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Suppose that you are interested in buying a bond that pays interest semi-annually. It has an annual coupon of 5% with interest payable on January 15th and July 15th. The bond accrued interest is determined using a 30/360 day count street convention. If the bond is currently priced at $1,180, what is the invoice price for the bond using a settlement date of December 18? Please explain in detail.

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Sixta Kovacek
Sixta KovacekLv2
28 Sep 2019

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Action Items:

Go to the http://www.federalreserve.gov/releases/h15/data.htm to examine historical daily interest rates on U.S. Treasuries.

Scroll down to "Treasury constant maturities" and in the row "1-month" under "Nominal" click "Business day."

As you can see, rates on the one-month U.S. Treasury bill are provided for each business day from July 31, 2001 to the present. For this assignment you are asked to pick a business date five years ago this month. (For example, in January 2012 I would pick a business date in January 2007.)

Then, using this row and the subsequent rows below it under “Treasury Constant Maturities” determine the shape of the yield curve (See Figure 6.11in the textbook for examples of Treasury yield curves) on that date five years ago based on the rates published by the Fed by completing the table below for the listed Treasury maturities (see example below):

Business Date Chosen Five Years Ago

7/15/2010

1-month Nominal T-bill Rate on that Date

0.16

3-month Nominal T-bill Rate on that Date

0.15

6-month Nominal T-bill Rate on that Date

0.2

1-year Nominal T-note Rate on that Date

0.27

5-year Nominal T-note Rate on that Date

1.76

10-year Nominal T-note Rate on that Date

3

20-year Nominal T-bond Rate on that Date

3.77

30-year Nominal T-bond Rate on that Date

3.97

Answer the following questions:

On your selected date was the yield curve rising, falling, or flat? What explanation(s) would you give for this shape?

From my selected date, the yield curve is rising. This is due to the fact that the longer money is invested the more you’re compensated and earn due to the fact that the interest rates being higher.

Assume that two U.S. Treasury securities were purchased at par ($1000) on your selected date five years ago: 1) a 10-year T-note and 2) a 20-year T-bond. Also assume that for each of the two securities the reported nominal rate that you found above was the coupon rate at issuance.

Assuming semi-annual coupon payments, calculate the value of each bond today after 5 years based on the current 5-year Treasury constant maturity nominal rate for the original 10-year note and a current 15-year rate (assume it is the average of the current Treasury constant maturity nominal 10- and 20-year rates) for the original 20-year bond at http://www.federalreserve.gov/releases/h15/data.htm.

Complete the following tables (see example below):

10-Year Bond Purchased for $1000 5 Years Ago

Original Value

$1000

Coupon Rate (From table you completed above at the chosen date from 5 years ago, the original 10-year Nominal T-bond Rate divided by 2 for semi-annual payments)

Current 5-Year Yield to Maturity (The most recent 5-year Nominal T-note Rate reported at the Fed site divided by 2 for semi-annual payments)

Number of Semi-Annual Periods Remaining

Current Value*

Gain or Loss on the Bond over the 5 years

20-Year Bond Purchased for $1000 5 Years Ago

Original Value

$1000

Coupon Rate (From table you completed above at the chosen date from 5 years ago, the original 20-year Nominal T-bond Rate divided by 2 for semi-annual payments)

Current 15-Year Yield to Maturity (Take the average of the most recent 10- and 20-year Nominal T-bond Rates reported at the Fed site, and then divide this average rate by 2 for semi-annual payments)

Number of Semi-Annual Periods Remaining

30

Current Value*

Gain or Loss on the Bond over the 5 years

*Current Value = PVBond = Coupon Payment +

b) Did you gain or lose more on one bond relative to the other? Explain.

QUESTION 1 The largest investors in corporate bonds are life insurance companies and pension funds. True False 5 points QUESTION 2 Most secondary market transactions for corporate bonds take place through dealers in the over-the-counter (OTC) market. True False 5 points QUESTION 3 The value (or price) of a bond is the present value of its expected future cash flows. True False 5 points QUESTION 4 Bond prices decline when the interest rate decreases. True False 5 points QUESTION 5 The face or par value for bonds is the amount paid to bondholders at maturity and is usually equal to $1,000. True False 5 points QUESTION 6 The yield to maturity of a bond is the discount rate that makes the present value of the coupon and principal payments equal to the price of the bond. True False 5 points QUESTION 7 Zero coupon bonds have no coupon payments so they sell for more than their par value. True False 5 points QUESTION 8 Interest rate risk is the risk that bond prices will fluctuate when the interest rate changes. True False 5 points QUESTION 9 US Treasury securities are considered risky investments because the coupon payments are unpredictable. True False 5 points QUESTION 10 Bonds are very difficult to value because their future cash flows are very difficult to predict. True False 5 points QUESTION 11 If the bond's coupon rate is equal to the market rate then the bond will sell at a price equal to its face value greater than its face value less than its face value equal to its foreign currency value, e.g., its price in British pounds 5 points QUESTION 12 When calculating the price of a bond that pays a semiannual coupon one needs to use double the number of years until maturity for the number of payments use half the annual coupon payment use half the annual rate of return as the discount rate all of the above 5 points QUESTION 13 The yield to maturity of a bond is the discount rate that makes the present value of the coupon and principal payments more than the price of the bond equal to zero equal to the price of the bond less than the price of the bond 5 points QUESTION 14 Which one of the following statements is true? All else equal long-term bonds have lower price volatility than short-term bonds. There is an inverse relation between bond prices and market interest rates. All else equal short-term bonds are more risky than long-term bonds. All else equal US government bonds are more risky than corporate bonds. 5 points QUESTION 15 An investor owns a 10-year US government bond with a 9 percent coupon rate. If the yield-to-maturity on the bond is 8 percent then this bond is selling for its par value. a discount. a premium. its face value. 5 points QUESTION 16 BA Corp is issuing a 10-year bond with a coupon rate of 8 percent and a par value of $1,000. The market interest rate on similar bonds is currently 6 percent. If the coupon payments are made annually, what is the value of this bond? 5 points QUESTION 17 Knight, Inc. has issued a 3-year bond with a $1,000 par value and an annual coupon rate of 6 percent. The current market rate of interest is 5 percent. What is the value of this bond if the coupon payments are made semiannually? 5 points QUESTION 18 Diane Carter is interested in buying a 5-year zero coupon bond with a face value of $5,000. If the market interest rate on these types of bonds is currently 9 percent, what is the current price of this bond? 5 points QUESTION 19 Rudy Sandberg wants to invest in 4-year bonds that are currently priced at $933.76. The bonds have a coupon rate of 6 percent and annual coupon payments. If the par value of the bonds is $1,000, what is the bond's yield-to-maturity? 5 points QUESTION 20 You own a 5-year bond with a face value of $1,000 and a coupon rate of 5 percent with annual payments. The bond is currently worth $810.46. If market interest rates remain unchanged, what will be the value of the bond next year when there are 4 years left until maturity?

A CAPITAL BUDGETING CASE

The E-Check Company, a manufacturer of pollution detection systems, has enjoyed considerable success. In 2015, the company completed its 25th year in business and generated a return on common equity of 20%. Rusty Rivet, Company C.E.O., is certain the Company can continue this performance. One thing that contributes towards his confidence is that almost all of the Company’s sales are to governmental programs that, in order to help control pollution, force residents in communities located next to interstate highways to pay a fee to have their vehicle emissions systems tested. Given the high test pass-rates, the pollution in these areas obviously comes largely from traffic passing through the communities rather than from the local’s vehicles, but governments have come to rely on the income emission testing generates and are reluctant to cut the testing requirements. Another reason for his confidence is the fact that most of the Company’s top managers hold an advanced engineering degree awarded by a variety of prestigious universities. Rusty also believes that stockholders like the fact that the Company pays out all earnings not needed to pay preferred dividends as common dividends (and because he is the majority stockholder in the Company it is unlikely this policy will change). It is estimated that the common dividend will continue to grow annually at an 8% rate.

In January 2016, managers of the Company have expansion plans; they have just completed an evaluation of six capital budgeting projects. The net cash flows (in millions of dollars) and risk assessment of each project are shown below. Company policy requires that average risk projects have an IRR at least equal to the Company’s weighted average cost of capital (WACC). Policy also requires that the hurdle rate be increased (decreased) by 250 basis points when evaluating projects that are above (below) average risk. Management has determined that the Company’s WACC is 9.63% and, therefore, management is making plans raise $52 million to implement all of the projects except Project E. As a part of your management training, you have been asked to review the analysis. In particular, management wants you to verify both the WACC calculation and project selection.

Project A B C D E F

0 (10) (12) (15) (5) (11) (10)

1 3.15 4.3 7 2 0 1

2 3.15 4.3 6.4 2 0 3

3 3.15 4.3 5.5 1 0 5

4 3.15 4.3 .5 0 3

5 3.15 .5 0 .55

6 .5 0

7 0

8 22

Risk High Ave. Ave. Low Ave. Low

The Company has one outstanding bond issue. It has an annual stated rate of 8% with annual interest payments. $50,000,000 of the bond issue, with an original term to maturity of 15 years was publicly placed 7 years ago at face value. The most recent price at which a bond traded on the secondary market was $900 (a $100 discount from face value). Any new long-term debt would be raised in the form of a new bond issue. Matilda Angle, E-Check’s treasurer, has pointed out that the company would like any new bond issue to have an initial maturity of 15 years to lock in the interest rate for a long time, and she also points out that the good news is that the yield curve at this time is essentially flat. In addition, any new bond issues will be privately placed so there will be no flotation costs.

The company has 10 million shares of $1 par common stock outstanding. These shares are currently trading for $10.00 per share on the Cincinnati Stock Exchange. The company paid total dividends of $1,700,000 on these shares during 2015. The company’s underwriter will charge flotation costs equal to 10% of the value of any new shares sold.

The company also has 100,000 shares of $200 par preferred stock outstanding. These shares are currently trading at $175 per share. The preferred share annual dividend (paid quarterly) is 9.5%. The underwriter will charge flotation costs of 5% of the value of new shares sold.

Management’s WACC Calculation

Shown below are E-Check’s simplified financial statements for 2015. Managers used information from the balance sheet to come up with the weights for their WACC calculation.

E-Check

Balance Sheet

December 31, 2015

Current assets 30,000,000 Current liabilities 30,000,000

Long-term assets 88,000,000 Long-term liabilities 50,000,000

Total assets 118,000,000 Total liabilities 80,000,000

Common shares 10,000,000

Preferred shares 20,000,000

Retained earnings 8,000,000

Total equity 38,000,000

Total liabilities & equity 118,000,000

E-Check

Income Statement

2015

Revenues 200,000,000

Cost of goods sold 110,000,000

Gross profit margin 90,000,000

Operating expenses 80,000,000

Operating income 10,000,000

Interest expense 4,000,000

Taxable income 6,000,000

Income tax 2,400,000

Net income 3,600,000

Specifically, the WACC was calculated as follows:

WACC = (Kd * wtd) + (Kp * wtp) + (Ke * wte)

= (8 * (80/118)) + (9.5 * (20/118)) + (17 * (18/118))

= 5.423 + 1.61 + 2.593

= 9.63%

Maria Sliderule, Company controller, has explained to you that 8% was used as the cost of debt because this is the stated rate of interest on the firm’s existing bond issue; 9.5% was used as the cost of preferred shares because this is the dividend rate on the Company’s preferred stock, 17% was used as the cost of equity because dividends of $1.7 million were paid on the common shares with a book value of $10 million; and that the weights in the WACC calculation were derived directly from the balance sheet.

Internal announcement of the expansion possibilities has fostered some debate. One manager, Mel Lever, asserts that the Company should raise all the money needed in the form of debt, and since the cost of debt is only 8%, all projects should be accepted. Olm Meter, a Norwegian engineer who just joined the E-Check management team, argues that it makes no sense to invest in a project with an IRR less than the WACC. The input of all these individuals cannot be ignored because each is a valuable member of the management team and highly respected in the area of pollution detection technology. This is why you have been asked to review the analysis.

1. Please address the comments of Mr. Lever and Mr. Meter.

2. In which of the proposed capital budgeting projects should the Company invest?

3. What do you think is the Company’s WACC?

4. List any errors in the 9.63% calculation?

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