Excel Financial Functions

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1 Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint()

2 Future Value How much will your money grow? Present Value Interest Rate Compounding Periods Payments/Deposits Future Value

3 Future Value Example: College Fund You wish to open a account for you newborn s college in 18 years. You plan on making an initial deposit of $5,000 and monthly deposits of $200. The account compounds monthly with a nominal rate of 4%. How much will you have in 18 Years?

4 What is Compounding? Interest is earned not only on the initial deposit but also on previously earned Interest Period Beginning Balance Interest (.06/2 x Beginning Balance) Ending Balance (Beginning Balance + Interest) Year 1 - June $ $3.00 $ Year 1 Dec. $ $3.09 $ Year 2 - June $ $3.18 $ Year 2 Dec. $ $3.28 $ Year 3 June $ $3.38 $ Year 3 Dec. $ $3.48 $119.41

5 FV(Rate,#periods,Pmts,PV,Type) Returns the Future value of an initial deposit and/or a series periodic deposits of an equal amount. Notes: Rate must be constant. If making payments/deposits, they must be: Of the same Amount Made periodically (i.e. monthly, yearly, etc.)

6 FV(Rate,#periods,Pmts,PV,Type) This is the rate for a single compounding period. For example: Yearly Rate of 6% with monthly compounding:.06/12 or.005 Yearly Rate of 6% with semi-annual compounding:.06/2 or.03 Yearly Rate of 6% with yearly compounding:.06

7 FV(Rate,#periods,Pmts,PV,Type) This is the total number of compounding periods. For example: 5 year loan compounded monthly: 5*12 = 60 5 year load compounded semi-annually: 5*2 = 10 5 year loan compounded yearly: 5

8 FV(Rate,#periods,Pmts,PV,Type) Use if you are making periodic deposits/ payments of equal amount over the life of the investment/loan. #of payments must equal #of compounding periods: You are making monthly payments into an account which compounds monthly. You are making yearly payments into an account which compounds yearly.

9 FV(Rate,#periods,Pmts,PV,Type) Used to find the FV of a lump sum invested at the beginning of the time frame. Example: You deposited $10K in a saving account and you wish to see what it will be worth in 20 years.

10 FV(Rate,#periods,Pmts,PV,Type) Type applies only when making periodic payments (Pmts). There are two types: 0 and 1 0 = Regular Annuity. (Interest compounded at the end of each period) 1 = Annuity Due (Interest compounded at the beginning of each period

11 You wish to open a account for your newborn s college fund in 18 years. You plan on making an initial deposit of $5,000 and monthly deposits of $200. The account compounds monthly with a yearly rate of 4%. How much will you have in 18 Years? FV_Ex1

12 You are opening an account with $100. The account compounds semi- annually. At 6% yearly interest, what will you have in 3 years? FV_Ex2

13 You are depositing $5,000 into an account yearly for the next 10 years at 4% annual interest. Interest is compounded yearly at the beginning of the period. What is the Future Value? FV_Ex3

14 Nominal vs. Effective Rate Nominal Rate This is the yearly stated rate. Effective Rate The yearly rate you are actually getting because of compounding.

15 6% Annually Rate compounded Semi-Annually Period Beginning Balance Interest (.06/2 x Beginning Balance) Ending Balance (Beginning Balance + Interest) Year 1 - Period 1 $ $3.00 $ Year 1 - Period 2 $ $3.09 $ Accounting for both periods in Year 6% x $100 = $106.00? What rate could we multiple $100 by to get $106.09?? x $100 = $106.09

16 When to Use Effective Rate? Comparing Loan Rates When you wish to compare loan rates with different # of compounding periods per year. # Pmts/year # Comp Periods/year You are making yearly payments into an account which compounds semi-annually.

17 Effect( Nominal Rate, # of Compounding Periods Per Year ) This is the stated yearly rate. It is the rate quoted on the account, bond, loan, etc. This is the number of times the account is compounded per year. (i.e. for monthly compounding use 12; semi-yearly, use 2)

18 Effective Rate Example 1: Comparing Different Loan Rates We are looking for a credit card company that offers the best rate and have found three we wish to compare. The first has a nominal rate of 17% and compounds monthly, the second has a rate of 17.5% and compounds semiannually (twice a year), and the third has a rate of 18% and compounds quarterly. Which one has the best effective rate? (i.e. the lowest?) Eff_Rate_Ex1

19 Effective Rate Example 2: # Pmts # Comp. Periods per Year We are making yearly payments of $1000 for 5 years into an account which compounds monthly. The annual nominal interest rate is 6%. The payments are made at the end of each year (regular annuity). Find the Future Value. Eff_Rate_Ex2

20 Nominal( Effective Rate, # of Compounding Periods Per Year ) This is the actually yearly rate you are getting when compound is taken into consideration. This is the number of times the account is compounded per year. (i.e. for monthly compounding use 12; semi-yearly, use 2)

21 We are making semi- yearly payments of $1000 into an account for 5 years. The account compounds monthly. The annual nominal interest rate is 4%. The payments are made at the end of each period (regular annuity). Find the Future Value. The number of payments we are making per year must equal the number of compounding periods per year. Step 1: Find the effective yearly rate of an account which compounds monthly. Step 2: Use nominal() to convert the effective yearly rate into a nominal yearly rate for an account which compounds semi- annually. Eff_Rate_Ex2

22 Present Value How much would a future amount be worth today? Present Value Interest Rate Compounding Periods Payments/Deposits Future Value

23 Present Value Loan Payback You are loaning an associate $1,000. For repayment options, they suggest the scenarios below. The going market rate is 4% compounded monthly. Which option should you take? Assume risk is the same for all three options. OPTION A: OPTION B: OPTION C: Will pay you $1,200 after 1 year. Will pay you $1,400 at the end of 2 years. Will pay you $100 per month for 12 months then $150 at the end.

24 PV(Rate,#periods,Pmts,FV,Type) Returns the present value of a lump and/or series of cash flows made in the future. Notes: Rate must be constant. If making payments/deposits, they must be: Of the same Amount Made periodically (i.e. monthly, yearly, etc.)

25 PV(Rate,#periods,Pmts,FV,Type) This is the rate for a single compounding period. For example: Yearly Rate of 6% with monthly compounding:.06/12 or.005 Yearly Rate of 6% with semi-annual compounding:.06/2 or.03 Yearly Rate of 6% with yearly compounding:.06

26 PV(Rate,#periods,Pmts,FV,Type) This is the total number of compounding periods. For example: 5 year loan compounded monthly: 5*12 = 60 5 year load compounded semi-annually: 5*2 = 10 5 year loan compounded yearly: 5

27 PV(Rate,#periods,Pmts,FV,Type) Use if you are making periodic deposits/ payments of equal amount over the life of the investment/loan. #of payments must equal #of compounding periods: You are making monthly payments into an account which compounds monthly. You are making yearly payments into an account which compounds yearly.

28 PV(Rate,#periods,Pmts,FV,Type) Use to find the PV of a lump sum paid at the end of the time frame. Example: You will receive $1,000 in ten years. What would it be worth today?

29 PV(Rate,#periods,Pmts,FV,Type) Type applies only when making periodic payments (Pmts). There are two types: 0 and 1 0 = Regular Annuity. (Interest compounded at the end of each period) 1 = Annuity Due (Interest compounded at the beginning of each period

30 Present Value Example 1: You are loaning an associate $1,000. For repayment options, they suggest the scenarios below. The going market rate is 4% compounded monthly. Which option should you take? Assume risk is the same for all three options. OPTION A: Will pay you $1,200 after 1 year. OPTION B: Will pay you $1,400 at the end of 2 years. OPTION C: Will pay you $100 per month for 12 months then $150. PV_Ex1

31 Bond Cash Flow Discounting Example PV() We have purchased a 3 year bond with a face value of $1,000 for $ Its coupon rate is 6% resulting in yearly payments of $60 (face value x coupon rate). The market is currently paying about 5% for investments of equal risk. What is its Present Value? PV_Ex2

32 Payments Determining what your payments would be given a present value, rate, and time. Rate Present or Future Value Time Pmt Pmt Pmt

33 Payments Loan Payments You are taking out a 5 year loan of 20K at 6% to purchase a new car. What are your monthly payments? Retirement Goal You would like to have $1,000,000 in your savings account by the time you retire. You have 30 years until retirement and you have found a fund which pays 5.5% annual interest. You plan on making yearly payments into an account which compounds monthly. How much do you have to deposit each year to reach your goal?

34 PMT(Rate,#periods,PV,FV,Type) This is the rate for a single compounding period. For example: Yearly Rate of 6% with monthly compounding:.06/12 or.005 Yearly Rate of 6% with semi-annual compounding:.06/2 or.03 Yearly Rate of 6% with yearly compounding:.06

35 PMT(Rate,#periods,PV,FV,Type) This is the total number of compounding periods. For example: 5 year loan compounded monthly: 5*12 = 60 5 year load compounded semi-annually: 5*2 = 10 5 year loan compounded yearly: 5

36 PMT(Rate,#periods,PV,FV,Type) Use when a lump sum at the beginning of the time frame is involved. Example: You borrowed 20,000.

37 PMT(Rate,#periods,PV,FV,Type) Use when a lump sum at the end of the time frame is involved. Example: You wish to have 1,000,000 in an account at the end of 30 years.

38 PMT(Rate,#periods,PV,FV,Type) Type applies only when making periodic payments (Pmts). There are two types: 0 and 1 0 = Regular Annuity. (Interest compounded at the end of each period) 1 = Annuity Due (Interest compounded at the beginning of each period

39 PMT() - Car Loan You are planning to buy a new car. You are taking out a 5 year loan of $20,000 to help you pay for it and you are borrowing at a yearly interest rate of 6%. What will the monthly loan payments be? PMT_Ex1

40 PMT() Amortization Table Create an Amortization Table for PMT Example 1 1. Initial Balance = Loan Amount =B10 3. Principle= Monthly Payment - Interest = - B$14-C18 PMT_Ex1 2. Interest = Previous Balance * Rate/12 =D17 * B$8/12 4. Balance = Previous Balance - Principle = D17 B18

41 PMT() - Retirement Planning You would like to have $1,000,000 in your savings account by the time you retire. You have 30 years until retirement and you have found a CD account which pays 5.5% annual interest. You plan on making yearly payments into an account which compounds monthly. How much do you have to deposit each year to reach your goal? PMT_Ex2

42 Payment Array Table We wish to build a payment table for various loan amounts and interest rates.

43 About Array Formulas Input Highlight if you need multiple cell output. Control + Shift + Enter tells Excel to process cells in a range of a formula one at a time. Editing You must press Control + Shift + Enter after editing an Array formula. Deleting Highlight all array output to delete the array.

44 Payment Array Table Step 1 Type in Loan Amounts and Rates as shown.

45 Payment Array Table Step 2 Highlight the area where the payments will go..

46 Payment Array Table Step 3 With the area still highlighted, type the formula shown in B2 but don t press enter.

47 Payment Array Table Step 4 Press CONTROL + SHIFT + ENTER.

48 Number of Periods Determine how long it will take to save a specific amount with a given deposit or periodic deposits. NPER(Rate,Pmts,PresentValue,FutureValue,Type)

49 NPER(Rate, Pmts, Present, Value Future, Value Type) This is the rate for a single compounding period. For example: Yearly Rate of 6% with monthly compounding:.06/12 or.005 Yearly Rate of 6% with semi-annual compounding:.06/2 or.03 Yearly Rate of 6% with yearly compounding:.06

50 NPER(Rate, Pmts, Present, Value Future, Value Type) Use if you are making periodic deposits/ payments of equal amount over the life of the investment/loan. #of payments must equal #of compounding periods: You are making monthly payments into an account which compounds monthly. You are making yearly payments into an account which compounds yearly.

51 NPER(Rate, Pmts, Present, Value Future, Value Type) Use when a lump sum at the beginning of the time frame is involved. Example: You borrowed 20,000.

52 NPER(Rate, Pmts, Present, Value Future, Value Type) Use when a lump sum at the end of the time frame is involved. Example: You wish to have 1,000,000 in an account at the end of 30 years.

53 NPER(Rate, Pmts, Present, Value Future, Value Type) Type applies only when making periodic payments (Pmts). There are two types: 0 and 1 0 = Regular Annuity. (Interest compounded at the end of each period) 1 = Annuity Due (Interest compounded at the beginning of each period

54 NPER() Example You are planning on making monthly deposits of $100 into a savings account which compounds monthly with a yearly rate of 4%. How many years will it take you to have $25,000? What will the date be? NPER()

55 Rate What rate are you getting on your investment? Rate(#periods,Pmts,PV,FV,Type,Guess)

56 Rate(#periods,Pmts,PV,FV,Type,Guess) This is the total number of compounding periods. For example: 5 year loan compounded monthly: 5*12 = 60 5 year load compounded semi-annually: 5*2 = 10 5 year loan compounded yearly: 5

57 Rate(#periods,Pmts,PV,FV,Type,Guess) Use if you are making periodic deposits/ payments of equal amount over the life of the investment/loan. #of payments must equal #of compounding periods: You are making monthly payments into an account which compounds monthly. You are making yearly payments into an account which compounds yearly.

58 Rate(#periods,Pmts,PV,FV,Type,Guess) Use when a lump sum at the beginning of the time frame is involved. Example: You borrowed 20,000.

59 Rate(#periods,Pmts,PV,FV,Type,Guess) Use when a lump sum at the end of the time frame is involved. Example: You wish to have 1,000,000 in an account at the end of 30 years.

60 Rate(#periods,Pmts,PV,FV,Type,Guess) Type applies only when making periodic payments (Pmts). There are two types: 0 and 1 0 = Regular Annuity. (Interest compounded at the end of each period) 1 = Annuity Due (Interest compounded at the beginning of each period

61 Rate(#periods,Pmts,PV,FV,Type,Guess) (Optional) This gives Excel a place to start looking for the rate. If you don t guess Excel will guess for you at 10%. What you guess does not affect the answer returned but you may get an error if the actual rate varies greatly from the guess.

62 Rate Example 1: Car Resale 5 Years ago you purchased a car for $5,000. You sold it today for $12,000. What return did you get on your investment? Find the Yearly Rate if Compounded Yearly. Find the Yearly Rate if Compounded Monthly. Rate_Ex1

63 Rate Example 2: Annuity You are investing in an annuity that requires you to deposit $50 at the end of every 6 months for 2 years (i.e. total of 4 payments). At the end of the 2 years you will receive a payment of $ What Yearly Rate are you Getting? Rate_Ex2

64 Net Present Value The Present Value of future cash flows less the cost of the investment. An NPV greater than zero is a good investment.

65 Net Present Value You are investing $3,000 today and will receive the following amounts at the end of each year for the following 5 years: $500, $600, $700, $900, and $850. The going interest rate of investments of similar risk is 6%. Should you make the investment? Cost: $3,000 $500 $600 $700 $900 $850 Y1 Y2 Y3 Y4 Y5

66 Net Present Value 6 % Interest Rate Cost: -$3,000 $500 $600 $700 $900 $850 Y1 Y2 Y3 Y4 Y5 $ $ $ $ $ Cost: -$3,000 $ NVP =

67 NPV(DiscountRate,Values) This is the rate you feel the market would return on a similar investment. This is a range containing the cash inflows and if the initial investment is in the future, it should also contain the initial investment.

68 Rules for NPR() Cash flows must be in the order they occur and periods must be of equal increments.

69 Rules for NPR() The initial investment is negative and only included if it is made in the future.

70 Rules for NPR() Gains on the investment are entered as positive. Losses are entered as Negative.

71 Rules for NPR() Unlike an annuity, the cash flows may vary in amount.

72 NPV() Example 1 Investment Made Today You are considering an investment opportunity that will cost you $3,000 and pay the following amounts at the end of each year for the following 5 years: $500, $600, $700, $900, and $850. The going interest rate of investments of similar risk is 6%. Should you make the investment? NPV()

73 NPV() Example 2 Investment In One Year You are considering an investment opportunity that will cost you $3,000 a year from now and pay the following amounts at the end of each year for the following 5 years: $500, $600, $700, $900, and $850. The going interest rate of investments of similar risk is 6%. Should you make the investment? NPV()

74 Internal Rate of Return It is the interest rate received for an investment consisting of returns at regular intervals. When comparing multiple investments, the higher the rate the better and negative rates are always bad.

75 Technically, IRR is the rate which sets the sum of the present value of these cash flows to zero. Rate: 6 % Cost: -$3,000 $500 $600 $700 $900 $850 Y1 Y2 Y3 Y4 Y5 $ $ $ $ $ Cost: -$3,000 $ NVP =

76 Technically, IRR is the rate which sets the sum of the present value of these cash flows to zero. Rate:???? Cost: -$3,000 $500 $600 $700 $900 $850 Y1 Y2 Y3 Y4 Y5 $ $ $ $ $ Cost: -$3,000 $3,000 NVP = 0

77 IRR(Values,Guess) This is a range containing your initial investment and all future cash inflows resulting from that investment. (Optional) This gives Excel a place to start looking for the rate. If you don t guess Excel will guess for you at 10%. What you guess does not affect the answer returned but you may get an error if the actual rate varies greatly from the guess.

78 Rules for IRR() Cash flows must be in the order they occur and periods must be of equal increments.

79 Rules for IRR() Returns must all be positive. IRR() cannot handle negative years.

80 Rules for IRR() Unlike an annuity, the cash flows may vary in amount.

81 IRR Example You are investing 3K and will receive the following payment at the end of each year: 500, 600, 700, 900, & 850. IRR()

82 Modified Internal Rate of Return Similar to IRR() except: Negative cash flows are allowable.

83 Modified Internal Rate of Return Similar to IRR() except: Reinvested at 4% Borrowed at 3% Investment Rate can differ from Reinvestment Rate

84 MIRR(Values,FinanceRate,ReinventRate) Range of all cash flows including investment and returns. Rate any negative future cash flows are borrowed at. Rate all positive cash inflows are reinvested at.

85 MIRR Example You are investing 200K to purchase an oil well and will receive the profits shown below. In the final year, you will incur a cost of $30K for hazardous waste clean up. Profits are reinvented at 5% and the 30K is financed at 6%. MIRR()

86 Bonds Loans you make to Companies and Governments

87 How Bonds Work You purchased a bond for $ It is a 3 year bond with a Face Value of $1,000 and a Coupon Rate of 6%. At the end of each year you will receive a $60 Coupon Payment (Face Value x Coupon Rate) and on its Maturity Date at the end of 3 years you will receive the face value of $1,000. Y 1 Y2 Y3 - $ $1,000 Purchase Price $60 $60 $60 Face Value Coupon Payments Coupon Rate x Face Value 6% x 1000 = $60

88 Bond Evaluation: Purchased on Issue Date Use: PV(), NVP(), IRR(), or Rate() Purchase Date Y 1 Y2 Y3 - $ $1,000 Purchase Price $60 $60 $60 Face Value

89 Bond Evaluation - Purchased After Issue Date Use: Yield() When Bonds are purchased after the Issue Date, you must pay the owner any interest which would have accrued since the last payment date (or issue date if the first payment date hasn t occurred) as well as the Bond s purchase price. Interest is not typically quoted in the purchase price. Purchase Date Y 1 Y2 Y3 - $ $1,000 Purchase Price $60 $60 $60 Face Value

90 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) Settlement Date This is the date you purchased the bond.

91 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) Maturity Date This is the date the bond is due.

92 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) Coupon Rate This is the annual interest rate written on the bond.

93 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) PR The Market Price as a non-decimal percent of Face Value entered as a positive value. For example, a bond costing $ with a face value of $1,000 would be written as: /1000 = % *100 =

94 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) Redemption The Face Value as a non-decimal percent of Face Value. For example, a bond with a face value of $1,000 would be written as: 100 $1,000/$1,000 = 1.00% 1.00% * 100 = 100

95 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) Frequency The number of coupon payments per year. For example, you would type a 2 for a bond which pays semi-annually.

96 Yield(Settlement, Date Maturity, Date Coupon, Rate PR, Redemption, Frequency, Basis) Basis Method used to calculate the number of days between coupons dates. 0 = (or omitted): US (NASD) 30/360 1 = Actual/actual 2 = Actual/360 3 = Actual/365 4 = European 30/360

97 Example: Bond YTM using Yield() Bond Not Purchased on Coupon Date On March 3, 2009 you purchased a bond with a face value of $1,000 and a coupon rate of 8% paid semi-annually. The bond s last coupon date was on 12/15/2008 and the price quoted to you not including accrued interest was $ The bond matures on 12/15/2019. What is the Yield to Maturity? Bonds_YTM_Yield()

98 Bond Price What is the maximum price you will pay based on your required rate of return?

99 Clean vs. Dirty Price Price() Returns the clean price as a percent of face value. ( Clean price doesn t include accrued interest.) Accrint() This function returns accrued interest for bonds sold between coupon dates. Dirty Price (Price with accrued interest)

100 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Settlement Date This is the date you purchased the bond.

101 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Maturity Date This is the date the bond is due.

102 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Coupon Rate This is the annual interest rate written on the bond.

103 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Rate Required This is the minimum desired rate of return you are willing to accept.

104 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Redemption The Face Value as a non-decimal percent of Face Value. For example, a bond with a face value of $1,000 would be written as: 100 $1,000/$1,000 = 1.00% 1.00% * 100 = 100

105 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Frequency The number of coupon payments per year. For example, a bond which pays semi-annually you would type a 2.

106 Price( Settlement, Date Maturity, Date Coupon, Rate, Redemption, Frequency, Basis) Rate Required Basis Method used to calculate the number of days between coupons dates. 0 = (or omitted): US (NASD) 30/360 1 = Actual/actual 2 = Actual/360 3 = Actual/365 4 = European 30/360

107 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) Issue Date Date the bond was issued.

108 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) First Interest Date Date of the first interest payment.

109 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) Settlement Date The date you purchased the bond.

110 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) Par (Face value) This is the bond s face value (par). If you omit it, Excel uses 1,000.

111 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) Frequency The number of coupon payments per year.

112 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) Basis Method used to calculate the number of days between coupon dates. 0 = (or omitted): US (NASD) 30/360 1 = Actual/actual 2 = Actual/360 3 = Actual/365 4 = European 30/360

113 Accrint( Issue Date First Settlement Face Freq Basis,,,,,, Interest date Value Date Calc Method ) Calc Method (Optional) Used when the settlement date is after the first coupon payment. Type 1 Returns interest from Issue Date to Settlement Date. Type 0 Returns interest from 1 st Payment to Settlement Date. Type 1 Accrued Interest Issue Date 1st Interest Payment Type 0 Accrued Interest Settlement (Purchase) Date

114 Example: Bond Pricing Model Create a model which returns the maximum price we are willing to pay based on our minimum required return. Bonds_Price()

115 Bond Practice Exercises PV, Rate, NPV, & IRR

116 Example: Bond Evaluation PV() Our bond is a 3 year bond with a 6% coupon rate paid annually, and a $1,000 face value which we purchased for $ The market is currently paying about 5% for investments of equal risk. What is the Present Value of your cash inflows?

117 Example: Bond Evaluation Rate() You have purchased a bond with a face value of $1,000 and coupon rate of 6% at a discount of It is a 3 year bond and pays semi- annually. What is the Yield to Maturity?

118 Example: Bond Evaluation NPV() Our bond is a 3 year bond with a 6% coupon rate paid annually, and a $1,000 face value which we purchased for $ The market is currently paying about 5% for investments of equal risk. What is the Present Value of your cash inflows?

119 Example: Bond Evaluation IRR() You have purchased a bond with a face value of $1,000 and coupon rate of 6% at a discount of It is a 3 year bond and pays semi- annually. What is the Yield to Maturity?

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