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# Bond payments and coupon rates, business and finance homework help

1.  A 25-year bond with a face value of \$1,000 has a coupon rate of 8.50%, with semiannual payments.

1. What is the bond payment for this bond?

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2. Enter the cash flows for the bond on a timeline

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2. Assume that a bond will make payments every six months as shown on the following timeline:

Period 0     1              2           17         18

Cashflow  \$45.00  \$45.00  \$45.00  \$1,045.00

1. What is the maturity of the bond (in years)?

2. What is the coupon rate (in percent)?

3. What is the face value?

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3. Explain why the yield of a bond that trades at a discount exceeds the bond’s coupon rate.

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4. Suppose a seven-year, \$1,000 bond with a 4.08% coupon rate and semiannual coupons is trading with a yield to maturity of 2.81%.

a. Is this bond currently trading at a discount, at par, or at a premium? Explain

b. If the yield to maturity of the bond rises to 3.28% (APR with semiannual compounding), at what price will the bond rate?

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5. Assume the zero-coupon yields on default-free securities are as summarized in the following table:

Maturity  1 yr  2 yrs  3 yrs  4 yrs  5 yrs

Zero-Coupon Yields  3.80%  4.20%  4.50%  4.80%  5.20%

What is the price today of a five-year, zero-coupon default-free security with a face value of \$1,000?

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6. Assume the zero-coupon yields on default-free securities are as summarized in the following table:

Maturity  1 yr  2 yrs  3 yrs  4 yrs  5 yrs

Zero-Coupon Yields  3.70%  4.20%  4.50%  4.80%  5.20%

What is the price today of a three-year, default-free security with a face value of \$1,000 and an annual coupon rate of 2%?

What is the yield to maturity for this bond?

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7. Why does the expected return of a corporate bond not equal its yield to maturity?

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8. Grummon Corporation has issued zero-coupon corporate bonds with a five-year maturity (assume \$100 face value bond). Investors believe there is a 20% chance that Grummon will default on these bonds. If Grummon does default, investors expect to receive only 50 cents per dollar they are owed. If investors require a 6% expected return on their investment in these bonds, what will be the

a. price of these bonds?

b. yield to maturity on these bonds?

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9. What does it mean for a country to “inflate away” its debt?

Why might this be costly for investors even if the country does not default?

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11. Your brother wants to borrow \$10,000 from you. He has offered to pay you back \$13,000 in a year. If the cost of capital of this investment opportunity is 8%, what is its NPV?

Should you undertake the investment opportunity?

Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

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12. You are considering investing in a start up company. The founder asked you for \$290,000 today and you expect to get \$980,000 in 14 years. Given the riskiness of the investment opportunity, your cost of capital is 21%. What is the NPV of the investment opportunity?

Should you undertake the investment opportunity?

Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

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13. You have been offered a very long-term investment opportunity to increase your money one hundredfold. You can invest \$500 today and expect to receive \$50,000 in 40 years. Your cost of capital for this (very risky) opportunity is 23%. What does the IRR rule say about whether the investment should be undertaken?

Do you agree?

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14. You are considering opening a new plant. The plant will cost \$104.8 million upfront and will take one year to build. After that, it is expected to produce profits of \$28.5 million at the end of every year of production. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 6.7%. Should you make the investment?

Calculate the IRR. Does the IRR rule agree with the NPV rule?

Below is the cash flow timeline:

Years  0 1  2  3  4  Forever

Cashflow (\$ million)  -104.8  \$28.5  \$28.5  28.5  28.5

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15. You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost \$6,000 and will be posted for one year. You expect that it will generate additional revenue of \$660 a month.

What is the payback period?

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16. You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost \$5,000 and will be posted for one year. You expect that it will generate additional revenue of \$500 a month. What is the payback period?

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17. You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of \$9.8 million. Investment A will generate \$2.08 million per year (starting at the end of the first year) in perpetuity. Investment B will generate \$1.42 million at the end of the first year, and its revenues will grow at 2.2% per year for every year after that.

a. Which investment has the higher IRR?

b. Which investment has the higher NPV when the cost of capital is 6.6%?

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18. You have just started your summer internship, and your boss asks you to review a recent analysis that was done to compare three alternative proposals to enhance the firm’s manufacturing facility. You find that the prior analysis ranked the proposals according to their IRR, and recommended the highest IRR option, Proposal A. You are concerned and decide to redo the analysis using NPV to determine whether this recommendation was appropriate. But while you are confident the IRRs were computed correctly, it seems that some of the underlying data regarding the cash flows that were estimated for each proposal was not included in the report. For Proposal B, you cannot find information regarding the total initial investment that was required in Year 0. And for Proposal C, you cannot find the data regarding additional salvage value that will be recovered in Year 3. Here is the information you have (in \$ millions):

Proposal  IRR  Year 0  Year 1  Year 2  Year 3

A  60.0%  -\$100  \$30  \$153  \$88

B  51.9%  ?  \$0  \$206  \$95

C  50.7%  -\$100  \$37  \$0  \$204+?

1. Fill in the missing values “?”

2. Suppose the appropriate cost of capital for each alternative in 10%. Using this information, determine the NPV of each proposal. Which project should the firm choose?

3. Can the IRR rule be used in this situation? Justify.

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19. Natasha’s Flowers, a local florist, purchases fresh flowers each day at the local flower market. The buyer has a budget of \$985 per day to spend. Different flowers have different profit margins, and also a maximum amount the shop can sell. Based on past experience the shop has estimated the following NPV of purchasing each type:

NPV per bunch  Cost per bunch  Max. Bunches

Roses  \$3  \$25  \$25

Lilies  \$10  \$29  \$10

Pansies \$4  \$29  \$10

Orchids  \$21  \$81  \$5

What combination of flowers should the shop purchase each day?

The profitability index for each choice is:????

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20. You own a car dealership and are trying to decide how to configure the showroom floor. The floor has 2000 square feet of usable space. You have hired an analyst and asked her to estimate the NPV of putting a particular model on the floor and how much space each model requires:

Model  NPV  Space Requirement (sq. ft).

MB345  \$2,500  200

MC237  \$4,000  250

MY456  \$3,500  240

MG231  \$1,500  150

MT347  \$9,000  450

MF302  \$2,000  200

MG201  \$2,500  150

In addition, the showroom also requires office space. The analyst has estimated that office space generates a NPV of \$14 per square foot. What models should be displayed on the floor and how many square feet should be devoted to office space?

Complete the PI table below: (Round to two decimal spaces)

Model  NPV  Space Requirement (sq. ft).  PI

MB345  \$2,500  200  ?

MC237  \$4,000  250  ?

MY456  \$3,500  240  ?

MG231  \$1,500  150  ?

MT347  \$9,000  450  ?

MF302  \$2,000  200  ?

MG201  \$2,500  150  ?