Attached are two exercises on Bond Pricing and Time value of money how can you guide me on the exercise

2016 Spring2 Financial Concepts Week3 Exercise6 Time Value of Money Student Name: Instructions Note: Unless otherwise stated, assume that interest is calculated on an annual basis. Leave all answers to TWO decimal places. For the boxes below, put calculator input numbers in the second row and your computed answer in the third row. Also, observe cash flow sign conventions: negative numbers for outflows [pay, invest, etc.]; positive numbers for inflows [receive, borrow, etc.] Some additional notes and guidance at the end of the document. 1) Ian invests $10,000 today in a 3 year CD paying 2.00% annually. He receives the full amount of principal and accrued interest in 3 years. How much will he receive in 3 years? monkey2 ing2 N ? i ? PV ? PMT ? FV =? 2) How much would Sylvia have to invest in a CD today to receive $15,000 in 5 years' time if the interest rate payable on the CD is 3.00% APR? N ? i ? PV PMT ? FV ? =? 3) A zero coupon bond is sold at a discount and pays no interest during its life. John, who is planning for retirement, invests $75,000 in this zero coupon bond which promises to pay $100,000 in 20 years' time. What is the rate of return on the investment? Assume annual TVM compounding. N BU MET AD-632OL i PV -1- PMT FV Wk4 Ex6 2016 Spring2 4) Mary has the opportunity to invest $10,000 in a 5 year CD. She has the option to receive a 3.65% return compounded annually; 3.62% compounded quarterly; or 3.60% compounded monthly. What option will give her the highest total return and how much will she receive in 5 years' time? [i.e. find the FVs of each of the options ...] Also calculate the Effective Annual Rate [EAR] of these of the investment options. PS: ... the one with the highest FV and EAR is the best investment option. Annual compounding: N i ? ? PV ? PMT ? FV EAR =? =? Quarterly compounding: N i PV PMT FV EAR Monthly compounding: N i PV PMT FV EAR 5) Upon retirement, Chris invests $200,000 in a 10-year ordinary annuity when the prevailing interest rate is 4.0% APR. How much will he receive annually? N i PV PMT FV 6) Using TVM on the financial calculator and the Rule of 72s, how long will it take a $10,000 investment to double if the interest rate is 6.0%? Assume annual TVM compounding. Using the calculator: N i PV PMT FV Using Rule of 72s: show calculation here ... What if the TVM compounding is on a monthly basis? Would your answer be the same? Explain by showing calculations below ... BU MET AD-632OL -2- Wk4 Ex6 2016 Spring2 7a) Helen purchases a condo and obtains a $400,000 fully amortizing level payment 30 year mortgage bearing an (annual) [quoted] fixed interest rate of 6.00% [interest compounded monthly]. How much will her monthly blended principal and interest payment be? [\"blended\" refers to calculating your PMT, which in an Amortized Loan, is made up of principal and interest components] N i PV PMT FV [i.e. your calculated PMT above should equal Interest + Amortization of Principal for each period [row] of payment below] 7b) For months 1, 2 and 3 of the mortgage, determine how much of the total payment is principal and how much is interest and construct an amortization table as follows: monkey2 column: [a] [b] [c] [d] = prev row's [e]= PMT from (7a)= [a] x APR 12 Mth 1 2 3 Beginning Principal 400,000.00 Payment from 7a) from 7a) from 7a) Interest 8) Johnson Corp is considering a Capital Expenditure $200,000. It will have a 5 year lifetime and will following years: Year 1 Year 2 Year 3 Year 4 Year 5 [e] = [b] - [c] = [a] - [d] Amortization of Principal Ending Principal project that will require an initial investment of return the following amounts at the end of the $20,000 $30,000 $40,000 $50,000 $60,000 a) If at the end of year 5, the project has no salvage value, what is the company's expected annual rate of return (IRR)? Show work below [i.e. fill in the CF numbers below; then use your calculator to get the IRR]: CF0 = ?, CF1 = ?, CF2 = ?, CF3 = ?, CF4 = ?, CF5 = ?, etc. IRR = ? b) If at the end of year 5 the project has a salvage value of $20,000, what is the company's expected annual rate of return? [Hint: The salvage value will add to the cash flow that Johnson receives in year 5; assume no tax on the salvage value] Show work below [i.e. fill in the CF numbers below; then use your calculator to get the IRR]: CF0 = ?, CF1 = ?, CF2 = ?, CF3 = ?, CF4 = ?, CF5 = ?, etc. IRR = ? c) If the required rate of return of project is 6%, calculate the Net Present Value (NPV) of (a). Show work below [i.e. fill in the CF numbers below; then use your calculator to get the NPV]: CF0 = ?, CF1 = ?, CF2 = ?, CF3 = ?, CF4 = ?, CF5 = ?, etc. I=? NPV = ? BU MET AD-632OL -3- Wk4 Ex6 2016 Spring2 Some notes on TVM and its use on a financial calculator 1) Make sure your P/Y is set to 1. This makes the calculator calculate in \"period mode\" since not all Time Value problems are on an annual basis. PS: if you are using a HP 12C, this is always set as such; no need to fiddle with it. PS: some other brands of calculators (e.g TI), fresh out of the box, has a factory setting of \"12\"; this is bad!!! Set it to 1. 2) Having done (1), the \"N\" or \"n\" is the number of periods (e.g. years, months, semiannual, etc.) depending on the question, and \"I/Y\" or \"i\" is the periodic rate ... PS: different calculators label their buttons differently as in above. 3) ... where number of periods and the periodic rate = number of years x compounding frequency = APR compounding frequency 4) For example, if a CD investment [Question #1] compounds interest on an annual rate, then N and I/Y will respectively be entered as \"number of years\" and \"annual interest rate\". 5) For example, if a 30-year mortgage [Question #7] has a quoted 6.00% APR with interest compounded monthly and payments being made on a monthly basis, then N = 30x12 or 360 periods (months) and I/Y = 6.00%/12 or 0.50% periodic rate (monthly rate). 6) For your calculator's \"I/Y\" or \"i\" button, you enter its number as a percent, NOT as a decimal. For example, if the periodic rate is 3%, then you enter \"3\2016 Spring2 Financial Concepts Week4 Exercise7 Bond Pricing Student Name: Instructions Leave all answers in TWO decimal places. For the boxes in Question 1 through 5, put calculator input numbers in the second row and your computed answer in the third row. Question 1 thru 5 cash flow sign conventions: negative PV [assuming we are buying bonds]. Therefore PMT and FV are positive numbers [receiving periodic coupons and receiving face value at maturity]. All bonds have a face value of $1,000. Assume that all coupon payments are made annually unless the problem specifically states otherwise. Some additional notes and guidance at the end of the document. 1) What is the current value of a 30-year bond with a 4% coupon rate if the current market interest rate is 5.00%? N ? i ? PV PMT ? FV ? =? 2) A zero coupon bond is sold at a discount and pays no cash interest during its lifetime. At maturity it pays the face value of the bond. What is the current value of a 10-year zero coupon bond if the current market interest rate is 4.00%? monkey2 N ? i ? PV PMT ? FV ? =? 3) What is the current value of a 20-year bond with a coupon rate of 6% (annual) with semiannual coupon payments if the current market interest rate is 3.0% (annual)? [The coupon frequency is explicitly stated here because we want to compare this PV(bond) to the next question. Everything else being equal, the frequency of coupons DO affect the price of the bond.] N ? i ? PV PMT ? FV ? =? MET AD-632OL -1- Financial Concepts 2016 Spring2 4) What is the current value of a 15-year bond with a coupon rate of 5% with quarterly coupon payments if the current market interest rate is 6.0%? N ? i ? PV PMT ? FV ? =? 5) What is the Yield to Maturity (YTM) and the Yield to Call (YTC) for a bond which is currently priced at $975 if the bond has a coupon of 6%, matures in 10 years but could be called at a price of $1,025 in 5 years? Spring2 Fall2 Calculate YTM: N ? YTM PV ? PMT ? FV ? PV ? PMT ? FV ? monkey2 =? Calculate YTC: N ? YTC =? MET AD-632OL -2- Financial Concepts 2016 Spring2 6a) In each of the blue cells below, calculate the value of the respective bonds with various combinations of market interest rate, coupon rate, and maturity assumptions: [assume annual coupons; $1,000 face value] [you can leave the following bond prices as positive numbers; easier to calculate % change] Market Interest Rate = 5% Maturity 10-Yr Scenario1 2016 Spring2 1% coupon 5% coupon 8% coupon 30-Yr What value? What value? 1,000.00 1,000.00 What value? Market Interest Rate = 2% What value? Maturity 10-Yr 1% coupon What value? What value? 5% coupon What value? What value? 8% coupon Scenario2 30-yr What value? What value? In each of the red cells below, calculate the respective change in bond value from Scenario1 to Scenario2: % change in Bond value from Scenario 1 to 2 Maturity: 10-Yr 30-Yr 1% coupon % change? % change? 5% coupon % change? % change? 8% coupon % change? % change? 6b) What do you conclude about the relative sensitivity of bond prices to changes in interest rate? [Hint: use the above calculated numbers to make comments on the following comparisons with regard to how sensitive are bond price changes when its market interest rate changes] 1) Longer maturities relative to shorter maturities? Put your response here .... 2) Higher coupon bonds relative to lower coupon bonds? Put your response here .... MET AD-632OL -3- Financial Concepts 2016 Spring2 Some notes on bond calculations using the financial calcula 1) As usual, make sure your P/Y is set to 1. This makes the calculator calculate in \"period mode\" since not all Time Value problems are on an annual basis. PS: if you are using a HP 12C, this is always set as such; no need to fiddle with this. PS: some other brands of calculators (e.g TI), fresh out of the box, has a factory setting of \"12\"; this is bad!!! Set it to 1. 2) Having done (1), \"N\" or \"n\" is the number of periods (e.g. years, months, semi-annual, etc.) depending on the question, and \"I/Y\" or \"i\" is the periodic rate, and \"PMT\" is the periodic payment. PS: different calculators label their buttons differently as in above. 3) ... where number of periods = number of years x number of coupon payments per year and the periodic rate = the bond's yield number of coupon payments per year and each coupon payment = coupon rate x face value number of coupon payments per year 4) For example, if a 15-year bond, 4% coupon rate makes semi-annual payments, then N = 15x2 or 30 periods (i.e. 6-month semi-annual periods) and PMT = 4% x $1,000 2 or $20 periodic payment (i.e. each coupon payment is $20 and there are 2 coupon payments per year). PMT in this case is the periodic repetition of the same amount of coupon payment, i.e. an annuity. 5) In a similar fashion, if you are asked to calculate a bond's YTM or YTC, you still continue to enter the number of periods in \"N\" and the periodic coupon payments in PMT. Once you calculated the \"i\" or the \"I/Y\