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:
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.
题中给的5.5 不是coupon rate 么？
FV 是5250 000， PV计算不是需要PMT和YI么？PMT 不是 coupon 么？为什么这个题目用这种方式May Year 5 having a par value of SEK4,976,303 (= SEK5,250,000/1.0550).
