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

# Saskatoon ballpark construction interest rate 5 per

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Saskatoon Ballpark Construction Interest Rate: 5% per month Proposed Expenditure Schedule: \$10,000,000 (end of Months 1 to 9) \$25,000,000 (end of Month 12) \$20,000,000 (end of Months 13 to 21) \$30,000,000 (end of Month 24) In this case, we intend to compute the future value of the construction of the Saskatoon Ballpark. Notice that we have a varying pattern of cash flows that will require us to act carefully. In principle, we could use the following While we could use both formulas, it becomes tricky to work with those in the context of complex annuities. As a result, we will bring everything to the present, then send everything to the future For months 1 to 9, we have It would be nice to have MLB games here! Annuity FV Factor Basic PV Equation Annuity PV Factor For months 12 and 24, we have For months 12 to 21, we have to adjust the value. As a result, we have 9 1 9 1 1 (1 0.05) PV 10,000,000 0.05 to 1 9 PV 10,000,000 7.1078 to 1 9 PV \$71,078,216.76 to (1 ) 1 FV PV (1 ) , and FV t t r r C r 1 1 FV (1 ) PV , and PV (1 ) t t t r C r r 12 24 12 24 25,000,000 30,000,000 PV (1 0.05) (1 0.05) and 12 24 PV 13,920,935.45 9,302,037.31 and 12 24 PV \$23,222,972.76 and

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Complex Annuities End of Period: Future Value Saskatoon Ballpark Construction Interest Rate: 5% per month Proposed Expenditure Schedule: \$10,000,000 (end of Months 1 to 9) \$25,000,000 (end of Month 12) \$20,000,000 (end of Months 13 to 21) \$30,000,000 (end of Month 24) It would be nice to have MLB games here! Now we can finally add up the present value of all expenditures. We have With the net present value in hand, we can send it the future. As a result, we have How about equally distributed expenditures? Annuity FV Factor Why are the numbers so high? How could one reduce costs? 21 12 13 21 1 1 1 1 (1 0.05) (1 0.05) PV 20,000,000 0.05 0.05 to 13 21 1 21 1 12 PV PV PV to to to 13 21 PV 20,000,000 (12.8212 8.8633) to 13 21 PV \$79,158,021.42 to 1 9 12 24 13 21 PV PV PV PV ballpark to and to PV 71,078,216.76 23,222,972.76 79,158,021.42 ballpark PV \$173,459,210.94 ballpark Future Value (FV ) Present Value (PV) (1 ) t t t r 24 FV PV (1 ) ballpark ballpark r 24 FV 173,459,210.94 (1 0.05) ballpark FV 173,459,210.94 3.2251 ballpark FV \$559,423,291.42 ballpark (1 ) 1 FV PV (1 ) , and FV t t r r C r 24 (1 0.05) 1 FV 559,423,291.42 0.05 ballpark C 559,423,291.42 \$12,570,745.26 44.5020 C
Specific Type of Annuity Growing Perpetuity In this case, we intend to compute today’s stock price of LMLHI. To do so, we assume that LMLHI will remain on the market forever. Because the cash flow (i.e., dividend payment) is growing at a constant rate, we have the case of growing perpetuity . We have We can bring all future dividends to the present by using the following general

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