In: Finance
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?
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 | ||||||