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Chapter 4: Q9BP (page 322)

Look at Table 10-1 again, and now assume interest rates in the market (yield to maturity) increase from 9 to 12 percent.

a. What is the bond price at 9 percent?

b. What is the bond price at 12 percent?

c. What would be your percentage return on the investment if you bought when rates were 9 percent and sold when rates were 12 percent?

Short Answer

Expert verified
  1. Bond price at 9 percentyield to maturity is $1,091.33
  2. Bond price at 12 percentyield to maturity is $850.67
  3. Percentage return on the investment is (28.29)%

Step by step solution

01

Computing bond price at 9 percent

Coupon=ParValue脳CouponRate=$1,000脳10%=$100

  • Par value of bond (P) is $1,000.
  • Yield to maturity (r) is 9%.
  • Years to maturity (n) is 20
  • BondPrice=Coupon脳[1-11+rn]r+P(1+r)n=$100脳[1-11+0.0920]0.09+$1,000(1+0.09)20=$100脳9.129+178.43=$1,091.33
02

Computing bond price at 12 percent 

  • Par value of bond (P) is $1,000.
  • Yield to maturity (r) is 12%.
  • Years to maturity (n) is 20.
  • BondPrice=Coupon脳[1-11+rn]r+P(1+r)n=$100脳[1-11+0.1220]0.12+$1,000(1+0.12)20=$100脳7.47+103.67=$850.67
03

Computing percentage return on the investment 

PercentageReturn=Bondpriceat12%-Bondpriceat9%Bondpriceat12%=$850.67-$1,091.33$850.67=(28.29)%

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Most popular questions from this chapter

Dr. Harold Wolf of Medical Research Corporation (MRC) was thrilled with the response he had received from drug companies for his latest discovery, a unique electronic stimulator that reduces the pain from arthritis. The process had yet to pass rigorousFederal Drug Administration (FDA) testing and was still in the early stages ofdevelopment, but the interest was intense. He received the three offers described in the following paragraph. (A 10 percent interest rate should be used throughout this analysisunless otherwise specified.)

Offer I\(1,000,000 now plus \)200,000 from year 6 through 15. Also if the productdid over \(100 million in cumulative sales by the end of year 15, he wouldreceive an additional \)3,000,000. Dr. Wolf thought there was a 70 percentprobability this would happen.

Offer IIThirty percent of the buyer鈥檚 gross profit on the product for the next fouryears. The buyer in this case was Zbay Pharmaceutical. Zbay鈥檚 gross profitmargin was 60 percent. Sales in year one were projected to be \(2 millionand then expected to grow by 40 percent per year.

Offer IIIA trust fund would be set up for the next eight years. At the end of thatperiod, Dr. Wolf would receive the proceeds (and discount them back tothe present at 10 percent). The trust fund called for semiannual paymentsfor the next eight years of \)200,000 (a total of $400,000 per year).

The payments would start immediately. Since the payments are coming at thebeginning of each period instead of the end, this is an annuity due. Assumethe annual interest rate on this annuity is 10 percent annually (5 percent semiannually).Determine the present value of the trust fund鈥檚 final value. Hint:See the section on Annuities Due.

Required: Find the present value of each of the three offers and indicatewhich one has the highest present value.

Question: Mrs. Crawford will receive $7,600 a year for the next 19 years from her trust. If a 14 percent interest rate is applied, what is the current value of the future payments?

Assume a \(250,000 investment and the following cash flows for two products:

Year

Product X

Product Y

1

\)90,000

$50,000

2

90,000

80,000

3

60,000

60,000

4

20,000

70,000

Which alternatives would you select under the payback method?

Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage Systems. His broker quotes a price of \(1,180. Jim is concerned that the bond might be overpriced based on the facts involved. The \)1,000 par value bond pays 14 percent interest, and it has 25 years remaining until maturity. The current yield to maturity on similar bonds is 12 percent. Compute the new price of the bond and comment on whether you think it is overpriced in the marketplace.

Wilson Oil Company 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 in time as described next:

Real rate of return ........................ 8%

Inflation premium ......................... 3

Risk premium .............................. 4

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

Assume that 10 years later, due to bad publicity, the risk premium is now 7 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity. Compute the new price of the bond.
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