Question

In: Finance

Smith's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000...

Smith's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 6%; and the yield to maturity is 8%. What is the bond's current value? If the market interest rate on Smith's bond decreased to 4%, what would the price of the bond be today?

Solutions

Expert Solution

ANSWER = 1
CALCULATION OF THE PRESENT VALUE OF THE BOND WITH YIELD TO MATURITY 8%
Step 1 : Calculation of Annual Coupon Payments
Par value of the bond issued is   = $             1,000.00
Annual Coupon % 6.00%
Annual Coupon Amount $                   60.00
Step 2: Calculate number of years to Maturity
Number of years to maturity = 10 years
Step 3 : Yield to Maturity = 8%, So discount rate = 8%
PVF = 1 / Discount rate = 1/ 1.08
Result of above will again divide by 1.08 , repeat this till last period
Option 1= Life of the bond is 10 years
CALCULATION OF CURRENT MARKET PRICE OF THE BOND OR PURCHASE PRICE
Years Interest Amount PVF @ 8% PresentValue
1 Interest $                    60.00                     0.9259 $               55.56
2 Interest $                    60.00                     0.8573 $               51.44
3 Interest $                    60.00                     0.7938 $               47.63
4 Interest $                    60.00                     0.7350 $               44.10
5 Interest $                    60.00                     0.6806 $               40.83
6 Interest $                    60.00                     0.6302 $               37.81
7 Interest $                    60.00                     0.5835 $               35.01
8 Interest $                    60.00                     0.5403 $               32.42
9 Interest $                    60.00                     0.5002 $               30.01
10 Interest $                    60.00                     0.4719 $               28.32
10 Bond Value $              1,000.00                     0.4719 $             471.93
Total $             875.06
Current Value of the Bond = $                875.06
ANSWER = 2
CALCULATION OF THE PRESENT VALUE OF THE BOND WITH YIELD TO MATURITY 4%
Step 1 : Calculation of Annual Coupon Payments
Par value of the bond issued is   = $             1,000.00
Annual Coupon % 6.00%
Annual Coupon Amount $                   60.00
Step 2: Calculate number of years to Maturity
Number of years to maturity = 10 years
Step 3 : Market rate of interest Rate = 4%, So discount rate = 4%
PVF = 1 / Discount rate = 1/ 1.04
Result of above will again divide by 1.04 , repeat this till last period
Option 1= Life of the bond is 10 years
CALCULATION OF CURRENT MARKET PRICE OF THE BOND OR PURCHASE PRICE
Years Interest Amount PVF @ 4% PresentValue
1 Interest $                    60.00                     0.9615 $               57.69
2 Interest $                    60.00                     0.9246 $               55.47
3 Interest $                    60.00                     0.8890 $               53.34
4 Interest $                    60.00                     0.8548 $               51.29
5 Interest $                    60.00                     0.8219 $               49.32
6 Interest $                    60.00                     0.7903 $               47.42
7 Interest $                    60.00                     0.7599 $               45.60
8 Interest $                    60.00                     0.7307 $               43.84
9 Interest $                    60.00                     0.7026 $               42.16
10 Interest $                    60.00                     0.6756 $               40.53
10 Bond Value $              1,000.00                     0.6756 $             675.56
Total $         1,162.22
Bonds Price is the today= $             1,162.22

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