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Chapter 4: Q8BP (page 322)

Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 11 percent to 8 percent:

a. What is the bond price at 11 percent?

b. What is the bond price at 8 percent?

c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent?

Short Answer

Expert verified
  1. Bond price at 11% yield to maturity is $920.33
  2. Bond price at 8% yield to maturity is $1,196.37
  3. Percentage return on investment is 29.99%

Step by step solution

01

a.Computing annuity amount 

CouponAmount=BondParValue脳Annualinterest=$1,000脳10%=$100

02

a.Computing bond price at 11 percent

  • Par value of bond (P) is $1,000.
  • Yield to maturity (r) is 11%.
  • Years to maturity (n) is 20.

BondPrice=Coupon脳[1-11+rn]r+P(1+r)n=$100脳[1-11+0.1120]0.11+$1,000(1+0.11)20=$100脳7.963+124.034=$920.33

03

b.Computing bond price at 8 percent

  • Par value of bond (P) is $1,000.
  • Yield to maturity (r) is 8%.
  • Years to maturity (n) is 20.
  • BondPrice=Coupon脳[1-11+rn]r+P(1+r)n=$100脳[1-11+0.0820]0.08+$1,000(1+0.08)20=$100脳9.818147+214.5482=$1,196.37
04

c. Computigpercentage return on investment

PercentageReturn=Bondpriceat8%-Bondpriceat11%Bondpriceat11%=$1,196.37-$920.33$920.33=29.99%

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Most popular questions from this chapter

Question: What is the present value of a 10-year annuity of $3,000 per period in which payments come at the beginning of each period? The interest rate is 12 percent.


Question:Ecology Labs Inc. will pay a dividend of \(6.40 per share in the next 12 months (D1). The required rate of return (Ke) is 14 percent and the constant growth rate is 5 percent.

a. Compute P0. (For parts b, c, and d in this problem, all variables remain the same except the one specifically changed. Each question is independent of the others.)

b. Assume Ke, the required rate of return, goes up to 18 percent. What will be the new value of P0?

c. Assume the growth rate (g) goes up to 9 percent. What will be the new value of P0? Ke goes back to its original value of 14 percent.

d. Assume D1 is \)7.00. What will be the new value of P0? Assume Ke is at its original value of 14 percent and g goes back to its original value of 5 percent.

Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described next:

Real rate of return ........................ 4%

Inflation premium ......................... 6

Risk premium .............................. 5

Total return ............................... 15%

Assume that five years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 20 years remaining until maturity. Compute the new price of the bond.

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a. What was the original issue price?

b. What is the current value of this preferred stock?

c. If the yield on the Standard & Poor鈥檚 Preferred Stock Index declines, how will the price of the preferred stock be affected?

Question: Determine the amount of money in a savings account at the end of 10 years, given an initial deposit of $5,500 and a 12 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly.
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