lecture_chap05_06A

60 n 10000 pv 20758 pmt cpt iy 75 annuity finding

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Unformatted text preview: ula: • PV = 50000[1 – 1 / 1.07525] / .075 = 557,347 Finding the Payment • Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year. If you take a 4 year loan, what is your annual payment? • Formula Approach • 20,000 = C[1 – 1 / 1.084] / .08 • C = 6038.42 • Calculator Approach • 4 = N; 20,000 PV; 8 I/Y; CPT PMT = 6038.42 Finding the Number of Payments – Example 1 • Suppose you borrow $2000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan? Finding the Number of Payments – Example 1 continued • Formula Approach • • • • • 2000 = 734.42(1 – 1/1.05t) / .05 .136161869 = 1 – 1/1.05t 1/1.05t = .863838131 1.157624287 = 1.05t t = ln(1.157624287) / ln(1.05) = 3 years • Calculator Approach • • • • • Sign convention matters!!! 5 I/Y 2000 PV -734.42 PMT CPT N = 3 years Finding the Rate On the Financial Calculator • Suppose you borrow $10,000 to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? • Calculator Approach • • • • • Sign convention matters!!! 60 N 10,000 PV -207.58 PMT CPT I/Y = .75% Annuity – Finding the Rate Without a Financial Calculator • Trial and Error Process • Choose an interest rate and compute the PV of the payments based on this rate • Compare the computed PV with the actual loan amount • If the computed PV > loan amount, then the interest rate is too low • If the computed PV < loan amount, then the interest rate is too high • Adjust the rate and repeat the process until the computed PV and the loan amount are equal Future Values for Annuities – Example 1 • Suppose you begin saving for your retirement by depositing $2000 per year in an RRSP. If the interest rate is 7.5%, how much will you have in 40 years? • Formula Approach • FV = 2000(1.07540 – 1)/.075 = 454,513.04 • Calculator Approach • • • • • Remember the sign convention!!! 40 N 7.5 I/Y -2000 PMT CPT FV = 454,513.04 Annuity Due – Example 1 • You are saving for a new house and you put $10,000 per year in an account paying 8% compounded annually. The first payment is made today. How much will you have at the end of 3 years? Annuity Due – Example 1 Timeline 0 10000 1 10000 2 3 10000 32,464 35,061.12 Annuity Due – Example 1 continued • Formula Approach • FV = 10,000[(1.083 – 1) / .08](1.08) = 35,061.12 • Calculator Approach • • • • • • Reset calculator to BEGIN mode (2nd BGN 2nd Set) 3N -10,000 PMT 8 I/Y CPT FV = 35,061.12 2nd BGN 2nd Set (be sure to change it back to an ordinary annuity) Perpetuity – Example 1 • The Home Bank of Canada want to sell preferred stock at $100 per share. A very similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every year. What dividend would the Home Bank have to offer if its preferred stock is going to sell? Perpetuity – Example 1 continued • Perpetuity formula: PV = C / r • First, find the required return for the comparable issue: • 40 = 1 / r • r = .025 • Then, using the required return found above, find the dividend for new preferred issue: • 100 = C / .025 • C = 2.50 Growing Perpetuity • The perpetuities discussed so far are annuities with constant payments • Growing perpetuities have cash flows that grow at a constant rate and continue forever • Growing perpetuity formula, where C1 is the payment at time 1: C1 PV = r −g Growing Perpetuity – Example 1 • Holmes Corporation is expected to pay a dividend of $3 per share next year. Investors anticipate that the annual dividend will rise by 6% per year forever. The required rate of return is 11%. What is the price of the stock today? PV = $3.00 = $60.00 0.11 − 0.06 Growing Annuity • Growing annuities have a finite number of growing cash flows • Growing annuity formula: 1 + g T C1 PV = 1 − r − g 1+ r Growing Annuity – Example 1 • Greg Annuitson has just been offered a job at $50,000 a year. He anticipates his salary will increase by 5% a year until his retirement in 40 years. Given an interest rate of 8%, what is the present value of his lifetime salary? 40 $50,000 1.05 PV = = $1,126,571 1 − 0.08 − 0.05 1.08...
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