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FINA 4400: Financial Markets and Institutions Chapter 3 End of Chapter Question #4 What is the value of a $1,000 bond with a 12-year maturity and an 8 percent coupon rate (paid semi-annually) if th * 5% * 6% * 8% * 10% Face Value (FV) $1

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FINA 4400: Financial Markets and Institutions Chapter 3 End of Chapter Question #4 What is the value of a $1,000 bond with a 12-year maturity and an 8 percent coupon rate (paid semi-annually) if th * 5% * 6% * 8% * 10% Face Value (FV) $1.000 $1.000 $1.000 $1.000 Number of Payments (N) Periodic Coupon Payment (PMT) Required Return (YTM) 5,00% 6,00% 8,00% 10,00% End of Chapter Question #6 What is the yield to maturity on the following bonds; all have a maturity of 10 years, a face value of $1,000 and a c The bonds' current market values are $945.50, $987.50, $1,090.00, and $1,225.875, respectively. Market Value (PV) Bond 1 Bond 2 Bond 3 Bond 4 Number of Payments (N) Periodic Coupon Payment (PMT) Face Value (FV) on rate (paid semi-annually) if the required rate of return is: The Bond Value will be: (PV) s, a face value of $1,000 and a coupon rate of 9 percent (paid semiannually). 5, respectively. The yield to maurity will be: (YTM) Chapter 3: Duration Application Duration is a measure of how sensitive a bond price is to changes in interest rates. It is often used to predict the change in bo of a bond if interest rates go up by 1%. Instead of calculating the bond's price using TVM, we can estimate the change in bond As we saw in class, there are limitations to using durations in predicting bond price changes. Duration is based on a linear mo exercise is to demonstrate those limitations by highlighting the prediction errors, which can be see graphically in Figure 3-7 in For the first part of this exercise, we will calculate the "true" bond price given several scenarios of interest rates changes. The For the second part of this exercise, we will calculate bond duration, both Macaulay and modified duration, and then use eac first part. These predicted prices represent the straight line in Figure 3-7, which is called the Duration Model. In part three, you'll describe the relationship between prediction error and (1) the direction of the interest rate change and (2 Part 1: True Bond Prices after Interest Rate Changes Inputs Settlement date 1/6/2021 Maturity 2/1/2028 Par $ 1000 Coupon 7,125% Frequency 2 Yield [YIELD FORMULA] $ Value of investment $ Bond Price 1.328,61 132,861% New Yield Change in Yield New Bond Price Bond Price Change ($) Scenario 1 1/6/2021 2/1/2028 1000 7,125% 2 [INPUT] [GIVEN IN SCENARIO] [PRICE FORMULA] [CALCULATE] Part 2: Calculating Duration measures and using those measures to predict or estimate bond price changes Macualay Duration [DURATION FORMULA] Modified Duration [MDURATION FORMULA] Scenario 1 Interest rate change 0,50% Price change Prediction Error In this cell, you'll enter the formula that you get when you rearrange the equation ?? = −?? × ??? to solve for ΔP, which is ? the notation for the change in price. If more information is need, this equation is on page 84 in the textbook. In this cell, you'll take the between the true bond p part 1 for each scenario a from the predict bond pri part 2 for each scenario. Part 3: #1. Describe the relationship between the prediction error and the direction of the interest rate change. Is this consistent w Increase in interest rates: Decrease in interest rates: #2. Describe the relationship between the prediction error and the magnitude of the interest rate change. Is this consisten Change of 50 bps: Change of 100 bps: predict the change in bond prices based on a specific change in interest rates. For example, let's say we want to know the price mate the change in bond price using duration. is based on a linear model, but the true relationship between bond prices and interest rates is not linear. The purpose of this aphically in Figure 3-7 in the textbook. erest rates changes. These prices represent the points along the bold black curve in Figure 3-7. ration, and then use each to estimate or predict what the bond price will be given the same interest rate scenarios from the Model. erest rate change and (2) the size of the interest rate change. Scenario 2 1/6/2021 2/1/2028 1000 7,125% 2 Scenario 3 Scenario 4 1/6/2021 1/6/2021 2/1/2028 2/1/2028 1000 1000 7,125% 7,125% 2 2 #1 #2 #3 #4 Scenarios 50 bps increase 50 bps decrease 100 bps increase 100 bps decrease These are the true bond prices after the interest rate changes. Scenario 2 Scenario 3 n this cell, you'll take the difference etween the true bond price calculated in art 1 for each scenario and subtract it rom the predict bond price estimated in art 2 for each scenario. ange. Is this consistent with Figure 3-7? Scenario 4 hange. Is this consistent with Figure 3-7? ant to know the price The purpose of this cenarios from the FINA 4400: Financial Markets and Institutions Help Topics THE PV FUNCTION The present value formula, PV, "returns the present value of an investment," or "the total amount a series of future payments is worth now." Examples include the present value of a loan to the lender or the present value of $100 received from an investment a number of years from now. The syntax for this formula is: PV(rate,nper,pmt,fv,type) The first three variables in this function are required. Rate is the interest rate per period. Remember that rate must be for the actual period. For example, a 10 percent annual interest rate is equivalent to 10%/12, or 0.0083 per month. Nper is the total number of payment periods. For example, a four year monthly loan would have 48 periods. Pmt is the constant amount received or paid each period. In many cases, this function can also be completed by typing in the formula for the present value of a cash flow. See the example below. Interest Rate Periods Cash Flow Present Value Present Value 7% 3 100 =C27/(1+$C$25)^c26 81,63 THE FV FUNCTION The future value function, FV, "returns the future value of an investment," or the total amount a single investment or series payments will be worth in the future. Examples include the of an investment in a CD at the bank. The syntax for this formula is: FV(rate,nper,pmt,pv,type) The first three variables in this function are required. Rate is the interest rate per period. Remember that rate must be for the actual period. For example, a 10 percent annual interest rate is equivalent to 10%/12, or 0.0083 per month. Nper is the total number of payment periods. For example, a four year monthly loan would have 48 periods. Pmt is the constant amount received or paid each period; enter 0 here if you are calculating the future value of a lump sum and place that amount under pv. In many cases, this function can also be completed by typing in the formula for the future value of a cash flow. See the example below. Interest Rate Periods Cash Flow Present Value Present Value 7% 3 100 =C53*(1+$C$51)^c52 122,50 THE RATE FUNCTION Use Excel's RATE function to find the interest rate for a given payment and period. The syntax for this formula is: RATE(nper,pmt,pv,fv,type,guess) The first three variables are required: Nper is the total number of payment periods. For example, a four year monthly loan would have 48 periods. Pmt is the constant amount received or paid each period. pv is the the current value of the annuity (this value is entered as a negative, or outflow). For example, suppose someone is willing to sell you a ten year annuity paying $15 each year fo What is the rate of return on this annuity? Periods Cash Flow Present Value 10 -15 80 Interest Rate 13% THE (Macauley) DURATION FUNCTION DURATION(settlement,maturity,coupon, yld, frequency, [basis]) The first five variables are requried: Settlement is the day that the new bondholder assumes ownership of the bond. Coupon is the securities annual coupon rate. Enter this as a percent. Yld is the securities annual yield. Frequency is the number of coupon payments per year. Annual frequency =1; semiannual frequ Basis is optional, but refers to the type of day count for accrued interest. THE (Modified Macauley) DURATION FUNCTION MDURATION(settlement,maturity,coupon, yld, frequency, [basis]) The first five variables are requried: Settlement is the day that the new bondholder assumes ownership of the bond. Coupon is the securities annual coupon rate. Enter this as a percent. Yld is the securities annual yield. Frequency is the number of coupon payments per year. Annual frequency =1; semiannual frequ Basis is optional, but refers to the type of day count for accrued interest. Note: For both duration formula the security has an assumed par value of $100 ENTERING FORMULAS IN EXCEL Select the cell in which you want to enter the formula and type an equal sign. Enter the formula using standard formula operoters such as plus (+) and minus (-). For multiplic Use a forward slash (/) for division; and the caret (^) for exponents. You control the order of calculation by using parentheses to group operations that should be per One of the best uses of formulas is a reference to another cell. The cell that contains the formul as a dependent cell when its value depends on the values in other cells. For example, the formula in the cell below calculates a value depending on what is entered in th 25 50 ent," or "the total e present value estment a number t rate per period. ercent annual monthly loan ch period. mula for the ," or the total e. Examples include the future value t rate per period. ercent annual monthly loan Bond Valuation Duration Help Topics FINA 4400: Financial Markets and Institutions Chapter 3 End of Chapter Question #4 What is the value of a $1,000 bond with a 12-year maturity and an 8 percent coupon rate (paid semi-annually) if the required rate of return is: * 5% * 6% * 8% * 10% Number of Payments (N) Periodic Coupon Payment (PMT) The Bond Value will be: (PV) Face Value (FV) $1,000 $1,000 $1.000 $1,000 Required Return (YTM) 5.00% 6.00% 8.00% 10.00% End of Chapter Question #6 What is the yield to maturity on the following bonds; all have a maturity of 10 years, a face value of $1,000 and a coupon rate of 9 percent (paid semiannually). The bonds' current market values are $945.50, $987.50, $1,090.00, and $1,225.875, respectively. Market Value (PV) Number of Payments (N) Periodic Coupon Payment (PMT) Face Value (FV) The yield to maurity will be: (YTM) Bond 1 Bond 2 Bond 3 Bond 4 FINA 4400: Financial Markets and institutions Help Topics THE PV FUNCTION The present value formula, PV, "returns the present value of an investment," or "the total amount a series of future payments is worth now." Examples include the present value of a loan to the lender of the present value of $100 received from an investment a number of years from now. The syntax for this formula is: PV(rate,nper, pmt,fv, type) The first three variables in this function are required. Rate is the interest rate per period. Remember that rate must be for the actual period. For example, a 10 percent annual interest rate is equivalent to 10%/12, or 0.0083 per month. Nper is the total number of payment periods. For example, a four year monthly loan would have 48 periods. Pmt is the constant amount received or paid each period. In many cases, this function can also be completed by typing in the formula for the present value of a cash flow. See the example below. Interest Rate Periods Cash Flow Present Value Present Value 7% 3 100 1=C27/(1+$C$25)^c26 81.63 THE FV FUNCTION The future value function, FV, "returns the future value of an investment," or the total amount a single investment or series payments will be worth in the future. Examples include the future value of an investment in a c at the bank. The syntax for this formula is: FV(rate,nper,pmt,pv.type) The first three variables in this function are required. Rate is the interest rate per period. Remember that rate must be for the actual period. For example, a 10 percent annual interest rate is equivalent to 10%/12, or 0.0083 per month. Nper is the total number of payment periods. For example, a four year monthly loan would have 48 periods. Pmt is the constant amount received or paid each period; enter O here if you are calculating the future value of a lump sum and place that amount under pv. In many cases, this function can also be completed by typing in the formula for the future value of a cash flow. See the example below. Interest Rate Periods Cash Flow Present Value Present Value 7% 3 100 1=C53"(1+$C$51)^c52 122.50 THE RATE FUNCTION Use Excel's RATE function to find the interest rate for a given payment and period. The syntax for this formula is: RATE(nper,pmt,pv,fv, type,guess) The first three variables are required: Nper is the total number of payment periods. For example, a four year monthly loan would have 48 periods. Pmt is the constant amount received or paid each period. pv is the the current value of the annuity (this value is entered as a negative, or outflow). For example, suppose spmeone is willing to sell you a ten year annuity paying $15 each year for $8 What is the rate of return on this annuity? Periods Cash Flow Present Value 10 -15 80 Interest Rate 13% THE (Macauley) DURATION FUNCTION DURATION(settlement, inaturity.coupon, yld, frequency, (basis]) The first five variables are requried: Settlement is the day that the new bondholder assumes ownership of the bond. Coupon is the securities annual coupon rate. Enter this as a percent. Yld is the securities annual yield. Frequency is the number of coupon payments per year. Annual frequency =1; semiannual frequendy =2; quarterly frequency=4 Basis is optional, but refers to the type of day count for accrued interest. THE (Modified Macauley) DURATION FUNCTION MDURATION(settlement maturity.coupon, yld, frequency, [basis]) The first five variables are requried: Settlement is the day that the new bondholder assumes ownership of the bond. Coupon is the securities annual coupon rate. Enter this as a percent. Yld is the securities annual yield. Frequency is the number of coupon payments per year. Annual frequency =1; semiannual frequency=2; quarterly frequency=4 Basis is optional, but refers to the type of day count for accrued interest. Note: For both duration formula the security has an assumed par value of Shoo ENTERING FORMULAS IN EXCEL Select the cell in which you want to enter the formula and type an equal sign Enter the formula using standard formula operoters such as plus (+) and minus (-). For multiplication use (*) Use a forward slash (1) for division; and the caret (M) for exponents. You control the order of calculation by using parentheses to group operations that should be perforned first. One of the best uses of formulas is a reference to another cell. The cell that contains the formula is nown as a dependent cell when its value depends on the values in other cells. For example, the formula in the cell below calculates a value depending on what is entered in the cel to its right 25 50