Concept explainers
a.
To calculate: The number of 5-year maturity zeros required to be sold to make the initial cash flow equal to zero, if you buy the one 3 year maturity zero coupon bond.
Introduction:
Initial cash flow: It is supposed to be the amount of money received or paid at the start of a project or investment.
b.
To determine: The cash flows involved in this strategy each year.
Introduction:
Cash flows: It is the total amount of money which comes into the firm or goes out of firm. It mainly affects the liquidity position of the firm.
c.
To calculate: The effective 2-year interest rate on the effective 3-year-ahead forward loan.
Introduction:
Forward mortgage loan: It is one of the fixed-rate mortgages. In this type of loan, the interest rates to be charged ahead can be locked in advance at the start of the mortgage term.
d.
To evaluate: Whether the effective 2-year forward rate is equal to and
Introduction:
Forward rate of interest: It is supposed to be interest rate related to future period that is confirmed or locked by the parties involved in the financial transaction.
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- Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 уг 2 yr 3 yr 3.24 3.79 4.09 5.05 2.07 2.46 2.71 Rate (EAR %) a. Calculate the present value of an investment that pays $1,000 in two years and $3,000 in five years for certain. b. Calculate the present value of receiving $100 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average rate in year 3 and year 5.) c. Calculate the present value of receiving $1,800 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.)arrow_forwardSuppose you want to detemine the forward rates for your client, a lender who is considering a Forward Rate Ageement (FRA). You have collected and organized the data for the risk-free zero interest rates with continuous compounding in the following table: Maturity(years) Zero Rate (% per annum) 1 2 3 4 2 3 5 6 5 What is the forward rate for the fourth year? (sample answer: 2.50%) Blank 1 What is the forward rate for the fifth year? (sample answer: 2.50%) Blank 2 7arrow_forwardSuppose the interest rate on a 3-year Treasury Note is 1.25%, and 5-year Notes are yielding a 3.50%. Based on the expectations theory, what does the market believe that 2 year treasuries will be yielding 3 years from now?arrow_forward
- You are researching interest rates and their forecasts. Your research provides you with the following: 1-year rate = 6% 2-year rate = 6.125% 3-year rate = 8.5% 1-year rate, 2 years from now = 6.5% Assuming you can borrow $1 million, can you use this interest rate information to earn some risk-free profit. if yes, compute the profit. Show detailed workings. Assume that the pure expectations theory applies.arrow_forwardand the effective annual interest rate on a two-year zero coupon 6.4.5 The effective annual yield on a one-year zero coupon bond is 80, and the effective annual interest rate on a two-year zero coupon bond is 8.5%. You are able to arrange a one-year forward loan rate i for a one-year period. Suppose that under these conditions it is possible to make a riskless profit with the following strategy: (i) borrow amount 1 for one year at 8% effective annual, (ii) invest amount 1 for 2 years at 8.5% per year effective annual, (iii) arrange a one-year forward one-year length loan of amount 1.08 at rate i (starting one year from now) and repay the loan in (i), (iv) use the proceeds from (ii) to repay loan (iii) at the end of the second year. vai by For what full range of i will this strategy result in a positive amount left over after all 3 transactions are settled at the end of the second year?arrow_forwardff.2arrow_forward
- Urgently need the solutionarrow_forwardSuppose the interest rate on a 3-year treasury note is 2.75%, and 6-year notes are yielding 3.50%. Based on the expectations theory, what does the market believe that 3-year treasuries will be yielding 3 years from now?arrow_forwardSuppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 yr 2 yr 3 yr 2.42 2.77 3.31 3.75 4.15 4.93 1.98 Rate (EAR %) What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? The present value of the investment is $294.08. (Round to the nearest cent.) If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? The discount rate you should use if you want to use the annuity formula is 2.94%. (Round to two decimal places.)arrow_forward
- suppose the interest rate on a 3 year treasury note is 1.00% and 5 year notes are yielding 3.50% Based on the expectatiions theory, what does the market believe that 2 year treasuries will be yielding 3 years from now?arrow_forwardAssume you have the following asset and liability in your Balance Sheet: Asset - Bond A Modified Duration = 2.6 years Value = RM1.5 million Liability - Bond B Modified Duration = 3.1 years Value = RM1.0 million a. Calculate the duration gap. b. What is the expected change in Net Worth if interest increases by 1%? c. What should or could you to achieve immunised balance sheet? Note: Please show all workings.arrow_forwardI (Interest rates) 1. Consider a bank account paying interest rate R2 = 4% with semi-annual compounding frequency. What is the equivalent rate R1 with yearly compounding frequency? What is the equivalent rate Rc with continuous compounding? 2. Explain briefly (in words) what are the potential pitfalls of using the Internal Rate of Return (IRR) for the evaluation of investment projects. 3. Consider the following two bonds: bond (A) is a zero-coupon bond with maturity TA and duration DA = TA; bond (B) is a coupon bond with maturity TB > TA and duration DB = TA. Which of the two bonds has a greater convexity? (Justify your answer.)arrow_forward
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