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15. A junior bond with a face value of 200 matures in 5 years. A senior bond on the same firms also matures in 5 years, and has a face value of 100. Assume sA=.5 and the riskfree rate=.04. Firm value is equal to 400. Using the Merton model, what is the value of the junior bond? (The following table includes figures that will reduce the time required to answer this but it also includes figures that are irrelevant to the problem and some that are strictly wrong).
|
d1 |
d2 |
N (d1) |
N (d2) |
|
1.978 |
0.860 |
.9761 |
.8051 |
|
1.978 |
0.860 |
.8051 |
.9761 |
|
0.9952 |
-.1228 |
.8413 |
.5478 |
|
0.9952 |
-1.505 |
.8413 |
.0661 |
|
0.9952 |
-.1228 |
.8413 |
.4522 |
A. 99.07
B. 174.55
C. 75.48
D. 16.63
Correct answer is Afficeffice" />
A is correct. To get this answer use the first and last row of the table to make the calculation of the Black-Scholes formula go faster. Plug in the values given into the B-S formula and use the first row to get the value of the equity if the leverage were just 100 (the face value of the senior bond). Subtract this off 400 to get the value of the senior bond. Plug in the values of the B-S formula assuming a strike of 300 (the total debt) to get the value of the equity. Use the last row of the table to make this go faster. Subtracting the value of the equity and the senior debt from 400 gives us the answer, a.
B is incorrect because it is the value of the total debt of the firm, not the value of the junior debt alone.
C is incorrect because it is the value of the senior debt, not the junior debt.
D is incorrect because it uses the wrong line in the table to calculate the junior debt. It uses the second line instead of the first. One needs to use the B-S to calculate d1 and d2 and find their normal distribution values in the table. All of the rows except the second line from the bottom have the correct values of d1 and d2 but they do not always have the correct normal distribution value that goes with d1 and d2. In particular, the middle line is incorrect because a negative value for d2 has a normal distribution value that is less than .5 The second line is easily detected as wrong because the normal area for a large number should be larger than that of a small number ? here they are reversed.
Reference: Stulz, Risk Management and Derivatives, Chapter 18
富二代炫富，富二代为博美人一笑，不惜万金这些事情已经屡见不鲜。但是富二代为追美女不惜送上宝马豪车，这也不算多夸张，但是让人HOLD不住的却是这位富二代小伙为博得美人笑，送出了宝马豪车，可惜最后却落得苦笑不得。
广西南宁一富二代小伙，为追女送上宝马豪车一部，可惜并没有获得女方的应许，只是得到了一个真实相告。对方称自己已经近50岁，不敢奢望小伙的厚爱，而且自己的子女跟他年龄差不了多少。便将宝马豪车退回。
这样雷人到家的事件确实发生了，有消息称，这位50岁的大龄“美女”真名为许燕玲，相信吗？她走在街上风韵犹存，雍容华贵，看上去跟30岁的美丽少妇没有任何区别，身材近乎完美，回头率更是不用说，Fashion这个词用来形容她一点都不为过。正常人都会认为她是一个漂亮少妇，更有甚者以为她的电影明星。但所有人并不知道的是，她已经是一位块50岁的女人。
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