NO.PZ2023032703000086
问题如下：
Alfred Simonsson is assistant treasurer
at a Swedish lumber company. The company has sold a large tract of land and now
has sufficient cash holdings to retire some of its debt liabilities. The
company’s accounting department assures Alfred that its external auditors will
approve of a defeasement strategy if Swedish government bonds are purchased to
match the interest and principal payments on the liabilities. Following is the
schedule of payments due on the debt as of June Year 1 that the company plans to
defease:
The following
Swedish government bonds are available. Interest on the bonds is paid annually
in May of each year.
How much in par value for each government bond will Alfred need to buy to defease the debt liabilities, assuming that the minimum denomination in each security is SEK10,000?
选项：
解释：
Correct Answer:
The cash flow matching portfolio is built by starting with the last liability of SEK5,250,000 in June Year 5.
If there were no minimum denomination, that liability could be funded with the 5.50% bonds due May Year 5 having a par value of SEK4,976,303 (= SEK5,250,000/1.0550). To deal with the constraint, however, Alfred buys SEK4,980,000 in par value.
This holding also pays SEK273,900 (= SEK4,980,000 × 0.0550) in coupon interest in May Year 2, 3, and 4.
Then move to the June Year 4 obligation, which is SEK4,136,100 after subtracting the SEK273,900 received on the 5.50% bond: SEK4,410,000 – SEK273,900 = SEK4,136,100.
Alfred buys SEK3,950,000 in par value of the 4.75% bond due May Year 4. That bond pays SEK4,137,625 (= SEK3,950,000 × 1.0475) at maturity and SEK187,625 in interest in May Year 2 and Year 3.
The net obligation in June Year 3 is SEK6,158,475 (= SEK6,620,000 – SEK273,900 – SEK187,625) after subtracting the interest received on the longer-maturity bonds.
The company can buy SEK5,950,000 in par value of the 3.50% bond due May Year 3. At maturity, this bond pays SEK6,158,250 (= SEK5,950,000 × 1.0350). The small shortfall of SEK225 (= SEK6,158,475 – SEK6,158,250) can be made up because the funds received in May are reinvested until June. This bond also pays SEK208,250 in interest in May Year 2.
Finally, Alfred needs to buy SEK2,960,000 in par value of the 2.75% bond due May Year 2. This bond pays SEK3,041,400 (= SEK2,960,000 × 1.0275) in May Year 2. The final coupon and principal, plus the interest on the 5.50%, 4.75%, and 3.50% bonds, total SEK3,711,175 (= SEK3,041,400 + SEK273,900 + SEK187,625 + SEK208,250). That amount is used to pay off the June Year 2 obligation of SEK3,710,000. Note that the excess could be kept in a bank account to cover the Year 3 shortfall.
In sum, Alfred buys the following portfolio:
1. 老师，请问下这里计算par value也是按照四舍五入的原则吗？比如第三个bond（mature in May Year 3）实际算出来是5950217，我本来以为是为了defease liability 素以par value应该无论如何和其他的coupon加起来应该要超过这一年的liability，但是看答案是四舍五入为5950000了。
2. 以下是我的答案，请问考试中这样回答是否足够？感觉答案写了很多步骤考试中可能没时间写
First Swedish government bonds (mature in May Year 5 with coupon 5.5%) has a par value of SEK4980000.
Second Swedish government bonds (mature in May Year 4 with coupon 4.75%) has a par value of SEK3950000.
Third Swedish government bonds (mature in May Year 3 with coupon 3.5%) has a par value of SEK5950000.
Fourth Swedish government bonds (mature in May Year 2 with coupon 2.75%) has a par value of SEK2960000.