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Bond Valuation Practice Problems, Exercises of Mathematics

Mathematics

Bond Valuation Practice Problems

Typology: Exercises

2019/2020

Uploaded on 08/23/2020

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Bond Valuation Practice Problems
1. The $1,000 face value ABC bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond
is priced to yield 8%, what is the bond's value today?
oFV = $1,000
oCF = $60/2 = $30
oN = 5 x 2 = 10
oi = 8%/2 = 4%
oPV = $918.89
2. The $1,000 face value EFG bond has a coupon of 10% (paid semi-annually), matures in 4 years, and has current price of $1,140.
What is the EFG bond's yield to maturity?
oFV = $1,000
oCF = $100/2 = $50
oN = 4 x 2 = 8
oPV = $1,140
oi = 3%
oyield-to-maturity = 3% x 2 = 6%
3. The HIJ bond has a current price of $800, a maturity value of $1,000, and matures in 5 years. If interest is paid semi-annually
and the bond is priced to yield 8%, what is the bond's annual coupon rate?
oPV = $800
oFV = $1,000
oN = 5 x 2 = 10
oi = 8% / 2 = 4%
oCF = $15.34
oCoupon = $30.68 per year or 3.068%
4. The KLM bond has a 8% coupon rate (with interest paid semi-annually), a maturity value of $1,000, and matures in 5 years. If
the bond is priced to yield 6%, what is the bond's current price?
oCF = $40
oFV = $1,000
oN = 10
oi = 6%/2 = 3%
oPV = $1,085
5. The NOP bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price
of $1,200. What is the NOP's yield-to-maturity?
oCF = $40
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Bond Valuation Practice Problems

  1. The $1,000 face value ABC bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond's value today? o FV = $1, o CF = $60/2 = $ o N = 5 x 2 = 10 o i = 8%/2 = 4% o PV = $918.
  2. The $1,000 face value EFG bond has a coupon of 10% (paid semi-annually), matures in 4 years, and has current price of $1,140. What is the EFG bond's yield to maturity? o FV = $1, o CF = $100/2 = $ o N = 4 x 2 = 8 o PV = $1, o i = 3% o yield-to-maturity = 3% x 2 = 6%
  3. The HIJ bond has a current price of $800, a maturity value of $1,000, and matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond's annual coupon rate? o PV = $ o FV = $1, o N = 5 x 2 = 10 o i = 8% / 2 = 4% o CF = $15. o Coupon = $30.68 per year or 3.068%
  4. The KLM bond has a 8% coupon rate (with interest paid semi-annually), a maturity value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond's current price? o CF = $ o FV = $1, o N = 10 o i = 6%/2 = 3% o PV = $1,
  5. The NOP bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price of $1,200. What is the NOP's yield-to-maturity? o CF = $

o FV = $1, o N = 5 x 2 = 10 o PV = $1, o i = 1.797% o yield-to-maturity = 1.797% x 2 = 3.594%

  2. P8. The C. Alice Stone Company’s preferred stock pays a $10 dividend every year, with the next

  3. dividend due in one year. Investors require a 10% return on this preferred stock. What is its

  4. current market price? What will the price be immediately after the next dividend payment (P

  5. 1

20.) is due a year later after that. So next year’s price is P

  1. 1 22.=D
  2. 2 24./r = 10/0.1 = 25.100. So next year’s price is also $100. There is no expected appreciation in the price. The entire 26.10% return comes from the dividend payment.

27.P9. Propulsion Sciences’ (PS) stock dividend has grown at 10 percent per year for as long as anyone 28.can remember. Investors believe that a year from now the company will pay a dividend of $3 and 29.that dividends will continue their 10 percent growth indefinitely. If the market’s required return 30.on PS stock is 12 percent, what does the stock sell for today, and how much will it sell for a year

35.10 percent growth in the stock price, exactly matching the 10 percent increase in the dividend. 36.P10. Investors believe that a certain stock will pay a $4 dividend next year. The market price of the 37.stock is $66.67, and investors expect a 12 percent return on the stock. What long-run growth rate 38.in dividends is consistent with the current price of the stock? 39.A10. $66.67 = $4/(0.12-g)

40.g = 0.06 or 6% 41.P11. Petscan Radiology’s stock pays a dividend once each year, and it just paid a dividend of $0. 42.yesterday. The current market price of the stock is $12.14. If investors believe that Petscan will 43.increase it dividends by 7 percent per year forever, what is the required rate of return on Petscan’s 44.stock?

  1. is the dividend investors expect to be paid one year from now, not yesterday’s dividend. Since 58.dividends are expected to grow at 7% per year, we have: 59.D 1 = 1.07*(0.85) = $0. 60.Plug this into the valuation formula and solve for r:
  2. $0.9095/(r – 0.07) =12.
  3. r = (0.9095 + 0.07*12.14) / 12.14 = 0.145 or 14.5%

63.P8. The C. Alice Stone Company’s preferred stock pays a $10 dividend every year, with the next 64.dividend due in one year. Investors require a 10% return on this preferred stock. What is its 65.current market price? What will the price be immediately after the next dividend payment (P

  1. 1
  2. ) if
  1. 1 78.=D
  2. 2 80./r = 10/0.1 = 81.100. So next year’s price is also $100. There is no expected appreciation in the price. The entire 82.10% return comes from the dividend payment. 83.P9. Propulsion Sciences’ (PS) stock dividend has grown at 10 percent per year for as long as anyone

84.can remember. Investors believe that a year from now the company will pay a dividend of $3 and 85.that dividends will continue their 10 percent growth indefinitely. If the market’s required return 86.on PS stock is 12 percent, what does the stock sell for today, and how much will it sell for a year 87.from today after the stockholders receive their dividend?

92.P10. Investors believe that a certain stock will pay a $4 dividend next year. The market price of the 93.stock is $66.67, and investors expect a 12 percent return on the stock. What long-run growth rate 94.in dividends is consistent with the current price of the stock? 95.A10. $66.67 = $4/(0.12-g) 96.g = 0.06 or 6%

97.P11. Petscan Radiology’s stock pays a dividend once each year, and it just paid a dividend of $0. 98.yesterday. The current market price of the stock is $12.14. If investors believe that Petscan will 99.increase it dividends by 7 percent per year forever, what is the required rate of return on Petscan’s

  1. stock?
  2. A11. The constant growth valuation formula is:
  1. is the dividend investors expect to be paid one year from now, not yesterday’s dividend. Since
  2. dividends are expected to grow at 7% per year, we have:
  3. D 1 = 1.07*(0.85) = $0.
  4. Plug this into the valuation formula and solve for r:
  5. $0.9095/(r – 0.07) =12.
  6. r = (0.9095 + 0.07*12.14) / 12.14 = 0.145 or 14.5%

119. 3. Haswell Enterprises' bonds

have a 10-year maturity, a 6.25%

semiannual coupon, and a

parvalue of $1,000. The going

interest rate (rd) is 4.75%, based

on semiannual

compounding.What is the bond's

current price?

N=10*2=20I=4.75PMT=