Economic Principles in Agribusiness: Time Value of Money



-----------------------------------------Notes------------------------------------------------------------------------------------------Summary of Main Ideas---------------------------------------------------------------------------------------------------------Main Ideas, Key Points, Formulas------------------------------------------------------------Date _______________Topic___________________________________Time value of moneyInterestSix Functions of the DollarFuture value of a dollarRule of 72Future value of a dollar per periodAnnuity Date _______________Topic__________________________________-----------------------------------------Notes------------------------------------------------------------------------------------------Summary of Main Ideas---------------------------------------------------------------------------------------------------------Main Ideas, Key Points, Formulas------------------------------------------------------------Sinking fund factorPresent value of the dollarPresent value of a dollar per periodAmortization Calculating the Six Functions of a DollarFuture Value of a DollarIf land is currently priced at $8000 per acre, what will the value of land be in five years with an 8% annual inflation rate? Assume that no other factor is affecting the value of land.If you invested $100 in a savings account at 7% interest, how much money would you have in 40 years?Rule of 72How many years are required for $50 to double if it is earning 4% interest?How many years will it require for $1,000 to double if earning 16% interest?Future Value of an AnnuityFind the future value of a $5 annuity at 10% for five years.Find the future value of a $7 annuity at 8% for three years.Sinking Fund FactorsJoyce would like to buy a car following her college graduation after 4 more years of school. She estimates the car will cost $ 10,000 when she graduates. If her savings account pays a 5% annual rate of interest, compounded monthly, how much does she need to deposit monthly to have $10,000 when she graduates in 4 years? Present Value of the DollarA gentleman is investing in a savings bond. If the bond would be worth $50 when it matures at the end of five years at 5%, what would it be worth today?A timber buyer has offered to buy the timber in your woodlot for $13,000. After checking with the farm forester, you find that the forester estimates that this stand would be worth $20,000 ten years from now. If interest is 8%, should you sell now or wait 10 years? Assume there are practically no costs associated with waiting 10 years.Present Value of an AnnuityJill’s parents will receive $10,000 per year in annual installments from an annuity for the next 20 years. If the fund provides a minimum annual return of 7% on the investments, what is the present value of the annuity based on the minimum return? Amortization Jennifer plans to buy her first car and will need to borrow $5000. If she can get a 5 year, equal amortized monthly payment loan with a 6% fixed interest rate, what will her monthly payments be? Calculating the Six Functions of a DollarFuture Value of a DollarIf land is currently priced at $8000 per acre, what will the value of land be in five years with an 8% annual inflation rate? Assume that no other factor is affecting the value of land.FV=PV x (1+i)ntFV=8000 x (1+.08)5 = $11,755If you invested $100 in a savings account at 7% interest, how much money would you have in 40 years?FV=100 x (1+.07)40 = $1,497.40Rule of 72How many years are required for $50 to double if it is earning 4% interest?72/4 = 18 yearsHow many years will it require for $1,000 to double if earning 16% interest?72/16 = 4.5 yearsFuture Value of an AnnuityFind the future value of a $5 annuity at 10% for five years.Yr. 1 = $5 Yr. 2 = $5 + (5 x .10 = .5) + $5 = $10.50 Yr. 3 = $10.50 + (10.50 x .10) + $5 = $16.55 Yr. 4 = $16.55 + (16.55 x .10) + $5 = $23.21Yr. 5 = $23.21 + (23.21 x .10) + $5 = $30.53Find the future value of a $7 annuity at 8% for three years.Yr. 1 = $7Yr. 2 = $7 + (7 x .08) + $7 = $14.56Yr. 3 = $14.56 + (14.56 x .08) + 7 = $22.72Sinking Fund FactorsJoyce would like to buy a car following her college graduation after 4 more years of school. She estimates the car will cost $10,000 when she graduates. If her savings account pays a 5% annual rate of interest, compounded monthly, how much does she need to deposit monthly to have $10,000 when she graduates in 4 years? PMT = FV * in 1 + innt-1 PMT = 10,000 * .0512 1 + .051212(4)-1PMT = 10,000 x .0041666671.00416666748-1PMT = 41.66667 .22089534 PMT =$188.63Present Value of the DollarA gentleman is investing in a savings bond. If the bond would be worth $50 when it matures at the end of five years at 5%, what would it be worth today?PV= FV x 11+intPV= 50 x 1(1+.05)5 = $39.17A timber buyer has offered to buy the timber in your woodlot for $13,000. After checking with the farm forester, you find that the forester estimates that this stand would be worth $20,000 ten years from now. If interest is 8%, should you sell now or wait 10 years? Assume there are practically no costs associated with waiting 10 years.PV= FV x 11+intPV= 20,000 x 11+.0810 = $9263.87Because the $20,000 has a present value of only $9264, the farmer would probably want to sell the trees for $13,000.Present Value of an AnnuityJill’s parents will receive $10,000 per year in annual installments from an annuity for the next 20 years. If the fund provides a minimum annual return of 7% on the investments, what is the present value of the annuity based on the minimum return? PV = PMT1 + innt-11 + innt* in PV = 10,0001 + .0711(20)-11 + .0711(20)* .071 PV = 10,0001.0720-11.0720* .07 PV =10,0002.869684460.270877912 PV =28696.8446.270877912 PV =$105,940.14Amortization Jennifer plans to buy her first car and will need to borrow $5000. If she can get a 5 year, equal amortized monthly payment loan with a 6% fixed interest rate, what will her monthly payments be? PMT = PV in 1- 1 + in- nt PMT =5,000 .0612 1- 1 + .0612- (12)(5) PMT = 5,000 .005 1- 1.005- 60PMT = 25.0 1-0.7413272196 PMT = 25 0.258672804 PMT =$96.66Six Functions of a Dollar FormulasFuture Value of $ 1:FV = PV1 + intFuture Value of $ 1 Per Period:FV = PMT1 + innt-1in Sinking Funds Factor:PMT = FV * in 1 + innt-1Present Value of $ 1:PV= FV 1 + inntPresent Value of $ 1 Per Period:PV = PMT1 + innt-11 + innt* in Amortization (Partial Payment): PMT = PV in 1- 1 + in- ntAmortization PracticeJosh would like to purchase a pickup truck that will cost $20,000. He plans to put $3000 cash down and finance the balance on a 4 year, equal amortized annual installment note at 6% interest. What will his annual payments be? P = $ 17,000 loan ($ 20,000 - $ 3000 = PV)i = 6%, or .06 (interest)n = 1 (annual)t = 4 years PMT = $ ? Annual paymentJohn and Sue are looking to buy their dream home. They have the 20% down payment but need to borrow $200,000. If they can get a 30 year, equal amortized monthly pay loan with a 5.5% fixed interest rate, what will their monthly payments be? P = $ 200,000 loan (PV)i = 5.5%, or .055 (interest) n = 12 (monthly)t = 30 years PMT = $ ? Monthly paymentEthan purchased a new big screen TV at a cost of $3000. He financed the purchase on his credit card. The credit card terms require 48 monthly payments at an interest rate of 18%. Solve the following: a) What is Ethan’s monthly payment; and b) What is the total cost of the TV with finance charges? Solve for monthly payment:P = $ 3,000 loan (amount financed)i = 18%, or .18 (interest) n = 12 (monthly)t = 4 years (48 months)PMT = $ ? Monthly paymentSolve for total cost of TV:Total cost of TV and finance charges = $ XYZ Corporation is trading equipment that has a net trade difference of $150,000. The finance company is offering 7 year terms with equal amortized, semi-annual payments and a 5.25% fixed interest rate. If they finance the $150,000 net trade difference, what will the semi-annual payments be? P = $ 150,000 loan (PV)i = 5.25%, or .0525 (interest) n = 2 (semi-annual)t = 7 years PMT = ? Semi-annual paymentAmortization PracticeJosh would like to purchase a pickup truck that will cost $20,000. He plans to put $3000 cash down and finance the balance on a 4 year, equal amortized annual installment note at 6% interest. What will his annual payments be? P = $ 17,000 loan ($ 20,000 - $ 3000 = PV)i = 6%, or .06 (interest)n = 1 (annual)t = 4 years PMT = $ ? Annual paymentPMT = PV in 1- 1 + in- nt PMT = 17,000 .061 1- 1 + .061- (1)(4) PMT = 17,000 (0.06) 1-(1.06- 4PMT =1020 1-0.792093663 PMT =1020 0.207906337 PMT =$4,906.06John and Sue are looking to buy their dream home. They have the 20% down payment but need to borrow $200,000. If they can get a 30 year, equal amortized monthly pay loan with a 5.5% fixed interest rate, what will their monthly payments be? P = $ 200,000 loan (PV)i = 5.5%, or .055 (interest) n = 12 (monthly)t = 30 years PMT = $ ? Monthly paymentPMT = 200,000 .05512 1- 1 + .05512- 1230 PMT =200,000 0.0045833331- 1.004583333- 360 PMT = 916.66 1-0.192775275 PMT = 916.666 0.807224725 PMT =$1,135.58Ethan purchased a new big screen TV at a cost of $3000. He financed the purchase on his credit card. The credit card terms require 48 monthly payments at an interest rate of 18%. Solve the following: a) What is Ethan’s monthly payment; and b) What is the total cost of the TV with finance charges? Solve for monthly payment:P = $ 3,000 loan (amount financed)i = 18%, or .18 (interest) n = 12 (monthly)t = 4 years (48 months)PMT = $ ? Monthly paymentPMT = 3,000 .1812 1- 1 + .1812-124 PMT = 3,000 0.0151- 1.015- 48 PMT = 45 1-0.48936169PMT =$88.13Solve for total cost of TV:Total cost of TV and finance charges = $ 88.13 x 48 = $4230.24XYZ Corporation is trading equipment that has a net trade difference of $150,000. The finance company is offering 7 year terms with equal amortized, semi-annual payments and a 5.25% fixed interest rate. If they finance the $150,000 net trade difference, what will the semi-annual payments be? P = $ 150,000 loan (PV)i = 5.25%, or .0525 (interest) n = 2 (semi-annual)t = 7 years PMT = ? Semi-annual paymentPMT = 150,000 .05252 1- 1 + .05252-27 PMT = 3,000 (0.02625)1- 1.02625-14 PMT = 3.937.5 1-0.69575385PMT = 3937.5 0.30424615 PMT =$12,941.82Future Value of a Dollar Per Period PracticeLinda decides she would like to save $100 per month from her job to use towards buying a used car when she graduates in 4 years. If she deposits $100 per month into her savings account that pays 6% interest, compounded monthly, how much will she have at the end of 4 years? Pmt = $ 100 paymenti = 6%, or .06 Interestn = 12 (monthly)t = 4 years FV = $ ? Future Value at end of 4 yearsJohn recently graduated from college and has secured a good job in a career of his choice. He decides to invest $600 per month in an investment that guarantees a 5.25% nominal rate of interest, compounded monthly, over 20 years. What is the future value of his account at the end of 20 years? Pmt = $ 600 payment i = 5.25%, or .0525 Interestn = 12 (monthly)t = 20 years FV = $ ? Future Value in 20 yearsSara’s parents started her college fund when she was 6 years old. They deposited $500 per month and plan to continue to deposit this amount until she graduates school just before her 19th birthday. If her parents continue to deposit the same payment into this fund for 12 years that pays a 6% annual rate of interest, compounded monthly, how much will Sara have in her college fund at the end of the 12 year investment period? Pmt = $ 500 paymenti = 6%, or .06 Interest n = 12 (monthly)t = 12 years FV = $ ? Future Value end of 12 yearsAn investor owns 200 acres of farmland. After all expenses are paid, the investor determines she can place $25,000 per year in an investment account that pays 7%, compounded annually. What is the expected future value of the investment account at the end of 10 years? Pmt = $ 25,000 payment i = 7%, or .07 Interestn = 1 (annual) t = 10 years FV = $ ? Future Value at end of 10 yearsFuture Value of a Dollar Per Period PracticeLinda decides she would like to save $100 per month from her job to use towards buying a used car when she graduates in 4 years. If she deposits $100 per month into her savings account that pays 6%, compounded monthly, how much will she have at the end of 4 years? Pmt = $ 100 paymenti = 6%, or .06 n = 12 (monthly)t = 4 years FV = $ ? Future Value at end of 4 yearsFV = PMT1 + innt-1in FV = 1001 + .0612124-1.0612 FV = 1001.00548-10.005 FV = 1000.270489160.005 FV = 10054.097832FV =$5,409.78John recently graduated from college and has secured a good job in a career of his choice. He decides to invest $600 per month in an investment that guarantees a 5.25% nominal rate, compounded monthly, over 20 years. What is the future value of his account at the end of 20 years? Pmt = $ 600 payment i = 5.25%, or .0525 n = 12 (monthly)t = 20 years FV = $ ? Future Value in 20 yearsFV = 6001 + .0525121220-1.052512 FV = 6001.004375240-10.004375 FV =6002.851114-10.004375 FV = 6001.8511140.004375FV = 600423.11177 FV =$253,867.06Sara’s parents started her college fund when she was 6 years old. They deposited $500 per month and plan to continue to deposit this amount until she graduates school just before her 19th birthday. If her parents continue to deposit the same payment into this fund for 12 years that pays a 6% annual rate, compounded monthly, how much will Sara have in her college fund at the end of the 12 year investment period? Pmt = $ 500 paymenti = 6%, or .06 n = 12 (monthly)t = 12 years FV = $ ? Future Value end of 12 yearsFV = 5001 + .06121212-1.0612 FV = 5001.005144-10.005 FV = 5002.0507508-10.005 FV = 5001.05075080.005 FV = 500210.150163FV =$105,075.08An investor owns 200 acres of farmland. After all expenses are paid, the investor determines she can place $25,000 per year in an investment account that pays 7%, compounded annually. What is the expected future value of the investment account at the end of 10 years? Pmt = $ 25,000 payment i = 7%, or .07 n = 1 (annual) t = 10 years FV = $ ? Future Value at end of 10 yearsFV = 25,0001 + .071110-1.071 FV = 25,0001 .0710-10.07 FV = 25,0001.967151357-10.07 FV = 25,0000.9671513570.07 FV = 25,00013.81644796 FV =$345,411.20Future Value of a Dollar PracticeJill receives a $5000 gift on her 16th birthday. She decides to invest it in a 5- year certificate of deposit that pays a 5% nominal interest rate, compounded semi-annually. What is the future value of this investment at its maturity?PV = $ 5000 Initial Investmenti = 5%, or .05 (interest)n = 2 (semi-annual)t = 5 years FV = $ ? Future Value at maturityA couple desires to purchase a house during a depressed market, believing it represents an opportunity to a take advantage of low interest rates and expected real estate appreciation. If the house costs $75,000 today and they anticipate a 6% annual appreciation rate, what is the expected future value of the house at the end of 10 years? PV = $ 75,000 Initial Investmenti = 6%, or .06 (appreciation rate)n = 1 (annual)t = 10 years FV = $ ? Future Value in 10 yearsKevin receives a $30,000 gift from his grandparents’ estate and decides to invest in a savings account for future retirement. If the account pays an annual rate of 4% interest, compounded monthly, what would the future value of this account be at the end of 30 years?PV = $ 30,000 Initial Depositi = 4%, or .04 (interest)n = 12 (monthly)t = 30 years FV = $ ? Future Value in 30 yearsNathan locates a 200-acre farm that has a value of $800,000 ($4000 per acre). What is the expected future value at the end of 5 years assuming a 7% annual rate of appreciation? PV = $ 800,000 Initial value i = 7%, or .07 (appreciation rate)n = 1 (annual)t = 5 years FV = $ ? Future Value in 5 yearsFuture Value of a Dollar PracticeJill receives a $5000 gift on her 16th birthday. She decides to invest it in a 5- year certificate of deposit that pays a 5% nominal interest rate, compounded semi-annually. What is the future value of this investment at its maturity?PV = $ 5000 Initial Investmenti = 5%, or .05 (interest)n = 2 (semi-annual)t = 5 years FV = $ ? Future Value at maturityFV = PV1 + innt FV = 5,0001 + .0522(5) FV = 5,0001.02510FV = 5,000 X 1.28008454 FV =$6,400.42A couple desires to purchase a house during a depressed market, believing it represents an opportunity to a take advantage of low interest rates and expected real estate appreciation. If the house costs $75,000 today and they anticipate a 6% annual appreciation rate, what is the expected future value of the house at the end of 10 years? PV = $ 75,000 Initial Investmenti = 6%, or .06 (appreciation rate)n = 1 (annual)t = 10 years FV = $ ? Future Value in 10 yearsFV = 75,0001 + .0611(10) FV = 75,000(1.0610 FV = 75,000 X 1.79084769FV =$134,313.58Kevin receives a $30,000 gift from his grandparents’ estate and decides to invest in a savings account for future retirement. If the account pays an annual rate of 4% interest, compounded monthly, what would the future value of this account be at the end of 30 years?PV = $ 30,000 Initial Depositi = 4%, or .04 (interest)n = 12 (monthly)t = 30 years FV = $ ? Future Value in 30 yearsFV = 30,0001 + .041212(30) FV = 30,0001.003333333360FV = 30,000 X 3.313498014 FV =$99,404.94Nathan locates a 200-acre farm that has a value of $800,000 ($4000 per acre). What is the expected future value at the end of 5 years assuming a 7% annual rate of appreciation? PV = $ 800,000 Initial value i = 7%, or .07 (appreciation rate)n = 1 (annual)t = 5 years FV = $ ? Future Value in 5 yearsFV = 800,0001 + .0711(5) FV = 800,0001.075 FV = 800,000 X 1.402551731FV =$1,122,041.39Present Value of a Dollar PracticeJill recently received a $50,000 gift from her grandmother’s estate. She would like to set aside a portion of this gift into two accounts. The first account needs a lump sum deposit in a sufficient amount to grow with compound interest to $15,000 when she graduates from college in 6 years to buy a car. The second account needs a deposit in a sufficient amount that will grow with interest to $40,000 for the same time period. She plans to use this account for a down payment on a house. If both investments are invested for 6 years that pay a 6% nominal rate of interest, compounded monthly, how much does she need to deposit into each account to accumulate the desired amount for each? Problem for Car:FV = $ 15,000 Value at maturityi = 6 %, or .06 raten = 12 (monthly)t = 6 years PV = $ ? Required depositProblem for down payment:FV = $ 40,000 Value at maturityi = 6%, or .06 interest raten = 12 (monthly)t = 6 years PV = $ ? Required depositYou have set a goal to remodel and replace the roof on your house in 5 years with expected costs to be $20,000 at that time. How much do you need to deposit today into an investment account that pays 5% nominal rate of interest, compounded monthly, to meet the $20,000 cost at the end of 5 years? Formula: FV = $20,000 Value at maturityi = 5 %, or .05 raten = 12 (monthly)t = 5 years PV = $ ? Required depositYour business will need $400,000 in 5 years to purchase a new piece of equipment. How much do you need to deposit today into an investment account if the interest rate pays a nominal rate of 5.75%, compounded semi-annually for 5 years, to have the $400,000 when needed? FV = $ 400,000 Future Value equip costi = 5.75 %, or .0575 raten = 2 (semi-annual)t = 5 years PV = $ ? Required depositPresent Value of a Dollar PracticeJill recently received a $50,000 gift from her grandmother’s estate. She would like to set aside a portion of this gift into two accounts. The first account needs a lump sum deposit in a sufficient amount to grow with compound interest to $15,000 when she graduates from college in 6 years to buy a car. The second account needs a deposit in a sufficient amount that will grow with interest to $40,000 for the same time period. She plans to use this account for a down payment on a house. If both investments are invested for 6 years that pay a 6% nominal rate of interest, compounded monthly, how much does she need to deposit into each account to accumulate the desired amount for each? Problem for Car:FV = $ 15,000 Value at maturityi = 6 %, or .06 raten = 12 (monthly)t = 6 years PV = $ ? Required depositPV= FV 1 + innt PV= 15,000 1 + .061212(6) PV= 15,000 1.00572 PV= 15,000 1.432044278PV=$10,474.54Problem for down payment:FV = $ 40,000 Value at maturityi = 6%, or .06 interest raten = 12 (monthly)t = 6 years PV = $ ? Required depositPV= 40,000 1 + .061212(6) PV= 40,000 1.00572 PV= 40,000 1.432044279 PV=$27,932.10You have set a goal to remodel and replace the roof on your house in 5 years with expected costs to be $20,000 at that time. How much do you need to deposit today into an investment account that pays 5% nominal rate of interest, compounded monthly, to meet the $20,000 cost at the end of 5 years? Formula: FV = $20,000 Value at maturityi = 5 %, or .05 raten = 12 (monthly)t = 5 years PV = $ ? Required depositPV= 20,000 1 + .051212(5) PV= 20,000 1.00416666760 PV= 20,000 1.283358678 PV=$15,584.11Your business will need $400,000 in 5 years to purchase a new piece of equipment. How much do you need to deposit today into an investment account if the interest rate pays a nominal rate of 5.75%, compounded semi-annually for 5 years, to have the $400,000 when needed? FV = $ 400,000 Future Value equip costi = 5.75 %, or .0575 raten = 2 (semi-annual)t = 5 years PV = $ ? Required depositPV= 400,000 1 + .057522(5) PV=400,000 1.0287510 PV=400,000 1.327695497 PV=$301,273.90Present Value of a Dollar Per Period PracticeA young couple buys their first house with owner financing. Their payments are $1000 per month for 15 years with a 5% fixed interest rate. The note holder would like to sell the note to an investor. What would be the discounted present value of the note receivable with 15 years of payments remaining? Solve for present value of the note. PMT = $ 1,000 per periodi = 5%, or .05 interest n = 12 (monthly)t = 15 years PV = $ ? Solve for Present Value If the monthly payments to maturity of the note total $180,000 ($1000 per mo. x 180 payments), what is the dollar amount of the discount if the note is sold to the investor? Total value of 180 Payments = $Less Present Value (answer from a.) - $_____________ Total amount of discount = $Jack is considering a purchase of rental investment property that generates $10,000 net cash flow after all expenses and taxes are paid. If this income is expected over the next 20 years and the desired annual rate of return is 8%, what is the present value today of this rental property based on the net after tax cash flow? PMT = $ 10,000 per periodi = 8%, or .08 interestn = 1 (annual)t = 20 years PV = $ ? Present Value of Rental propertyA land contract pays $50,000 per year with annual installments on March 1st for the next 10 years. If the expected annual rate of return is 6%, what is the present value of this contract? PMT = $ 50,000 per periodi = 6%, or .06 interestn = 1 (annual)t = 10 years PV = $ ? Present Value of 10 yr. contractAn investor considers an investment that has a guaranteed annual net cash flow after expenses of $12,500 per year for the next ten years. If the investor desires a 10% return per year on the investment, what would current value today be for the 10 year cash flow? Solve for today’s value of 10 year cash flow:PMT = $ 12,500 paymenti = 10%, or .10 interestn = 1 (annual)t = 10 years PV = $ Today’s current Value Solve for today’s value of the 10 year cash flow with a 5% rate of return:Use the same investment and same annual net cash flow with a current value with a 5% return:PMT = $ 12,500 paymenti = 5%, or .05% interestn = 1 (annual)t = 10 years PV = $ ? Today’s current valuePresent Value of a Dollar Per Period PracticeA young couple buys their first house with owner financing. Their payments are $1000 per month for 15 years with a 5% fixed interest rate. The note holder would like to sell the note to an investor. What would be the discounted present value of the note receivable with 15 years of payments remaining? Solve for present value of the note. PMT = $ 1,000 per periodi = 5%, or .05 interest n = 12 (monthly)t = 15 years PV = $ ? Solve for Present ValuePV = PMT1 + innt-11 + innt* in PV = 1,0001 + .051212(15)-11 + .051212(15)* .0512 PV =1,000 1.004166667180-11.004166667180* .004166667 PV = 1,0001.1137040592.113704059* .00416666 PV =1113.7040590.008807101 PV =$126,455.21 If the monthly payments to maturity of the note total $180,000 ($1000 per mo. x 180 payments), what is the dollar amount of the discount if the note is sold to the investor? Total value of 180 Payments = $ 180,000 = 1,000 x 180 payments Less Present Value (answer from a.) - $__126,455___________ Total amount of discount = $ 53,545Jack is considering a purchase of rental investment property that generates $10,000 net cash flow after all expenses and taxes are paid. If this income is expected over the next 20 years and the desired annual rate of return is 8%, what is the present value today of this rental property based on the net after tax cash flow? PMT = $ 10,000 per periodi = 8%, or .08 interestn = 1 (annual)t = 20 years PV = $ ? Present Value of Rental propertyPV = 10,0001 + .0811(20)-11 + .0811(20)* .081 PV = 10,0001.0820-11.0820* 0.08 PV = 10,0003.6609571444.6600957144* 0.08 PV =36609.571440.37287657 PV =$98,181.47A land contract pays $50,000 per year with annual installments on March 1st for the next 10 years. If the expected annual rate of return is 6%, what is the present value of this contract? PMT = $ 50,000 per periodi = 6%, or .06 interestn = 1 (annual)t = 10 years PV = $ ? Present Value of 10 yr. contractPV = 50,0001 + .0611(10)-11 + .0611(10)* .061 PV = 50,0001.0610-11.0610* 0.06 PV = 50,0000.7908476971.790847697*0.06 PV =39542.380.10745 PV =$368,008.26An investor considers an investment that has a guaranteed annual net cash flow after expenses of $12,500 per year for the next ten years. If the investor desires a 10% return per year on the investment, what would current value today be for the 10 year cash flow? Solve for today’s value of 10 year cash flow:PMT = $ 12,500 paymenti = 10%, or .10 interestn = 1 (annual)t = 10 years PV = $ Today’s current Value PV = 12,5001 + .1011(10)-11 + .1011(10)* .101 PV = 12,5001.1010-11.1010* 0.10 PV = 12,5001.593742460.259374246 PV =19921.780750.259374246 PV =$76,807.09Solve for today’s value of the 10 year cash flow with a 5% rate of return:Use the same investment and same annual net cash flow with a current value with a 5% return:PMT = $ 12,500 paymenti = 5%, or .05% interestn = 1 (annual)t = 10 years PV = $ ? Today’s current valuePPV = 12,5001 + .0511(10)-11 + .0511(10)* .051 PV = 12,5001.0510-11.0510* 0.05 PV = 12,5000.6288946270.081444731 PV =7861.180.081444731 PV =$96,521.65Sinking Funds Factor PracticeA young couple plans to buy a house at the end of 10 years and will need $20,000 for their cash down payment. If they can invest in a fund that pays an annual rate of 6% interest, compounded quarterly, how much do they need to invest quarterly to have $20,000 at the end of 10 years? FV = $ 20,000 Future Value 10 yearsi = 6%, or .06 interestn = 4 (quarterly)t = 10 years Pmt = $ ? Quarterly depositJill would like to expand her business in 5 years. She estimates the cost to be $75,000 at the time of expansion and plans to make quarterly deposits to an investment fund. If the fund pays a 7% annual return, compounded quarterly, how much does she need to invest quarterly to have $75,000 at the end of 5 years? FV = $ 75,000 Future Value in 5 yearsi = 7%, or .07 interestn = 4 (quarterly)t = 5 years Pmt = $ ? Quarterly depositA young couple has an opportunity to take over a neighbor’s farm operation in 7 years due to the neighbor’s planned retirement. They also plan to purchase his line of equipment that will have an estimated value of $200,000 at that time. How much will they need to deposit annually into an investment account if the account pays a 4% nominal rate of interest, compounded annually, to have the $200,000 needed at the end of 7 years? FV = $ 200,000 Value needed in 7 yearsi = 4%, or .04 interestn = 1 (annual)t = 7 years Pmt = $ ? Annual depositJack has a seed cleaning business in addition to his farming operation. He would like it to stand on its own and meet its ongoing equipment replacement needs. If equipment replacement costs $75,000 every 5 years, how much does he need to invest monthly into a money market account if it pays 5% interest, compounded monthly, to meet the $75,000 future capital purchase requirement? FV = $ 75,000 (Future Value Equip Cost)i = 5%, or .05 interestn = 12 (monthly)t = 5 years Pmt = $ ? Monthly depositSinking Funds Factor PracticeA young couple plans to buy a house at the end of 10 years and will need $20,000 for their cash down payment. If they can invest in a fund that pays an annual rate of 6% interest, compounded quarterly, how much do they need to invest quarterly to have $20,000 at the end of 10 years? FV = $ 20,000 Future Value 10 yearsi = 6%, or .06 interestn = 4 (quarterly)t = 10 years Pmt = $ ? Quarterly depositPMT = FV * in 1 + innt-1PMT = 20,000 * .064 1 + .064410-1PMT = 20,000 * 0.0151.01540-1PMT = 3000.8140184PMT =$368.54Jill would like to expand her business in 5 years. She estimates the cost to be $75,000 at the time of expansion and plans to make quarterly deposits to an investment fund. If the fund pays a 7% annual return, compounded quarterly, how much does she need to invest quarterly to have $75,000 at the end of 5 years? FV = $ 75,000 Future Value in 5 yearsi = 7%, or .07 interestn = 4 (quarterly)t = 5 years Pmt = $ ? Quarterly depositPMT = 75,000 * .074 1 + .0744(5)-1PMT = 75,000 * 0.0175 1.017520-1PMT =1312.50.414778196PMT =$3,164.34A young couple has an opportunity to take over a neighbor’s farm operation in 7 years due to the neighbor’s planned retirement. They also plan to purchase his line of equipment that will have an estimated value of $200,000 at that time. How much will they need to deposit annually into an investment account if the account pays a 4 % nominal rate of interest, compounded annually, to have the $200,000 needed at the end of 7 years? FV = $ 200,000 Value needed in 7 yearsi = 4%, or .04 interestn = 1 (annual)t = 7 years Pmt = $ ? Annual depositPMT = 200,000 * .041 1 + .0411(7)-1PMT = 200,000 * 0.04 1.047-1PMT = 8,000 0.315931779PMT =$25,321.92Jack has a seed cleaning business in addition to his farming operation. He would like it to stand on its own and meet its ongoing equipment replacement needs. If equipment replacement costs $75,000 every 5 years, how much does he need to invest monthly into a money market account if it pays 5% interest, compounded monthly, to meet the $75,000 future capital purchase requirement? FV = $ 75,000 (Future Value Equip Cost)i = 5%, or .05 interestn = 12 (monthly)t = 5 years Pmt = $ ? Monthly depositPMT = 75,000 * .0512 1 + .051212(5)-1PMT = 75,000 * 0.004166667n 1.00416666760-1PMT =312.500.283358704PMT =$1,102.84Time Value of Money Blog EvaluationLocate three articles pertaining to time value of money, discounting, compounding, interest, inflation, etc. Use MSN Money, CNN Money, or Yahoo Money to begin your search. After reading and taking notes over all three articles, write a blog post about the key information in the articles. Include how you feel about the information, tips shared in the article, and how you plan to use the information in your own life. Once all student blog posts are complete, each student will be assigned two blog posts with which to read and respond in a short blog comment. This response should pertain to an agreement of the blog post, an opposition of the blog post, personal past experiences pertaining to the blog post, and/or how they personally might use this information in his/her life. Blog comments simply stating, “I agree,” “I disagree,” “Good point,” etc. will not be accepted. Blog comments must recall information learned from reading the initial blog post.Insurance Blog Evaluation Rubric20 points15 points10 points5 pointsContentBlog post provides comprehensive insight, clear understanding, and reflective thought about the topic. It builds a focused argument around the issue, poses questions to the reader, and/or makes an opposing statement supported by personal experiences. Blog post provides moderate insight, clear understanding, and reflective thought about the topic.Blog post provides minimal insight, understanding, and reflective thought about the topic.Blog post lacks insight, understanding and reflective thought about the topic.Viewpoint CreatedBlog post presents a focused viewpoint supported by examples from articles read and content learned in lesson to enhance blog viewpoint. Blog post presents a focused viewpoint supported by examples from articles read and content learned in lesson, but does not enhance blog viewpoint.Blog post presents a focused viewpoint, but is not supported by articles or content from lesson.Blog post lacks a focused viewpoint.Creativity in WritingBlog post is creatively written and easily stimulates dialogue and comments.Blog post is creatively written and can somewhat stimulate dialogue and comments.Blog post is brief and unimaginative, lacking the ability to easily connect with readers.Blog post does not stimulate dialogue and comments.Citations Quotations and comments directly from articles are used effectively and cited correctly.Quotations and comments directly from articles somewhat enhance the blog post and are cited correctly.Quotations and comments directly from articles do not enhance blog post and/or are cited incorrectly.Quotations and comments directly from articles are not used in blog post.Quality of WritingWriting is free of grammatical, spelling, and punctuation errors. Writing has 1-2 grammatical, spelling, or punctuation errors.Writing has 3-4 grammatical, spelling, or punctuation errors.Writing has 5 or more grammatical, spelling, or punctuation errors.Time Value of Money Alternative EvaluationAmortizationA company is purchasing $500,000 of new equipment and has offered additional equity to the lender to secure the finance request. Loan approval terms call for 10 year, equal amortized, quarterly payments at a 6.25% fixed rate of interest. What will the quarterly payments be? P = $ 500,000 loan (PV)i = 6.25%, or .0625 (interest)n = 4 (quarterly)t = 10 years PMT = $ ? Quarterly paymentHigh Profit Farms, LLC just closed on a new $5,000,000 real estate mortgage secured by 2,000 acres. The new loan repayment terms are on 25 year, equal amortized, semi-annual installments with interest fixed at a rate of 5.2%. What are the semi-annual payments for this new mortgage note? P = $ 5,000,000 loan (PV)i = 5.20%, or .0520 (interest)n = 2 (semi-annual)t = 25 years PMT = ? Semi-annual paymentFuture Value of a Dollar Per PeriodCourtney and her husband recently graduated from college. Both have excellent paying jobs in the city, but they would like to move back to the farm and take over their parents’ farm operation when they retire. They plan to live on Courtney’s salary for the next 10 years and invest her husband’s $ 4,000 per month net pay into an investment savings account. If the account earns 5% interest, compounded monthly, what is the expected future value of their account at the end of 10 years? Pmt = $ 4,000 paymenti = 5%, or .05 Interestn = 12 (monthly)t = 10 years FV = $ ? Future Value in 10 yearsA business determines it will need to replace equipment in 5 years. The business plan calls for $2500 per month deposits into a capital savings account that pays a 6% rate annual rate of interest, compounded monthly. What is the future value of the capital account at the end of 5 years? Pmt = $ 2,500 paymenti = 6%, or .06 Interestn = 12 (monthly)t = 5 years FV = $ ? Future Value in 5 yearsFuture Value of a DollarJoe decides to buy land as a hedge against inflation. He finds 100 acres for sale at $3000 per acre. Land values in this area consistently appreciate at an annual rate of 4%. If Joe buys the property for $3000 per acre, what is the future value per acre at the end of 15 years, assuming a 4% annual appreciation rate? PV = $ 3,000 per acre ( Initial value) i = 4%, or .04 (appreciation rate)n = 1 (annual)t = 15 years FV = $ ? Future Value per acre A young business owner is preparing his 5 year business plan and is trying to determine the impact of a 3% annual inflation rate to his operating expenses over the next 5 year period. If his first years operating expense is $200,000, what is the expected operating expense projection at the end of 5 years, assuming all expense inputs remain the same? PV = $ 200,000 Initial value i = 3%, or .03 (appreciation rate)n = 1 (annual)t = 5 years FV = $ ? Projected expense end of year 5Present Value of a Dollar Jill would like to buy a 15 year bond today that has a face value of $30,000 at its maturity. If the bond pays 4.5%, compounded monthly, what is expected present value of the bond? FV = $ 30,000 i = 4.5 %, or .045 raten = 12 (monthly)t = 15 years PV = $ ? Present Value of bondCalculate the present value (purchase price) of a property that is expected to be sold for $400,000 in 5 years, assuming an annual appreciation rate of 4%. Formula: FV = $ 400,000 i = 4 %, or .04 raten = 1 (annual)t = 5 years PV = $ ? Present Value of PropertyPresent Value of a Dollar Per PeriodThe company you worked for the past 25 years plans to downsize operations and will offer qualified employees early retirement packages. They offer you a choice of a) 20 years of equal monthly annuity payments of $2500 per month that guarantees a 4% minimum return on the annuity investments; or b) a lump sum cash settlement of $375,000. In this problem, you will determine a) the present value of the annuity (PV) payments and b) which option provides the largest present value (PV). Solve for present value of the annuity:PMT = $ 2500 (payment)i = 4%, or .04 interestn = 12 (monthly)t = 20 years PV = $ ? Present Value of AnnuityCalculate the difference between the cash settlement and present value of the annuity. Which is higher? PV of Annuity (from part a) = $ ? Cash settlement = $ 375,000 Net Difference =$ Sinking Funds FactorA young couple wants to buy 100 acres at the end of their first 10 years of farming and wants to save enough funds for a 35% cash down payment. If the 100 acres will cost $5000 per acre in 10 years, how much will they need for their 35% down payment? In addition, how much do they need to invest semi-annually in an investment account to then have the down payment amount if the account pays 3.75% annual rate of interest, compounded semi-annually? Problems: How much down payment will be needed in 10 years (Future Value)? What is the semi-annual deposit required to meet the 35% cash down payment needed in 10 years? FV = $ ? (Answer from a. for down payment)i = 3.75%, or .0375 interest raten = 2 (semi - annual)t = 10 years Pmt = $ ? Semi-Annual depositA young couple wants to buy their parents’ trucking business at the conclusion of the next 3 years to coincide with their parents’ retirement. The operation consists of 4 over the road tractor trailer units, and the parents have agreed to sell them at the end of 3 years for $ 25,000 each. Problems: How much is needed to complete the purchase at the end of 3 years? How much will the couple need to invest into their savings account quarterly if interest is compounded quarterly with a 4.75% nominal rate of interest to complete this purchase? FV = $ ? (From a. above Future Value)i = 4.75%, or .0475 interest raten = 4 (quarterly)t = 3 years Time Value of Money Alternative EvaluationAmortizationA company is purchasing $500,000 of new equipment and has offered additional equity to the lender to secure the finance request. Loan approval terms call for 10 year, equal amortized, quarterly payments at a 6.25% fixed rate of interest. What will the quarterly payments be? P = $ 500,000 loan (PV)i = 6.25%, or .0625 (interest)n = 4 (quarterly)t = 10 years PMT = $ ? Quarterly paymentPMT = PV in 1- 1 + in- nt PMT = 500,000 .06254 1- 1 + .06254- (4)(10) PMT = 500,000 (0.015625) 1- 1.015625- 40PMT = 7812.5 1-0.53785436 PMT =7812.5 0.46214564 PMT =$16,904.84High Profit Farms, LLC just closed on a new $5,000,000 real estate mortgage secured by 2,000 acres. The new loan repayment terms are on 25 year, equal amortized, semi-annual installments with interest fixed at a rate of 5.2%. What are the semi-annual payments for this new mortgage note? P = $ 5,000,000 loan (PV)i = 5.20%, or .0520 (interest)n = 2 (semi-annual)t = 25 years PMT = ? Semi-annual paymentPMT = PV in 1- 1 + in- nt PMT = 5,000,000 .0522 1- 1 + .0522- (2)(25) PMT = 130,0001-0.277097088PMT = 130,0000.722902912 PMT =$179,830.51Future Value of a Dollar Per PeriodCourtney and her husband recently graduated from college. Both have excellent paying jobs in the city, but they would like to move back to the farm and take over their parents’ farm operation when they retire. They plan to live on Courtney’s salary for the next 10 years and invest her husband’s $4,000 per month net pay into an investment savings account. If the account earns 5% interest, compounded monthly, what is the expected future value of their account at the end of 10 years? Pmt = $ 4,000 paymenti = 5%, or .05 Interestn = 12 (monthly)t = 10 years FV = $ ? Future Value in 10 yearsFV = PMT1 + innt-1in FV = 4,0001 + .05121210-1.0512 FV = 4,0001.004166667120-10.004166667 FV = 4,0001.647009498-10.004166667 FV = 4,0000.6470094980.004166667 FV = 4,000155.2822671 FV =$621,129.13A business determines it will need to replace equipment in 5 years. The business plan calls for $2500 per month deposits into a capital savings account that pays a 6% rate annual rate of interest, compounded monthly. What is the future value of the capital account at the end of 5 years? Pmt = $ 2,500 paymenti = 6%, or .06 Interestn = 12 (monthly)t = 5 years FV = $ ? Future Value in 5 yearsFV = 2,5001 + .0612125-1.0612 FV = 2,5001.00560-10.005 FV = 2,5001.348850-10.005 FV = 2,5000.34885010.005 FV = 2,50069.77002FV =$174,425.05Future Value of a DollarJoe decides to buy land as a hedge against inflation. He finds 100 acres for sale at $3000 per acre. Land values in this area consistently appreciate at an annual rate of 4%. If Joe buys the property for $3000 per acre, what is the future value per acre at the end of 15 years, assuming a 4% annual appreciation rate? PV = $ 3,000 per acre ( Initial value) i = 4%, or .04 (appreciation rate)n = 1 (annual)t = 15 years FV = $ ? Future Value per acre FV = PV1 + innt FV = 3,0001 + .0411(15) FV = 3,000(1.0415FV = 3,000 X 1.800943506 FV =$5,402.83A young business owner is preparing his 5 year business plan and is trying to determine the impact of a 3% annual inflation rate to his operating expenses over the next 5 year period. If his first years operating expense is $ 200,000, what is the expected operating expense projection at the end of 5 years, assuming all expense inputs remain the same? PV = $ 200,000 Initial value i = 3%, or .03 (appreciation rate)n = 1 (annual)t = 5 years FV = $ ? Projected expense end of year 5FV = PV1 + innt FV = 200,0001 + .0311(5) FV = 200,0001.035FV = 200,000 X 1.15927402 FV =$231,854.81Present Value of a Dollar Jill would like to buy a 15 year bond today that has a face value of $30,000 at its maturity. If the bond pays 4.5%, compounded monthly, what is expected present value of the bond? FV = $ 30,000 i = 4.5 %, or .045 raten = 12 (monthly)t = 15 years PV = $ ? Present Value of bondPV= FV 1 + innt PV= 30,000 1 + .0451212(15) PV= 30,000 1.00375180 PV= 30,000 1.961555008PV=$15,293.98Calculate the present value (purchase price) of a property that is expected to be sold for $400,000 in 5 years, assuming an annual appreciation rate of 4%. Formula: FV = $ 400,000 i = 4 %, or .04 raten = 1 (annual)t = 5 years PV = $ ? Present Value of PropertyPV= 400,000 1 + .0411(5) PV= 400,000 1.045 PV= 400,000 1.216652902 PV=$328,770.84Present Value of a Dollar Per PeriodThe company you worked for the past 25 years plans to downsize operations and will offer qualified employees early retirement packages. They offer you a choice of a) 20 years of equal monthly annuity payments of $2500 per month that guarantees a 4% minimum return on the annuity investments; or b) a lump sum cash settlement of $375,000. In this problem, you will determine a) the present value of the annuity (PV) payments and b) which option provides the largest present value (PV). Solve for present value of the annuity:PMT = $ 2500 (payment)i = 4%, or .04 interestn = 12 (monthly)t = 20 years PV = $ ? Present Value of AnnuityPV = PMT1 + innt-11 + innt* in PV = 2,5001 + .041212(20)-11 + .041212(20)* .0412 PV= 2,5001.00333333240-11.00333333240* 0.00333333 PV= 2,5001.2225803152.222580315* 0.00333333 PV =3056.4507870.007408594 PV =$412,554.77Calculate the difference between the cash settlement and present value of the annuity. Which is higher? PV of Annuity (from part a) = $ ? 412,555Cash settlement = $ 375,000 - 375,000 Net Difference =$ $37,555Sinking Funds FactorA young couple wants to buy 100 acres at the end of their first 10 years of farming and wants to save enough funds for a 35% cash down payment. If the 100 acres will cost $5000 per acre in 10 years, how much will they need for their 35% down payment? In addition, how much do they need to invest semi-annually in an investment account to then have the down payment amount if the account pays 3.75% annual rate of interest, compounded semi-annually? Problems: How much down payment will be needed in 10 years (Future Value)?100 acres x 5,000 per acre = $500,000 x .35 = $175,000 down paymentWhat is the semi-annual deposit required to meet the 35% cash down payment needed in 10 years? FV = $ ? (Answer from a. for down payment)i = 3.75%, or .0375 interest raten = 2 (semi - annual)t = 10 years Pmt = $ ? Semi-Annual depositPMT = FV * in 1 + innt-1 PMT = 175,000 * .03752 1 + .037522(10)-1 PMT = 175,000 * 0.018751.0187520-1PMT = 3,281.25 0.449948026 PMT =$7,292.51A young couple wants to buy their parents’ trucking business at the conclusion of the next 3 years to coincide with their parents’ retirement. The operation consists of 4 over the road tractor trailer units, and the parents have agreed to sell them at the end of 3 years for $25,000 each. Problems: How much is needed to complete the purchase at the end of 3 years?4 x 25,000 = $100,000 How much will the couple need to invest into their savings account quarterly if interest is compounded quarterly with a 4.75% nominal rate of interest to complete this purchase? FV = $ ? (From a. above Future Value)i = 4.75%, or .0475 interest raten = 4 (quarterly)t = 3 years PMT = 100,000 * .04754 1 + .047544(3)-1 PMT = 100,000 * 0.011875 1.01187512-1PMT =1187.50 0.15218546 PMT =$7,802.98Note to Teachers for Problem SolvingThe student needs to be proficient in the use of the scientific calculator for algebraic calculations. It is recommended students review calculator functions and practice working with the formula steps. A number of the formulas have similar calculations. The students should be reminded to look at the results and determine if the answer they have calculated is reasonable or not. Re-doing the calculations is strongly recommended. A variance in answers to the “Answer Key” should be allowed due to rounding and truncating some of the decimals. Students should be reminded to use rules learned in algebra. Steps in Calculating ProblemsReview calculators following functions:Exponent ^ carrot key is used to raise to the powerANS [ ANS ] provides answer for the calculationNegative sign [ ( -- ) ] use to enter a negative number and then press =. In the six functions formula, only amortization uses the negative sign.Enter [ Enter ] Be sure to hit enter after each calculation!Clear Button CLEAR Make sure to clear before all calculations.Read the questions more than once. Go back; write down what is given in the problem. Write the formula to be used to solve the problem; then substitute in the formula what is known and what is to be solved for. Calculate parenthesis first for both the numerator and denominators in the formula.Next calculate the Exponent for numerator and denominators in the formula.Limit rounding and /or truncating. It is best to let the calculator calculate and use the calculated factor for the next step. If rounding, round to no less than five or six numbers right of decimal point. Next calculate the brackets, if in the problemFollow progression of calculations left to right, reducing factors to decimal form for a multiplying factor to arrive at desired answer. Recommend practice of calculating the following calculations:Parenthesis calculations: ( i ) = interest expressed as decimal. Example .06 and (n) represents number of compound periods (example: 12 (monthly); 4 (quarterly); 2 (semi-annual) and 1 (annual)). In below example, ( i ) = .06 ( n) = 12 in= .061 = 0.06Parenthesis calculation plus 1: Same example above, plus 1 + in = 1 + .061 = 1 +0.06 = 1.06Parenthesis calculation plus 1 with exponent ( ^ ) (carrot key) calculation added: In this example, we use the( ^ )function to raise the sum calculated in parenthesis to the exponent [exponent factor is the number of compound periods (n) times the number value of time (t)]. In this example, (n) =1 compound period; (i ) = .06 Interest ( t) = 5 yearsSame example above, plus exponent of 5 represents time and 1 represents number of compound periods (annual): 1 + inn*(t) = 1 + .0611*(5) = 1 +0.065 = 1.065 = 1.338225578In the above formula, from left to right one would follow these steps: Step one: Write the formulaStep two: Substitute the known factors. In above, substitute for ( i ) ,( n ) and ( t ). Step three: Calculate the fraction first and enter as decimal. Then calculate exponents to find the total number of compounding periods (exponent) and enter as the exponent sum (5 above).Step four: Add 1 + the decimal 0.06 then press Enter ( let calculate, next press ^ carrot key), then enter the exponent (above number = 5) which equals total number of compounding periods (n) times number of years ( t ), then press Enter key. This number is normally expressed with eight + numbers right of decimal point. It is best not to round or truncate this number, but if rounded, carry out to a minimum of 5 numbers right of decimal point. Note, if formula calls for a negative exponent, as in the amortizations, enter your number first, press enter, the ^, next press [ (--) ] to enter as negative exponent, enter your exponent and let calculate for answer. We recommend following these steps in calculations or steps students are comfortable with as some may opt to use substitutions. Teachers and advisors may opt to use a financial calculator for alternative checks. Many businesses use the HP 12C financial calculators which easily calculate the six functions. ................
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