COMM 203 - F18 - C08 - Disc CF Val.pptx

# Expression by plugging in the numbers we have the sum

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expression By plugging in the numbers, we have The sum above converges as follows Annuity PV Factor (growing perpetuity) Considerations 1. C is the cash flow one period ahead 2. One condition must be met: g<r 3. C occurs at regular, discrete points of time Little Manitou Lake Hotels Inc. (LMLHI) Interest Rate: 6.50% per year Dividend Payment Amount: \$2.50 (today) Growth: 5.25% per year C 2.50 (1 0.0525) C \$2.63 . . 2.63 PV 0.0650 0.0525 fut div C r g . . 2.63 PV 0.0125 fut div . . PV \$210.40 fut div . . Stock Price 2.50 PV fut div Stock Price 2.50 210.40 \$212.90 1 . . 2 2.63 2.63 (1 0.0525) 2.63 (1 0.0525) PV ... 1 0.0650 (1 0.0650) (1 0.0650) n fut div n 1 . . 2 (1 ) (1 ) PV ... 1 (1 ) (1 ) n fut div n C C g C g r r r

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Little Manitou Lake Hotels Inc. (LMLHI) Interest Rate: 6.50% per year Dividend Payment Amount: \$2.50 (today) Growth: 5.25% per year Specific Type of Annuity Growing Annuity Now, let us assume that dividend payments are no longer perpetual. In this case, we can rewrite our formula as follows By plugging in the number, we have The sum above converges as follows Dividends will be paid for 30 years only! In fact, we have here the case of growing annuity , since we have a finite number of growing annual cash flows. This specific type of annuity occurs in a wide variety of financial transactions every single day. Yet, this is not the case of a stock price… Annuity PV Factor (growing annuity) Why? 30 . . 2.63 1 0.0525 PV 1 0.0650 0.0525 1 0.0650 fut div . . 1 PV 1 1 t fut div C g r g r . . PV 210.40 0.2983 fut div . . PV \$62.76 fut div . . Stock Price 2.50 PV fut div 29 . . 2 30 2.63 2.63 (1 0.0525) 2.63 (1 0.0525) PV ... 1 0.0650 (1 0.0650) (1 0.0650) fut div 1 . . 2 (1 ) (1 ) PV ... , 1 (1 ) (1 ) n fut div n C C g C g r r r where n   Stock Price 2.50 62.76 \$65.26
Effective Annual Rate Equation Comparing Rates Compounding and Effective Annual Rates Prince Albert Farming Co. (PAFC) Loan Amount: \$1,000 (payable in one year) Venues and interest rates Bank A: 9.72% compounded daily Bank B: 8.73% compounded monthly Bank C: 7.71% compounded quarterly Bank D: 6.61% compounded semi-annually In the first stage, we intend to find out where executives of PAFC should borrow \$1,000 payable in one year. In fact, there are four banks, but the information is quite misleading. To solve this issue, we have to standardize all the information into the same language. In fact, we will use the effective annual rate (EAR) , which is the interest rate stated as if it were compounded once a year. In other words,

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