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Chapter 8 - Master It! Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio
Chapter 8 - Master It! | ||||||||||
Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio since the proceeds of the portfolio are dedicated to the future liability. In such a case, the portfolio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed. | ||||||||||
Suppose Ice Cubes, Inc. has the following liability due in five years. The company is going to buy bonds today in order to meet the future obligation. The liability and current YTM are below. | ||||||||||
Amount of liability: | $ 100,000,000 | |||||||||
Current YTM: | 8% |
Bond A | Bond B | ||||
Settlement: | 1/1/2000 | 1/1/2000 | |||
Maturity: | 1/1/2003 | 1/1/2008 | |||
Coupon rate: | 7.00% | 8.00% | |||
YTM: | 7.50% | 9.00% | |||
Coupons per year: | 2 | 2 |
a. | Value of liability today: | |||||
b, c. | Coupon payment: | |||||
Original YTM | YTM decrease | YTM increase | ||||
Reinvestment YTM: | ||||||
Coupon rate: | ||||||
Year | Six-month period | Coupon payment | Value of reinvested coupons at Year 5 | Value of reinvested coupons at Year 5 | Value of reinvested coupons at Year 5 | |
1 | 1 | |||||
2 | ||||||
2 | 3 | |||||
4 | ||||||
3 | 5 | |||||
6 | ||||||
4 | 7 | |||||
8 | ||||||
5 | 9 | |||||
10 | ||||||
Future value of coupons: | ||||||
Par value received: | ||||||
Total portfolio value: | ||||||
d. | Since the liability is a lump sum in five years, the duration is equal to the maturity, or five years. | |||||
e. | Macaulay duration: | |||||
Bond A: | ||||||
Bond B: | ||||||
Bond weights: | ||||||
Bond A: | ||||||
Bond B: |
Please provide solutions for a., b., c., d., and e. Thank you.
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