PLEASE ANSWER (B), (D), (E), (F), (G) THANKS The following is the data on $ 1,00
ID: 2771951 • Letter: P
Question
PLEASE ANSWER (B), (D), (E), (F), (G)
THANKS
The following is the data on $ 1,000 par value bonds issued by PALMA CO, ZICO CO & REX CO. at the end of 2005. Assume that you are thinking of buying these bonds as of January 2006. Answer the following questions for each of the bonds.
(a) Calculate the values of the bonds if your required rates of returns are as follows: PALMA. Co 6%, ZICO CO 9% & REX 8%
PALMA CO
ZICO CO
REX CO
Coupon Interest Rate
7.8%
7.5%
7.975%
Years to Maturity
10
17
4
(b) In December 2005, the bonds were selling for the followings amounts:
PALMA CO
$ 1,030.
ZICO CO
$ 973
REX CO
$ 1,035
What were the expected rates of return for each bond?
(c) How would the values of the bonds change if:
(i) Your required rate of return increases by 3% points?
(ii) Your required rate of return decreases by 3% points?
(d) Explain the implications of your answers in question (b) and (c) as they relate to interest rate risk, premium bonds and discount bonds. (2 marks)
(e) Compute the duration for each of the bonds. Interpret your results. (10 marks)
(f) What are some of the things you can conclude from the above computations?
(3 marks)
(g) Should you buy the bonds? Explain.
PALMA CO
ZICO CO
REX CO
Coupon Interest Rate
7.8%
7.5%
7.975%
Years to Maturity
10
17
4
Explanation / Answer
B)
In general Price P of any Bond is PV of future cash flow discounted at expected rate of return r, T be time to maturity of the Bond with coupon.
P=Coupon/(1+r)+Coupon/(1+r)2+Coupon/(1+r)3 +................+Coupon/(1+r)T +FV/(1+r)T
GP with first term a=Coupon/(1+r),common ratio=R=1/(1+r) so above sum P=a*(1-R^T)/(1-R)
P=(Coupon/(1+r))*(1-(1/(1+r))T)/(1-(1/1+r))+FV/(1+r)T=Coupon*(1-(1/(1+r))T)/r+FV/(1+r)T
Solve for r the expected rate of return using P,T,Coupon and FV=1000 for each of the bonds using excel solver or calculator. Here i am using Calculator Texas BAII Plus to calculate r for PALMA CO using following steps:
1)clear TVM and Memory
2)Press PV and enter value -1030 and press enter.
3)Press PMT and enter value Coupon=7.8%*1000=78 and press enter.
4)Press FV and enter value 1000 and press enter.
5)Press N and enter value 10 and press enter.
6)Press keys CPT and -> together and then press I/Y to calculate I/Y as 7.365% which is nothing but expected rate of return r.
Check for PALMA CO in above formula,
P=78*(1-(1/(1+.07365))10)/.07365+1000/(1+.07365)10=78*(1-.4913)*13.577+491.33=538.745+491.33=1030 approx. Thus our expected rate of return for PALMA CO as 7.365% is correct.
Repeat above steps for other two bonds with required inputs,
For ZICO CO, PV =Price=-973,PMT=Coupon=75,FV=1000,T=N=17, we find r=7.791%
For REX CO, PV =Price=-1035,PMT=Coupon=79.75,FV=1000,T=N=4, we find r=6.943%
D) The results of C should imply that as rate of return increases the price of Bond decreases and vise versa. Also the Premium Bonds duration is lower than Discount Bonds as most of the cash flows are received earlier in the case of discount bonds therefore the percent change is higher for premium Bonds than discount bonds for a given change in rate of return.
E) PALMA CO duration,Price as r changes from 7.365% to 10.365%
P(+3%)=78*(1-(1/(1+10.365%))10)/10.365%+1000/(1+10.365%)10=471.852+372.98=844.83
P(-3%)=78*(1-(1/(1+4.365%))10)/4.365%+1000/(1+4.365%)10=621.31+652.305=1273.61
Duration=P(-3%)-P(+3%)/2*6%*1030=1273.61-844.83/123.6=3.47 its an approximate estimate. You can also get Prices using calculator and then divide by denominator 2*6%*1030.
1)clear TVM and Memory
2)Press I/Y and enter value 10.365% and press enter.
3)Press PMT and enter value Coupon=7.8%*1000=78 and press enter.
4)Press FV and enter value 1000 and press enter.
5)Press N and enter value 10 and press enter.
6)Press keys CPT and -> together and then press PV to calculate Price.
Similarly get duration for other Bonds.
f)We generally get a higher duration for Premium Bonds than Discount Bonds and rate of return is inversely dependent on the price of the Bond.
g) Buy Bond with highest rate of return which is ZICO CO.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.