Bond Price worksheet

1. Yield to maturity (annual): 15.631%

1. Find the coupon (C) paid each period: face value × coupon rate, split over 2 payments a year

   $C$$=\frac{\mathrm{\$1,400.00}\times 0.06}{2}$$=\mathrm{\$42.00}$

2. Count the coupon periods left (N): 2 per year for 9 years

   $N$$=2\times 9$$=18$

3. Find the yield per period (i) that makes all the payments, valued today, equal the price. There's no direct formula, so the calculator tries rates until they match

   $\mathrm{\$760.00}$$=\mathrm{\$42.00}\times \frac{1-{\left(1+0.07815578\right)}^{\mathrm{-18}}}{0.07815578}+\frac{\mathrm{\$1,400.00}}{{\left(1+0.07815578\right)}^{18}}$

4. Turn it into a yearly rate: yield to maturity = i × 2 periods a year

   $\mathrm{YTM}$$=0.07815578\times 2$$=0.15631157$$=\mathrm{15.6312\%}$

5. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$84.00}}{\mathrm{\$760.00}}$$=\mathrm{11.0526\%}$

2. Bond price: $565.60

1. Find the coupon (C) paid each period: face value × coupon rate, split over 12 payments a year

   $C$$=\frac{\mathrm{\$675.00}\times 0.05}{12}$$=\mathrm{\$2.81}$

2. Count the coupon periods left (N): 12 per year for 12 years

   $N$$=12\times 12$$=144$

3. Split the yearly yield into 12 equal parts, one per coupon period (i)

   $i$$=\frac{0.07}{12}$$=0.00583333$

4. Work out what all the coupons are worth today. Money paid later is worth less than money now

   $\mathrm{\$2.81}\times \frac{1-{\left(1+0.00583333\right)}^{\mathrm{-144}}}{0.00583333}$$=\mathrm{\$273.49}$

5. Work out what the face value (F), paid back at the end, is worth today

   $\frac{\mathrm{\$675.00}}{{\left(1+0.00583333\right)}^{144}}$$=\mathrm{\$292.12}$

6. Add the two together. That total is the bond's fair price

   $\mathrm{\$273.49}+\mathrm{\$292.12}$$=\mathrm{\$565.60}$

7. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$33.75}}{\mathrm{\$565.60}}$$=\mathrm{5.9671\%}$

8. Compare the price with the face value

   $\mathrm{\$565.60}-\mathrm{\$675.00}$$=\mathrm{-\$109.40}$$=\text{At a discount}$

3. Bond price: $702.20

1. Find the coupon (C) paid each period: face value × coupon rate, split over 12 payments a year

   $C$$=\frac{\mathrm{\$800.00}\times 0.05}{12}$$=\mathrm{\$3.33}$

2. Count the coupon periods left (N): 12 per year for 8 years

   $N$$=12\times 8$$=96$

3. Split the yearly yield into 12 equal parts, one per coupon period (i)

   $i$$=\frac{0.07}{12}$$=0.00583333$

4. Work out what all the coupons are worth today. Money paid later is worth less than money now

   $\mathrm{\$3.33}\times \frac{1-{\left(1+0.00583333\right)}^{\mathrm{-96}}}{0.00583333}$$=\mathrm{\$244.49}$

5. Work out what the face value (F), paid back at the end, is worth today

   $\frac{\mathrm{\$800.00}}{{\left(1+0.00583333\right)}^{96}}$$=\mathrm{\$457.71}$

6. Add the two together. That total is the bond's fair price

   $\mathrm{\$244.49}+\mathrm{\$457.71}$$=\mathrm{\$702.20}$

7. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$40.00}}{\mathrm{\$702.20}}$$=\mathrm{5.6964\%}$

8. Compare the price with the face value

   $\mathrm{\$702.20}-\mathrm{\$800.00}$$=\mathrm{-\$97.80}$$=\text{At a discount}$

4. Bond price: $1,286.97

1. Find the coupon (C) paid each period: face value × coupon rate, split over 4 payments a year

   $C$$=\frac{\mathrm{\$1,400.00}\times 0.06}{4}$$=\mathrm{\$21.00}$

2. Count the coupon periods left (N): 4 per year for 12 years

   $N$$=4\times 12$$=48$

3. Split the yearly yield into 4 equal parts, one per coupon period (i)

   $i$$=\frac{0.07}{4}$$=0.0175$

4. Work out what all the coupons are worth today. Money paid later is worth less than money now

   $\mathrm{\$21.00}\times \frac{1-{\left(1+0.0175\right)}^{\mathrm{-48}}}{0.0175}$$=\mathrm{\$678.17}$

5. Work out what the face value (F), paid back at the end, is worth today

   $\frac{\mathrm{\$1,400.00}}{{\left(1+0.0175\right)}^{48}}$$=\mathrm{\$608.80}$

6. Add the two together. That total is the bond's fair price

   $\mathrm{\$678.17}+\mathrm{\$608.80}$$=\mathrm{\$1,286.97}$

7. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$84.00}}{\mathrm{\$1,286.97}}$$=\mathrm{6.527\%}$

8. Compare the price with the face value

   $\mathrm{\$1,286.97}-\mathrm{\$1,400.00}$$=\mathrm{-\$113.03}$$=\text{At a discount}$

5. Yield to maturity (annual): 9.767%

1. Find the coupon (C) paid each period: face value × coupon rate, split over 2 payments a year

   $C$$=\frac{\mathrm{\$1,000.00}\times 0.05}{2}$$=\mathrm{\$25.00}$

2. Count the coupon periods left (N): 2 per year for 10 years

   $N$$=2\times 10$$=20$

3. Find the yield per period (i) that makes all the payments, valued today, equal the price. There's no direct formula, so the calculator tries rates until they match

   $\mathrm{\$700.00}$$=\mathrm{\$25.00}\times \frac{1-{\left(1+0.0488357\right)}^{\mathrm{-20}}}{0.0488357}+\frac{\mathrm{\$1,000.00}}{{\left(1+0.0488357\right)}^{20}}$

4. Turn it into a yearly rate: yield to maturity = i × 2 periods a year

   $\mathrm{YTM}$$=0.0488357\times 2$$=0.0976714$$=\mathrm{9.7671\%}$

5. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$50.00}}{\mathrm{\$700.00}}$$=\mathrm{7.1429\%}$

6. Bond price: $793.70

1. Find the coupon (C) paid each period: face value × coupon rate, split over 2 payments a year

   $C$$=\frac{\mathrm{\$1,000.00}\times 0.03}{2}$$=\mathrm{\$15.00}$

2. Count the coupon periods left (N): 2 per year for 9 years

   $N$$=2\times 9$$=18$

3. Split the yearly yield into 2 equal parts, one per coupon period (i)

   $i$$=\frac{0.06}{2}$$=0.03$

4. Work out what all the coupons are worth today. Money paid later is worth less than money now

   $\mathrm{\$15.00}\times \frac{1-{\left(1+0.03\right)}^{\mathrm{-18}}}{0.03}$$=\mathrm{\$206.30}$

5. Work out what the face value (F), paid back at the end, is worth today

   $\frac{\mathrm{\$1,000.00}}{{\left(1+0.03\right)}^{18}}$$=\mathrm{\$587.39}$

6. Add the two together. That total is the bond's fair price

   $\mathrm{\$206.30}+\mathrm{\$587.39}$$=\mathrm{\$793.70}$

7. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$30.00}}{\mathrm{\$793.70}}$$=\mathrm{3.7798\%}$

8. Compare the price with the face value

   $\mathrm{\$793.70}-\mathrm{\$1,000.00}$$=\mathrm{-\$206.30}$$=\text{At a discount}$

7. Yield to maturity (annual): 4.525%

1. Find the coupon (C) paid each period: face value × coupon rate, split over 12 payments a year

   $C$$=\frac{\mathrm{\$550.00}\times 0.06}{12}$$=\mathrm{\$2.75}$

2. Count the coupon periods left (N): 12 per year for 12 years

   $N$$=12\times 12$$=144$

3. Find the yield per period (i) that makes all the payments, valued today, equal the price. There's no direct formula, so the calculator tries rates until they match

   $\mathrm{\$625.00}$$=\mathrm{\$2.75}\times \frac{1-{\left(1+0.00377102\right)}^{\mathrm{-144}}}{0.00377102}+\frac{\mathrm{\$550.00}}{{\left(1+0.00377102\right)}^{144}}$

4. Turn it into a yearly rate: yield to maturity = i × 12 periods a year

   $\mathrm{YTM}$$=0.00377102\times 12$$=0.04525221$$=\mathrm{4.5252\%}$

5. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$33.00}}{\mathrm{\$625.00}}$$=\mathrm{5.28\%}$

8. Yield to maturity (annual): 9.166%

1. Find the coupon (C) paid each period: face value × coupon rate, split over 1 payments a year

   $C$$=\frac{\mathrm{\$1,200.00}\times 0.05}{1}$$=\mathrm{\$60.00}$

2. Count the coupon periods left (N): 1 per year for 8 years

   $N$$=1\times 8$$=8$

3. Find the yield per period (i) that makes all the payments, valued today, equal the price. There's no direct formula, so the calculator tries rates until they match

   $\mathrm{\$925.00}$$=\mathrm{\$60.00}\times \frac{1-{\left(1+0.09166041\right)}^{\mathrm{-8}}}{0.09166041}+\frac{\mathrm{\$1,200.00}}{{\left(1+0.09166041\right)}^8}$

4. Turn it into a yearly rate: yield to maturity = i × 1 periods a year

   $\mathrm{YTM}$$=0.09166041\times 1$$=0.09166041$$=\mathrm{9.166\%}$

5. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$60.00}}{\mathrm{\$925.00}}$$=\mathrm{6.4865\%}$

9. Bond price: $697.94

1. Find the coupon (C) paid each period: face value × coupon rate, split over 12 payments a year

   $C$$=\frac{\mathrm{\$750.00}\times 0.05}{12}$$=\mathrm{\$3.13}$

2. Count the coupon periods left (N): 12 per year for 9 years

   $N$$=12\times 9$$=108$

3. Split the yearly yield into 12 equal parts, one per coupon period (i)

   $i$$=\frac{0.06}{12}$$=0.005$

4. Work out what all the coupons are worth today. Money paid later is worth less than money now

   $\mathrm{\$3.13}\times \frac{1-{\left(1+0.005\right)}^{\mathrm{-108}}}{0.005}$$=\mathrm{\$260.29}$

5. Work out what the face value (F), paid back at the end, is worth today

   $\frac{\mathrm{\$750.00}}{{\left(1+0.005\right)}^{108}}$$=\mathrm{\$437.65}$

6. Add the two together. That total is the bond's fair price

   $\mathrm{\$260.29}+\mathrm{\$437.65}$$=\mathrm{\$697.94}$

7. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$37.50}}{\mathrm{\$697.94}}$$=\mathrm{5.3729\%}$

8. Compare the price with the face value

   $\mathrm{\$697.94}-\mathrm{\$750.00}$$=\mathrm{-\$52.06}$$=\text{At a discount}$

10. Yield to maturity (annual): 5%

1. Find the coupon (C) paid each period: face value × coupon rate, split over 4 payments a year

   $C$$=\frac{\mathrm{\$750.00}\times 0.05}{4}$$=\mathrm{\$9.38}$

2. Count the coupon periods left (N): 4 per year for 10 years

   $N$$=4\times 10$$=40$

3. Find the yield per period (i) that makes all the payments, valued today, equal the price. There's no direct formula, so the calculator tries rates until they match

   $\mathrm{\$750.00}$$=\mathrm{\$9.38}\times \frac{1-{\left(1+0.0125\right)}^{\mathrm{-40}}}{0.0125}+\frac{\mathrm{\$750.00}}{{\left(1+0.0125\right)}^{40}}$

4. Turn it into a yearly rate: yield to maturity = i × 4 periods a year

   $\mathrm{YTM}$$=0.0125\times 4$$=0.05$$=\mathrm{5\%}$

5. Current yield: the annual coupon divided by the price

   $\frac{\mathrm{\$37.50}}{\mathrm{\$750.00}}$$=\mathrm{5\%}$