Homework - Instructions - Provide answers to the following Problems using Excel.
Problem 1 - Calculate and present your answers below in two ways: using the Time Value of Money (TVM) formula as well as the Future Value Excel function.
a) You invest $1,000 now (in period 0). For this type of investment, the appropriate discount rate per period is 6.75%. What is the future value of this single cash flow at the end of period 13?
b) You invest $1,000 each period for 13 periods. For these cash flows, the appropriate discount rate per period is 6.75%. What is the future value of this annuity?
Problem 2 - You have the option to decide between two investment projects of equal risk which promise to return the following cash flows:
|
Year
|
Project A
|
Project B
|
|
0
|
$(10,000)
|
(8,000)
|
|
1
|
2,250
|
1,000
|
|
2
|
2,500
|
1,300
|
|
3
|
2,000
|
1,600
|
|
4
|
2,100
|
1,900
|
|
5
|
2,000
|
1,500
|
|
6
|
1,500
|
2,000
|
Project A requires an initial investment (at time 0) of $10,000. Project B requires an initial investment (at time 0) of $8,000.
a) Calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) of both projects, assuming a 4.15% discount rate. Would you invest in either or both of these projects? If so, why? If not, why not?
b) Calculate the NPV and IRR of both projects given a change in discount rate to 2.75%. Would you invest in either or both of these projects? If so, why? If not, why not?
Problem 3 - Using the Wall Street Journal, obtain the closing Asked Price and Asked Yield of the 2029 Aug 15, 6.125% coupon Treasury bond for the date January 26, 2018. (Note that this bond has semi-annual coupon payments). You may find the information in the Market Data section, Market Data Center, US Treasury Quotes, Treasury Notes and Bonds.
a) What is the Asked Price as quoted in the WSJ? What is the Asked Yield as quoted in the WSJ?
b) Calculate and verify the Asked Price from Part A using the discounting and compounding techniques we reviewed in class. You may use Excel functions as a check on your answer but not to answer the question. Assume there are 184 days between coupon payments. Is this the clean or dirty price? (Note - the price you calculate may be up to $0.25 off).
c) Using the Excel Yield function and WSJ-quoted price of the bond, calculate and verify the Asked Yield from Part A. (Note - using a day count convention of 1 you should be able to match the yield within 1 bps).
Problem 4 - Calculate the annualized Macaulay duration and modified duration for the bond in Question 3 at the Asked yield-to-maturity in Question 3a. For purposes of this problem, calculate these measures as of 8/15/2017 (in other words: as we have done in class - pretend you settled the purchase of the bond on 8/15/2017 instead of in January 2018 as you did for the previous problem).
Problem 5 -
a) Calculate and report the annualized convexity measure of the bond in Question 3 as of 8/15/2017. Again, pretend you settled the purchase of the bond on 8/15/2017 instead of in January 2018 as you did in Problem 3.
b) Using the duration approximation formula only what percentage change in the price of the bond would you expect if the yield decreases by 250 basis points?
Now using the duration approximation formula with a convexity adjustment, what percentage change in the price of the bond would you expect if the yield decreases by 250 basis points? Given the difference in the price change approximations is the shape of the bond's price function approximately linear or convex?
Attachment:- Assignment Files.rar