ASSIGNMENT 2

Due: Friday, beginning of second tutorial class

(Note: unless otherwise stated, all interest rates are annual rates, compounded

annually)

Question 1:

Your junior analyst reports the following prices (all bonds are $1000 face value two-year maturity bonds with annual coupons):

Bond Counon Rate PriceA 6% $964.33B 10% $1 025.66C 12% $1.071.33

I

a) Why do you ask your junior analyst to check her numbers? (HINT: part a) is

NOT an IRR question)

b) If the numbers are right what should you do?

c) Calculate the IRR for each of the bonds.

d) Why might IRR not be useful in comparing relative bond prices?

Question 2:

The current price of a 3-year zero coupon bond with $1000 face value is $840. The

price of a 3-year bond with a 6% annual coupon and a $1000 face value is $1000.

What would be the price of a 3-year 10% annual coupon bond with a $1500 face

value?

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Question 3:Assume that the yield curve is always flat (i.e. yields of all maturities are the same andchange together when the yield curve shifts).

a) What is today's duration (in years) ofa 12% semi-annual coupon bond (face value$1,000, coupon payments $60 every six months), with a maturity date 1 year fromnow? The bond was bought at $1,019.23 exactly six months ago (just after acoupon payment), and if the bond were sold today, then the selling price wouldresult in a semi-annually compounded holding period return of 8% peryear.(HINT: compute the yield on the bond first and then compute the duration.For the yield, you will need today's price)

b) What will be the duration (in years) of the bond six months from now if the yieldcurve remains where it is today? How about if the yield curve shifts down by1.5%?

c) If the yield curve shifted back to the level that it was six months ago, wouldtoday's price be higher than, lower than, or equal to its original value of$I,019.23.

NB: An (annually compounded) interest rate of 10% per annum means 10% is paidevery 12 months. A semi-annually compounded interest rate of 10% per annum means5% is paid every 6 months. Which would you prefer to be the recipient of: a semi-annually compounded rate of 10% per annum or an annually compounded rate of10%?

Question 4:a) The current price of a 3-year bond with $1,000 face value is $1,030. What must be

its (semi-annual) coupon payment if the current semi-annually compounded YTMis 8% per year? What would it be if the annually compounded yield on bonds were8%?

b) Here is a picture of the zero coupon yield curve (between the labelled points, theyield curve consists of straight lines!). What is the price of a 3 year, 10% (annual)coupon bond?

10%8%

""C 6%-~-- 4%~ 2%

0%

0

8%...•...

7%6%

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5 101Years

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Question 5:ABC Inc. currently manufactures and sells 10 million widgets per year. It isconsidering the outsourcing of the widget production to XYZ Corp, a diversifiedmanufacturing firm that makes many different products. The tax rate is 40% (ABCand XYZ are both profitable enough to use all possible tax shields fully).

The current situation: Widgets are being sold for $3.00 per unit. Widgets areproduced at a material cost of$1.50 per unit, labour cost of $0.20 per unit, and totalfixed costs (selling, general and administrative expenses) for the widget division of$0.5 million per year. Depreciation of the existing widget machinery is $5 million peryear for another 3 years (at which point the machines would be worth $0 on thebooks). There are 1 million widgets in ABC's inventory at all times. In 5 years fromnow, ABC's patent on the widgets will run out and there will no longer be profits inthe industry. Hence, ABC will get out of the widget market at that time (its machineswill have no more market value at that time). Total interest expenses for ABC are $4million per year.

Outsourcing Project: The widget machinery could be sold for $7 million today.Future widgets could be purchased from XYZ Corp. for $2.00 per unit for the next 5years. All inventories could be eliminated (at a 10% discount to get rid of all of it atonce), as XYZ would deliver widgets directly to ABC's customers.

All cash flows occur at the end of the year (except the outsourcing proceeds fromselling machines and inventories, which occur right away).

Cost of Capital: The project would be entirely financed with debt. ABC's recentlyissued $1,000 face value zero-coupon bonds with 7.5 remaining years to maturity aretrading at $600 (You should not include the tax shields on debt).

Is the outsourcing project a good idea for ABC? Answer the following questions todemonstrate your understanding of the issues:

1) What are the cash flows associated with the outsourcing project?2) What is the applicable cost of capital?3) Calculate the NPV of the Outsourcing Project.4) Suppose the cost of capital was higher than the number you calculated in 2).

Would that increase of decrease the NPV of the project? Without calculations,explain briefly.

You should assume that all tax shields are realisable in the year they occur.Clearly state all assumptions you make (marks will be awarded for both the correctanswer and assumptions made).