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# What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond... 1. What is the yield to maturity on a 10-year, 9% annual coupon,$1,000 par value bond that sells for $887.00? That sells for$1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between and the bond’s coupon rate?
2. What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held to maturity and the company does not default on the bond.)

## Solutions

##### Expert Solution

Discount bond :

The YTM is calculated using the RATE function in Excel with these inputs :

nper = 10 (number of coupon payments = number of years to maturity)

pmt = 1000 * 9% (annual coupon payment. this is entered as a positive number as it is a cash inflow to the bondholder)

pv = -887 (the current price of the bond - this is entered as a positive number as it is a cash inflow to the buyer of the bond)

fv = 1000 (the face value of the bond receivable by the bondholder on maturity. As it is a cash inflow to the bondholder, it is entered as a positive figure)

RATE is calculated to be 10.91%. This is the YTM of the bond

The YTM is calculated using the RATE function in Excel with these inputs :

nper = 10 (number of coupon payments = number of years to maturity)

pmt = 1000 * 9% (annual coupon payment. this is entered as a positive number as it is a cash inflow to the bondholder)

pv = -1134.20 (the current price of the bond - this is entered as a positive number as it is a cash inflow to the buyer of the bond)

fv = 1000 (the face value of the bond receivable by the bondholder on maturity. As it is a cash inflow to the bondholder, it is entered as a positive figure)

RATE is calculated to be 7.08%. This is the YTM of the bond

If a bond trades at a discount, the YTM > coupon rate , and if a bond trades at a premium, YTM < coupon rate

Total return = interest + capital gain

interest = 1000 * 9% * 10 = $900 capital gain = 1000 - 887 =$113

Total return = 900 + 113 = $1013 current yield = coupon payment / bond price = 90 / 887 = 0.1015, or 10.15% capital gains yield = capital gains / current price = 113 / 887 = 0.1274 , or 12.74% ## Related Solutions ##### A zero-coupon bond has a yield to maturity of 9% and a par value of$1,000....
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