I need question 4 done
Here is the question #1 mention in 4
4) As you sit at your desk scanning the bond market, you notice the $300 annuity from #1 is called Bond X. You also find bond Y, which offers $100 a year for 10 years, and currently sells for $700. Using the idea of a replicating portfolio, show an arbitrage here. This one is a little different than in class. You can buy the bonds (you pay cash foday, but you get the payments) or issue/sell short (you get cash today, but you owe the future payments). You can buy multiple bonds, too. 1) You own an asset that entitles you to receive a payment of $300 per year for ten years. You will receive the first payment one year from today. You are certain that all ten payments will be made in full and on time. The annual interest rate is 8% with certainty and in perpetuity. How much would you pay today to buy this asset? a) The brute force approach in Excel. First, put in the payment amounts: put the numbers 1, 2,.., 10 in Al:A 10, and $300 in each adjacent row of column B. Next, create the discount factors: put [1/(1+r)]'=(1/(1.08)]' in row i of the third column for i = 1,.,10. Let the entry in the ith row of the fourth column equal the product of the entry in the ith row of the second column and third columns. For example, your entry in the row for year 3 would start: 3 S300=1/1.0843 You can use the spreadsheet we made in lecture, or the "spreadsheer" from Module IA can help you put this together... Sum the entries in rows 1-10 of the third column in cell DI I. This will yield the present value of the asset. Please turn in a printed copy of this spreadsheet (you can cut & paste into Word to keep it compact). b) Now try using the Excel function PV(r.n.p) where r is the interest rate, n is the number of yearly payments you will receive (with the first payment due one year from today), and p is the amount of each payment. You should get the same answer as 1b, but as a negative. Briefly explain why PV returns a negative number c) Show how you could value this annuity using the "portfolio of perpetuities" approach. Show how the cash flows of your portfolio replicate the annuity (the table we did in lecture). Calculate the net cost of your portfolio, and show that it is the same value as the previous calculations. 4) As you sit at your desk scanning the bond market, you notice the $300 annuity from #1 is called Bond X. You also find bond Y, which offers $100 a year for 10 years, and currently sells for $700. Using the idea of a replicating portfolio, show an arbitrage here. This one is a little different than in class. You can buy the bonds (you pay cash foday, but you get the payments) or issue/sell short (you get cash today, but you owe the future payments). You can buy multiple bonds, too. 1) You own an asset that entitles you to receive a payment of $300 per year for ten years. You will receive the first payment one year from today. You are certain that all ten payments will be made in full and on time. The annual interest rate is 8% with certainty and in perpetuity. How much would you pay today to buy this asset? a) The brute force approach in Excel. First, put in the payment amounts: put the numbers 1, 2,.., 10 in Al:A 10, and $300 in each adjacent row of column B. Next, create the discount factors: put [1/(1+r)]'=(1/(1.08)]' in row i of the third column for i = 1,.,10. Let the entry in the ith row of the fourth column equal the product of the entry in the ith row of the second column and third columns. For example, your entry in the row for year 3 would start: 3 S300=1/1.0843 You can use the spreadsheet we made in lecture, or the "spreadsheer" from Module IA can help you put this together... Sum the entries in rows 1-10 of the third column in cell DI I. This will yield the present value of the asset. Please turn in a printed copy of this spreadsheet (you can cut & paste into Word to keep it compact). b) Now try using the Excel function PV(r.n.p) where r is the interest rate, n is the number of yearly payments you will receive (with the first payment due one year from today), and p is the amount of each payment. You should get the same answer as 1b, but as a negative. Briefly explain why PV returns a negative number c) Show how you could value this annuity using the "portfolio of perpetuities" approach. Show how the cash flows of your portfolio replicate the annuity (the table we did in lecture). Calculate the net cost of your portfolio, and show that it is the same value as the previous calculations
