.23.The bond has a coupon rate of 6%,a face value of $1,000,and yields 3.8%.In how many years will this bond mature?

Accepted Answer

Using a financial calculator:
I/Y = 3.8, PV = -1,180.23, PMT = 60, FV = 1,000, CPT N = 10

Question 17

Consider a 30 year coupon bond that pays $75 annual coupons (beginning one year from today).What is the sum (undiscounted)of the coupons?

Accepted Answer

Sum = number of Coupons × Coupon Amounts = 30 × 75 = $2,250

Question 18

3M bonds are currently trading at $1,104.07.The bonds have a face value of $1,000,an annual coupon rate of 6.75%,and mature in 4 years.What is the yield-to-maturity?

Accepted Answer

P_bond = C × 11ea7fdb_fbff_2844_a768_e33d75ed7872_TB2902_11 + 11ea7fdb_fbff_4f55_a768_83a6f27efd79_TB2902_11 $1,104.07 = $67.5 × 11ea7fdb_fbff_4f56_a768_4ba3fa15acdd_TB2902_11 + 11ea7fdb_fbff_4f57_a768_358cbcbb3a4d_TB2902_11 k_d = 3.89% Using a financial calculator: N = 4, PMT = 67.5, PV = $-1,104.07, FV = 1,000, CPT I/Y = 3.89%

Question 19

Acme Inc.just issued a bond with a $10,000 face value and a coupon rate of 7%.If the bond has a life of 30 years,pays semi-annual coupons,and the yield to maturity is 9%,what will the bond sell for?

Accepted Answer

P_bond = 11ea7fdb_fbfd_0629_a768_0946f39baea3_TB2902_11 × 11ea7fdb_fbfd_062a_a768_c9e794f14246_TB2902_11 + 11ea7fdb_fbfd_062b_a768_95c9379e4540_TB2902_11 P_bond = 350 × 11ea7fdb_fbfd_062c_a768_893d23ac9987_TB2902_11 + 11ea7fdb_fbfd_062d_a768_592b01d1e7d8_TB2902_11 = $7,936.20 Using a financial calculator: N = 60, I/Y = 4.5, PMT = -350, FV = -10,000, CPT PV = $7,936.20

Question 20

A U.S.Government T-Bond with a 15-year maturity has a coupon rate of 5%.The bond has a face value of $1,000 and pays its coupons semi-annually.The next coupon is due in six months.The bond trades for $949.38 to yield 5.5%.What are the cash flows from the bond?

Accepted Answer

The cash flows are the sum of the coupons and the face value.
Annual coupon = 0.05 × $1,000 = $50Sum of coupons = $750
Total Cash Flows = $1,000 + $750 = $1,750

Quiz 7: Interest Rates and Bond Valuation

Assume that Microsoft bonds have just left the printer and have a stated coupon of $100 (a coupon rate of 10%) and a yield-to-maturity of 15%.The bonds mature in three years and the next coupon is due in one year.What is the fair price for the bond today?