Problem 10

Intro

As corporate treasurer, you have to pay $29 million in one year and again in two years. Bonds of all maturities currently yield 7%.

Part 1

What is the duration of the liability?

Present value of liability:

= 29,000,0001+0.07+29,000,000(1+0.07)229,000,0001+0.07+29,000,000(1+0.07)2

= 52,432,52752,432,527

The duration is the weighted average time to each cash flow:

= 129,000,0001.07+229,000,0001.07252,432,527129,000,0001.07+229,000,0001.07252,432,527

= 1.4831.483

Multiplied by 10 millon to show more decimal places:

D=14,830,91810,000,000=1.483=14,830,91810,000,000=1.483

The duration is 1.483 years.

Part 2

If you buy zero-coupon bonds with a maturity equal to the duration calculated in the previous part, what should be their combined face value (in $)?

To fund your obligation, you need to buy zero-coupon bonds currently worth $52,432,527.

Face value of zero-coupon bonds:

= 52,432,527(1+0.07)1.48352,432,527(1+0.07)1.483

= 57,966,840

Part 3

If interest rates suddenly go up to 8%, what is your immediate funding surplus (positive number) or shortfall (negative number) (in $)? Use the exact duration, not the rounded one shown as solution to part 1.

Submit

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Part 4

If interest rates suddenly go down to 6%, what is your immediate funding surplus (positive number) or shortfall (negative number) (in $)? Use the exact duration, not the rounded one shown as solution to part 1.