Question 1

Universal Exports Inc.just issued $1,000 face bonds for $1,211.The bonds have a maturity of ten years and a coupon rate of 10%.What is the bonds' yield to maturity?

Accepted Answer

P_bond = C × 11ea7fdb_fc00_d61f_a768_93fa4a613015_TB2902_11 + 11ea7fdb_fc00_d620_a768_e96af85d11d7_TB2902_11 $1,211 = $100 × 11ea7fdb_fc00_d621_a768_59b14a3f74ca_TB2902_11 + 11ea7fdb_fc00_d622_a768_2170f1684eaf_TB2902_11 k_d = 7% Using a financial calculator: N = 10, PMT = 100, PV = $-1,211, FV = 1,000, CPT I/Y = 7%

Question 2

What is the yield to maturity for a four-year,5% annual coupon bond selling for $965.34?

Accepted Answer

P_bond = C × 11ea7fdb_fc01_2447_a768_0b6af2113feb_TB2902_11 + 11ea7fdb_fc01_2448_a768_c7af9f880f5e_TB2902_11 $965.34 = $50 × 11ea7fdb_fc01_2449_a768_410e6acca3a2_TB2902_11 + 11ea7fdb_fc01_244a_a768_55feb813ffcc_TB2902_11 k_d = 6% Using a financial calculator: N = 4, PMT = 50, PV = $-965.34, FV = 1,000, CPT I/Y = 6%

Question 3

Three-year T-Notes with a coupon of 10% are trading for $951.96 to yield 12%.(With a $1,000 face value.)Microsoft has just issued a three year bond with a 10% coupon and a face value of $1,000.Analysts estimate that the default risk premium on Microsoft bonds is 3% and the liquidity risk premium is the same as the T-Note.What is the fair price for the Microsoft bond today?

Accepted Answer

Since the Microsoft bond has the same maturity and liquidity risk as the T-Note, the only difference in the yield is the default risk premium of 3%. Thus, the yield on the Microsoft bond is 12% + 3% = 15%. P_bond = C × 11ea7fdb_fbff_eba6_a768_83ce83857d0b_TB2902_11 + 11ea7fdb_fbff_eba7_a768_cd0b1168b79a_TB2902_11 P_bond = $100 × 11ea7fdb_fbff_eba8_a768_6f43de65be7b_TB2902_11 + 11ea7fdb_fbff_eba9_a768_955fd37e1156_TB2902_11 = $885.84 Using a financial calculator: N = 3, I/Y = 15 PMT = 100, FV =1,000 CPT PV = $885.84

Question 4

Man-zeer Inc.,(a Kramer/Costanza joint venture)bonds are currently trading at $974.79.The bonds have a face value of $1,000,an annual coupon rate of 7.5% with payments made semi-annually,and mature in 20 years.What is the yield-to-maturity?

Accepted Answer

P_bond = C × 11ea7fdb_fbff_9d7c_a768_eff9a545e464_TB2902_11 + 11ea7fdb_fbff_9d7d_a768_732a171769d0_TB2902_11 $974.79 = $75 × 11ea7fdb_fbff_9d7e_a768_fb9b1056641c_TB2902_11 + 11ea7fdb_fbff_9d7f_a768_55505b5c81df_TB2902_11 k_d = 7.75% Using a financial calculator: N = 20, PMT = 75, PV = $-974.79, FV = 1,000, CPT I/Y = 7.75% As a quick check: Since the price is only a little below par, the yield to maturity should be only slightly above the coupon rate.

Question 5

The yield to maturity for a bond selling at par is

Accepted Answer

A bond selling "at par" means that the bond is selling for its face value, usually $1,000. The yield-to-maturity is the return that the bond holder will earn if she pays the price (P_bond) and holds the bond to maturity.

Question 6

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.On the maturity date,how much money do you have (in total)from the bond?

Accepted Answer

Step 1 - Calculate the future value of the coupon payments.
FV = C × 11ea7fdb_fbff_eba4_a768_077837a8875e_TB2902_11 FV = 80 × 11ea7fdb_fbff_eba5_a768_17ac4add7636_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

Question 7

What is the value of a six-year,6% semiannual bond if market yields on similar bonds are 4%? The face value of the bond is $1,000.

Accepted Answer

P_bond = 11ea7fdb_fc00_af0a_a768_67706719d3d1_TB2902_11 × 11ea7fdb_fc00_af0b_a768_47f446804401_TB2902_11 + 11ea7fdb_fc00_af0c_a768_69947198819e_TB2902_11 P_bond = 30 × 11ea7fdb_fc00_af0d_a768_a7606cb30cfa_TB2902_11 + 11ea7fdb_fc00_af0e_a768_afe7f8bffe02_TB2902_11 = $1,105.75 Using a financial calculator: N = 12, I/Y = 2, PMT = -30, FV = -1,000, CPT PV = $1,105.75

Question 8

What is the price of a four-year,10% annual coupon bond if the yield to maturity is 5%? The bond's face value is $1,000.

Accepted Answer

P_bond = C × 11ea7fdb_fc01_4b5b_a768_0d253387480c_TB2902_11 + 11ea7fdb_fc01_4b5c_a768_fb2d8f2409d4_TB2902_11 P_bond = $100 × 11ea7fdb_fc01_4b5d_a768_1d87e3963be4_TB2902_11 + 11ea7fdb_fc01_4b5e_a768_21deb56a22a5_TB2902_11 = $1,177.30 Using a financial calculator: N = 4, I/Y = 5 PMT = 100, FV =1,000 CPT PV = $1,177.30

Question 9

The ________ is the percentage return an investor will earn if a bond is purchased at the current market price and held until maturity.

Accepted Answer

The yield to maturity is defined as: An estimate of the annual return an investor will earn if they buy a bond and hold it to maturity.
The yield to maturity can also be thought of as the rate which discounts the bond's cash flows so that the present value equals the bond's price.

Question 10

A bond sold five weeks ago for $950.The bond is worth $900 in today's market.The face value of the bond is $1,000.Assuming no changes in risk,which of the following is mostly likely true?

Accepted Answer

The price has gone down. Prices vary inversely with interest rates, so interest rates must have gone up.

Question 11

What is the value of a 25-year bond with a $1,000 face value and an 8% coupon rate that yields 4%?

Accepted Answer

P_bond = C × 11ea7fdb_fc00_87f6_a768_576d67d49a3d_TB2902_11 + 11ea7fdb_fc00_87f7_a768_5f752947a68f_TB2902_11 P_bond = $80 × 11ea7fdb_fc00_87f8_a768_59a267394f1c_TB2902_11 + 11ea7fdb_fc00_87f9_a768_e33f3577b7ea_TB2902_11 = $1,624.88 Using a financial calculator: N = 25, I/Y = 4 PMT = 80, FV =1,000 CPT PV = $1,624.88

Question 12

What is the price of a five-year bond with a $1,000 face value and a 5% annual coupon rate that currently yields 7%?

Accepted Answer

P_bond = C × 11ea7fdb_fc00_39ce_a768_13e0943cd9d4_TB2902_11 + 11ea7fdb_fc00_39cf_a768_23649a2c0295_TB2902_11 P_bond = $50 × 11ea7fdb_fc00_39d0_a768_57e74ee993cd_TB2902_11 + 11ea7fdb_fc00_39d1_a768_e5170d112979_TB2902_11 = $918 Using a financial calculator: N = 5, I/Y = 7 PMT = 50, FV =1,000 CPT PV = $918

Question 13

What is the yield to maturity of a 10% annual coupon bond selling for $900 that matures in ten years?

Accepted Answer

P_bond = C × 11ea7fdb_fc00_fd33_a768_b5cc0616b379_TB2902_11 + 11ea7fdb_fc00_fd34_a768_d990c9d78030_TB2902_11 $900 = $100 × 11ea7fdb_fc00_fd35_a768_c5c313f8f855_TB2902_11 + 11ea7fdb_fc00_fd36_a768_ef05061514ac_TB2902_11 k_d = 11.75% Using a financial calculator: N = 10, PMT = 100, PV = $-900, FV = 1,000, CPT I/Y = 11.75%

Question 14

What is the yield to maturity of a bond with a 10% annual coupon rate,a price of $800,ten years to maturity and a face value of $1,000?

Accepted Answer

P_bond = C × 11ea7fdb_fc01_726f_a768_fda3c5205639_TB2902_11 + 11ea7fdb_fc01_7270_a768_89eb070ce621_TB2902_11 $800 = $100 × 11ea7fdb_fc01_7271_a768_953885944d1b_TB2902_11 + 11ea7fdb_fc01_7272_a768_17bbf12afdc3_TB2902_11 k_d = 13.81% Using a financial calculator: N = 10, PMT = 100, PV = $800, FV = 1,000, CPT I/Y = 13.81%

Question 15

Fortunate Frames Inc.just issued 20-year,6% coupon bonds at par.Lucky Lenses Inc.has 20-year bonds outstanding that are viewed by investors as having the same risk as Fortunate's bonds.Lucky's bonds are selling at a discount.What does this indicate about the coupon rates on these two bonds?

Accepted Answer

Lucky's bonds are selling at a discount, so its coupon rate must be less than its yield. The yield on Fortunate is 6%, so Lucky's coupon rate is less than 6%.

Question 16

A semi-annual coupon matures in one year.It has a face value of $1,000,a coupon rate of 4%,and the next semi-annual coupon is due in six months.The bond trades for $971.50.What is the yield to maturity of the bond?

Accepted Answer

P_bond = 11ea7fdb_fbff_ebaa_a768_c5c2dd0712bf_TB2902_11 + 11ea7fdb_fc00_12bb_a768_57e25cf09938_TB2902_11 $971.50 = 11ea7fdb_fc00_12bc_a768_614f1c4c6350_TB2902_11 + 11ea7fdb_fc00_12bd_a768_21977c54d4ca_TB2902_11 = 0.07 or 7% Using a financial calculator: N = 2, PV = -971.50, PMT = 20, FV =1,000 CPT I/Y = 3.5 × 2 = 7

Question 17

You are in possession of a bond that has 3 years remaining to maturity.The original maturity on the bond was 30 years.The bond has a $1,000 face value and a 9% coupon rate.If interest is paid annually and bonds with similar risk currently have an interest rate of 10%,what is the current value of the bond?

Accepted Answer

P_bond = C × 11ea7fdb_fc00_60e2_a768_df4987b1ad34_TB2902_11 + 11ea7fdb_fc00_60e3_a768_8f73924e33de_TB2902_11 P_bond = $90 × 11ea7fdb_fc00_60e4_a768_452a02bbc517_TB2902_11 + 11ea7fdb_fc00_60e5_a768_f5307e72852b_TB2902_11 = $975.13 Using a financial calculator: N = 3, I/Y = 10 PMT = 90, FV =1,000 CPT PV = $975.13

Question 18

If a five-year bond paying semiannual interest sells for $1,000 and has a yield to maturity of 10%,what is the semiannual coupon payment?

Accepted Answer

P_bond = C × 11ea7fdb_fc01_9983_a768_cdef5bb5a74b_TB2902_11 + 11ea7fdb_fc01_9984_a768_f395c3e8e0ba_TB2902_11 $1,000 = C × 11ea7fdb_fc01_9985_a768_4b831b571d7d_TB2902_11 + 11ea7fdb_fc01_9986_a768_63e79af4a1f3_TB2902_11 $1,000 = C × (7.721734929) C = 50 Using a financial calculator: N = 10, I/Y = 5, FV = 1,000, PV = -1,000, CPT PMT = 50

Question 19

You can buy a bond with a face value of $1,000 and annual coupon payments of $80.The yield to maturity on bonds of similar risk is 7%.This bond should sell

Accepted Answer

Coupon Rate = 11ea7fdb_fc01_c097_a768_15abc36c30d5_TB2902_11 Coupon Rate = 11ea7fdb_fc01_c098_a768_ab3ed998cbf7_TB2902_11 = 8%
Since the coupon rate (8%) is greater than the yield to maturity (7%), the bond should sell at a premium.

Question 20

Bank of America bonds are currently trading at $952.31.The bonds have a face value of $1,000,a coupon rate of 8% with payments made semi-annually,and mature in 20 years.What is the yield to maturity?

Accepted Answer

P_bond = C × 11ea7fdb_fbff_c490_a768_0314cbfb6d84_TB2902_11 + 11ea7fdb_fbff_c491_a768_219b423b90c8_TB2902_11 $952.31 = $40 × 11ea7fdb_fbff_c492_a768_0fadd175e41d_TB2902_11 + 11ea7fdb_fbff_c493_a768_25684f14d94a_TB2902_11 k_d = 4.25% (semi-annual), 4.25% × 2 = 8.5% (annual) Using a financial calculator: N = 40, PMT = 40, PV = $-952.31, FV = 1,000, CPT I/Y = 4.25% × 2 = 8.5%

Quiz 7: Interest Rates and Bond Valuation