1. Managerial Finance Session 4a Nicole Hruban

2. Bond Valuation – Simple Example A Miracle Enterprises Inc’s 8 7/8 percent bond matures in 15 years. Assume that the interest on these bonds is paid and compounded annually. Determine the value of a $1,000 denomination bond as of today if the required rate of return is 9 percent?

3. Bond Valuation – Annual Coupon Payments B 0 =Bond Value at time 0 I = Annual Interest Paid in Dollars or Coupon Interest (=Coupon Interest Rate x Par Value/ we used C in the earlier formula) r= required rate of return N=Number of years to Maturity M=Par value of the bond

4. Bond Valuation – Simple Example A Miracle Enterprises Inc’s 8 7/8 percent bond matures in 15 years. Assume that the interest/coupon on these bonds is paid and compounded annually. Determine the value of a $1,000 denomination bond as of today if the required rate of return is 9 percent? PMT (Coupon rate * face value): (0.08875*1000) = $88.75 N: 15 FV: $1,000 r: 0.09

5. Bond Valuation Assume you bought a bond from Savvy Solutions, Inc. one year ago for $829.73 when the market rate of interest was 10%. This bond matures 19 years from today, has a face value of $1,000 and is contracted to pay annual coupons at the rate of 8%. If the current market rate of interest is 13%, what would be the percentage change in bond value from the time you purchased this bond until today?

6. Bond Valuation Assume you bought a bond from Savvy Solutions, Inc. one year ago for $829.73 when the market rate of interest was 10%. This bond matures in 19 years, has a face value of $1,000 and is contracted to pay a annual coupons at the rate of 8%. If the current market rate of interest is 13%, what would be the percentage change in bond value from the time you purchased this bond until today? t=0t=11920 $80 + $1,000 $829,73 $80

7. Bond Valuation Assume you bought a bond from Savvy Solutions, Inc. one year ago for $829.73 when the market rate of interest was 10%. This bond matures in 19 years, has a face value of $1,000 and is contracted to pay an annual coupons at the rate of 8%. If the current market rate of interest is 13%, what would be the percentage change in bond value from the time you purchased this bond until today? B 0 = $829,73 PMT (Coupon rate * face value): (0.08*1000) = $80 N: 19 FV: $1,000 r: 0.13 Change: -21.29%

8. Bond Valuation – Semi annual payments James Bond Industries issues bonds that have a 10% coupon rate and a $1,000 face value. Coupons are paid semi- annually and the bond has 20 years to maturity. Investors require a 12% p.a. return. What is the bond’s market value?

9. Bond Valuation – Non-annual Coupon Payments B 0 =Bond Value at time 0 I = Annual Interest Paid in Dollars or Coupon Interest (=Coupon Interest Rate x Par Value/ we used C in the earlier formula) k= Coupon payment/compounding frequency r= required rate of return N=Number of years to Maturity M=Par value of the bond

10. Bond Valuation James Bond Industries issues bonds that have a 10% coupon rate and a $1,000 face value. Coupons are paid semi-annually and the bond has 20 years to maturity. Investors require a 12% p.a. return. What is the bond’s market value? PMT (Coupon rate * face value) / k: (0.1*1000)/2 = $50 N: Years to maturity * k = 20 *2 = 40 FV: $1,000 r/k: 0.12/2 = 0.06

11. Bond Valuation A U.S. government treasury bond will mature exactly 11.5 years from today. This bond was most likely first issued as a 30 year bond 18.5 years ago. The par value is $1000. The annual coupon rate is 14% and is paid out semiannually. Today, investors expect this and similar bonds to yield an of 8% return per year. What is the bond’s current value?

12. Bond Valuation A U.S. government treasury bond will mature exactly 11.5 years from today. This bond was most likely first issued as a 30 year bond 18.5 years ago. The par value is $1000. The annual coupon rate is 14% and is paid out semiannually. Today, investors expect this and similar bonds to yield a 8% return per year. What is the bond’s current market value? t=0t=0.5yrs11yrs11.5yrs $70 + $1,000 $70 PMT (Coupon rate * face value) / k: (0.14*1000)/2 = $70 N: Years to maturity * k = 11.5 *2 = 23 FV: $1,000 r/k: 0.08/2 = 0.04

13. Bond Valuation - BEY Speedy Shipment Inc, issued a 12% coupon interest rate, 10-year bond with a $1,000 par value that pays interest quarterly. Assuming 8% bond equivalent yield, what is the bond value at issue?

14. Bond Valuation - BEY Speedy Shipment Inc, issued a 12% coupon interest rate, 10-year bond with a $1,000 par value that pays interest quarterly. Assuming 8% bond equivalent yield, what is the bond value at issue? STEP 1): Find required return r from BEY Solve for r r = [(1+0.08/2)^(1/2) – 1]*4 = 0.07922

15. Bond Valuation - BEY Speedy Shipment Inc, issued a 12% coupon interest rate, 10-year bond with a $1,000 par value that pays interest quarterly. Assuming 8% bond equivalent yield, what is the bond value at issue? STEP 2): Find B 0 PMT (Coupon rate * face value) / k: (0.12*1000)/4 = $30 N: Years to maturity * k = 10 *4 = 40 FV: $1,000 r/k: 0.07922/4 = 0.019805 $1,279.85

16. Bond Valuation – Yield to Maturity Calculations A Coca Cola, Inc. bond has a coupon rate of 8.5%, matures in 12 years, and sells for $835.60 What is the YTM for this Coca Cola, Inc. corporate bond…. if the coupons are paid on an annual basis? if the coupons are paid on a semi-annual basis?

17. Yield to Maturity Yield to Maturity = interest rate at which the present value of stream of payments (consisting of coupon payments and the final face value redemption payment) is exactly equal to its current price.

18. Bond Valuation – Yield to Maturity Calculations A Coca Cola, Inc. bond has a coupon rate of 8.5%, matures in 12 years, and sells for $835.60 What is the YTM for this Coca Cola, Inc. corporate bond…. if the coupons are paid on an annual basis? AB 1Yield 2@ Yield (B3,B4,B5,B6,B7, B8, B9) 3Settlement (date of trade)1/1/2000 4Maturity (Date of Maturity)1/1/2012 5Coupon Interest0.085 6Price (per $100 of FV)83.56 7Redemption / Face Value (per $100 of FV)100.00 8Frequency (#pyments per year)1.00 9Basis (type of day count0.00 10Yield0.110366288

19. Bond Valuation – Yield to Maturity Calculations A Coca Cola, Inc. bond has a coupon rate of 8.5%, matures in 12 years, and sells for $835.60 What is the YTM for this Coca Cola, Inc. corporate bond…. if the coupons are paid on an semi-annual basis? YTM semi-annual: 5.5%