Duration (Macauley duration)

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Question 1c

(1) Cocoa-Mocha-Chai (CMC) Co is a large listed company based in Switzerland and uses Swiss Francs as its currency.

A four-year CHF60,000,000 loan taken out to part-fund the setting up of four branches.

Interest will be payable on the loan at a fixed annual rate of 2•2% or a floating annual rate based on the yield urve rate plus 0•40%.

The loan’s principal amount will be repayable in full at the end of the fourth year.

Required:

(c) As an alternative to paying the principal on the loan as one lump sum at the end of the fourth year, CMC Co could pay off the loan in equal annual amounts over the four years similar to an annuity. In this case, an annual interest rate of 2% would be payable, which is the same as the loan’s gross redemption yield (yield to maturity).

Required:

Calculate the modified duration of the loan if it is repaid in equal amounts and explain how duration can be used to measure the sensitivity of the loan to changes in interest rates. (7 marks)

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Question 3a

GNT Co is considering an investment in one of two corporate bonds. Both bonds have a par value of $1,000 and pay coupon interest on an annual basis. The market price of the first bond is $1,079•68. Its coupon rate is 6% and it is due to be redeemed at par in five years.

The second bond is about to be issued with a coupon rate of 4% and will also be redeemable at par in five years. Both bonds are expected to have the same gross redemption yields (yields to maturity).

GNT Co considers duration of the bond to be a key factor when making decisions on which bond to invest.

Required:

Estimate the Macaulay duration of the two bonds GNT Co is considering for investment. (9 marks)

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Question 3b

GNT Co is considering an investment in one of two corporate bonds. Both bonds have a par value of $1,000 and pay coupon interest on an annual basis. The market price of the first bond is $1,079•68. Its coupon rate is 6% and it is due to be redeemed at par in five years.

The second bond is about to be issued with a coupon rate of 4% and will also be redeemable at par in five years. Both bonds are expected to have the same gross redemption yields (yields to maturity).

GNT Co considers duration of the bond to be a key factor when making decisions on which bond to invest.

Required:

Discuss how useful duration is as a measure of the sensitivity of a bond price to changes in interest rates. (8 marks)

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