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**Unformatted text preview: **Financial management: lecture 4 Bond valuation The application of the present value concept Financial management: lecture 4 Today’s plan Review of what we have learned in the last lecture Interest rates and compounding Some terminology about bonds Value bonds The yield curve Default risk Financial management: lecture 4 What have we learned in the last lecture? The present value formulas of perpetuity and annuity The application of the PV of annuity Financial management: lecture 4 My solution year Beginning balance Interest payment Principle payment Total payment Ending balance 1 2 3 $20,000 13,809 7,154 $1,500 $6,191 $7,691 $13,809 1,036 6,655 537 7,154 7,691 7,691 7,154 Financial management: Lecture 4 Future value The formula for converting the present value to future value: = present value at time zero = future value in year i = discount rate during the i years i i t t i t r PV FV ) 1 ( = = = + × = = t PV i t r = i t FV = i t C = Financial management: Lecture 4 Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in 1629. Was this a good deal? Suppose the interest rate is 8%. Financial management: Lecture 4 Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in 1629. Was this a good deal? trillion FV 979 . 75 $ ) 08 . 1 ( 24 $ 374 = + × = To answer, determine $24 is worth in the year 2003, compounded at 8%. FYI - The value of Manhattan Island land is FYI - The value of Manhattan Island land is well below this figure. well below this figure. Financial management: lecture 4 Nominal and real interest rates Nominal interest rate • What is it? Real interest rate • What is it? Inflation • What is it? Their relationship • 1+real rate =(1+nominal rate)/(1+inflation) Financial management: lecture 4 Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows. Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures Inflation rule Financial management: lecture 4 Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease? 1 + real interest rate = 1+nominal interest rate 1+inflation rate Financial management: lecture 4 Inflation Example - nominal figures 99 . 429 , 26 $ 78 . 5970 8741.82 = 8000x1.03 4 56 . 6376 8487.20 = 8000x1.03 3 92 . 6809 8240 = 8000x1.03 2 73 . 7272 8000 1 10% @ PV Flow Cash Year 4 3 2 10 . 1 82 . 8741 3 10 . 1 20 . 8487 2 10 . 1 8240 1.10 8000 = = = = Financial management: lecture 4 Inflation Example - real figures Year Cash Flow [email protected]% 1 = 7766.99 2 = 7766.99 = 7766.99 = 7766.99 8000 1.03 7766.99 1.068 8240 1.03 8487.20 1.03 8741.82 1.03 2 3 4 = = = = 7272 73 6809 92 3 637656 4 5970 78 26 429 99 7766 99 1 068 7766 99 1 068 7766 99 1 068 2 3 4 ....

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