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Lecture9

# Lecture9 - Eco 635.02 Prof Zhylenko Lecture 9 Discounted...

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Lecture 9: Discounted Cash Valuation – III 1 Eco 635.02 Prof. Zhylenko

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Finding the Number of Payments Suppose you borrow \$2,000 at 5%, and you are going to make annual payments of \$734.42. How long before you pay off the loan? 2,000 = 734.42(1 – 1/1.05 t ) / .05 2,000*.05.136161869 = 1 – 1/1.05 t 1/1.05 t = .863838131 1.157624287 = 1.05 t t = ln(1.157624287) / ln(1.05) = 3 years Eco 635.02 Prof. Zhylenko 2
3 Why might credit card issuers want low required minimum payment amounts? Suppose Joe Borrower has a \$5,000 balance on his Mastercard, which carries a 10.5% stated rate. How long will it take to pay off the card (assuming no additional borrowing) if Joe makes a minimum monthly payment of \$80? How will the result change if Joe increases the payment to \$200? Credit Card Repayment Eco 635.02 Prof. Zhylenko

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Finding the Rate 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 Eco 635.02 Prof. Zhylenko 4
Future Values for Annuities Suppose you plan to contribute \$2,000 every year to a retirement account paying 7.5%. If you retire in 40 years, how much will you have? FV = 20,000[(1.075 40 – 1) / .0075]=454,513 Eco 635.02 Prof. Zhylenko 5 - + = r r C FV t 1 ) 1 (

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6 Same rule for both PV and FV: Annuity due value = Ordinary annuity value · (1+r) Example: You are saving for a new house, and you put \$10,000 per year in an account paying 8%. The first payment is made today. How much will you have at the end of 3 years? FV = 10,000[(1.08 3 – 1) / .08](1.08) = 35,061.12 Annuity Due Eco 635.02 Prof. Zhylenko
7 You want to have \$1 million to use for retirement in 35 years. You can earn 1% per month. How much do you need to deposit on a monthly basis if the first payment is made in one month? What if the first payment is made today? Ordinary Annuity vs. Annuity Due Eco 635.02 Prof. Zhylenko

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8 Suppose the Fellini Co. wants to sell preferred stock at \$100 per share. A similar issue of preferred stock already outstanding has a price of \$40 per share and offers a dividend of \$1 every quarter. What dividend will Fellini have to offer if the preferred stock is going to sell? Perpetuity – Example 6.7 Eco 635.02 Prof. Zhylenko Perpetuity formula: PV = C / r Current required return: 40 = 1 / r r = .025 or 2.5% per quarter Dividend for new preferred: 100 = C / .025 C = 2.50 per quarter
You are considering preferred stock that pays a quarterly dividend of \$1.50. If your desired return is 3% per quarter, how much would you be willing to pay? Perpetuity – Example

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Lecture9 - Eco 635.02 Prof Zhylenko Lecture 9 Discounted...

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