Economic Principles in Agribusiness: Time Value of Money Time...Economic Principles in Agribusiness...
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Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money Notes Page
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Time value of money Interest Six Functions of the Dollar Future value of a dollar Rule of 72 Future value of a dollar per period Annuity
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money Notes Page
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Sinking fund factor Present value of the dollar Present value of a dollar per period Amortization
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.1
Calculating the Six Functions of a Dollar
Future Value of a Dollar
If 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 72
How 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 Annuity
Find 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 Factors
Joyce 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?
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.1
Present Value of the Dollar
A 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 Annuity
Jill’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?
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.1 KEY
Calculating the Six Functions of a Dollar
Future Value of a Dollar
If 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)𝑛𝑡
𝐹𝑉 = 8000 𝑥 (1 + .08)5 = $11,755
If 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 = $1,497.40
Rule of 72
How many years are required for $50 to double if it is earning 4% interest?
72/4 = 18 years
How many years will it require for $1,000 to double if earning 16% interest?
72/16 = 4.5 years
Future Value of an Annuity
Find 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 = $23.21
Yr. 5 = $23.21 + (23.21 x .10) + $5 = $30.53
Find the future value of a $7 annuity at 8% for three years.
Yr. 1 = $7 Yr. 2 = $7 + (7 x .08) + $7 = $14.56 Yr. 3 = $14.56 + (14.56 x .08) + 7 = $22.72
Sinking Fund Factors
Joyce 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 ∗
𝑖
𝑛
(1 + 𝑖
𝑛)
𝑛𝑡−1
𝑃𝑀𝑇 = 10,000 ∗
.05
12
(1 + .05
12)
(12)(4)−1
𝑃𝑀𝑇 = 10,000 𝑥 .004166667
(1.004166667)48−1
𝑃𝑀𝑇 = 41.66667
. 22089534 𝑃𝑀𝑇 = $188.63
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.1 KEY
Present Value of the Dollar
A 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 1
(1 + 𝑖)𝑛𝑡
𝑃𝑉 = 50 𝑥 1
(1+.05)5 = $39.17
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.
𝑃𝑉 = 𝐹𝑉 𝑥 1
(1 + 𝑖)𝑛𝑡
𝑃𝑉 = 20,000 𝑥 1
(1+.08)10 = $9263.87
Because 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 Annuity
Jill’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 = 𝑃𝑀𝑇 [(1 +
𝑖
𝑛)
𝑛𝑡−1]
(1 + 𝑖
𝑛)
𝑛𝑡∗ (
𝑖
𝑛)
𝑃𝑉 = 10,000
[(1 + .07
1)
(1)(20)−1]
(1 + .07
1)
(1)(20)∗ (
.07
1)
𝑃𝑉 = 10,000 [(1.07)20−1]
(1.07)20∗ (.07)
𝑃𝑉 =10,000 [2.86968446]
0.270877912 𝑃𝑉 =
28696.8446
. 270877912 𝑃𝑉 = $105,940.14
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? 𝑃𝑀𝑇 = 𝑃𝑉 (
𝑖
𝑛)
1− (1 + 𝑖
𝑛)
− 𝑛𝑡 𝑃𝑀𝑇 =5,000 (
.06
12)
1− (1 + .06
12)
− (12)(5) 𝑃𝑀𝑇 = 5,000 (.005)
1− (1.005)− 60
𝑃𝑀𝑇 = 25.0
1 − 0.7413272196 𝑃𝑀𝑇 =
25
0.258672804 𝑃𝑀𝑇 = $96.66
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.2
Six Functions of a Dollar Formulas
1) Future Value of $ 1: 𝐹𝑉 = 𝑃𝑉(1 + 𝑖)𝑛𝑡
2) Future Value of $ 1 Per Period: 𝐹𝑉 = 𝑃𝑀𝑇 [(1 +
𝑖
𝑛)
𝑛𝑡−1
𝑖
𝑛
]
3) Sinking Funds Factor: 𝑃𝑀𝑇 = 𝐹𝑉 ∗
𝑖
𝑛
(1 + 𝑖
𝑛)
𝑛𝑡−1
4) Present Value of $ 1: 𝑃𝑉 = 𝐹𝑉
(1 + 𝑖
𝑛)
𝑛𝑡
5) Present Value of $ 1 Per Period: 𝑃𝑉 = 𝑃𝑀𝑇 [(1 +
𝑖
𝑛)
𝑛𝑡−1]
(1 + 𝑖
𝑛)
𝑛𝑡∗ (
𝑖
𝑛)
6) Amortization (Partial Payment): 𝑃𝑀𝑇 = 𝑃𝑉 (
𝑖
𝑛)
1− (1 + 𝑖
𝑛)
− 𝑛𝑡
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.3
Amortization Practice
1. Josh 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 payment
2. John 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 payment
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.3
3. Ethan 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?
a. 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 payment
b. Solve for total cost of TV:
Total cost of TV and finance charges
= $
4. 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 payment
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.3 KEY
Amortization Practice
1. Josh 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 payment
𝑃𝑀𝑇 = 𝑃𝑉 (
𝑖𝑛)
1 − (1 + 𝑖𝑛)
− 𝑛𝑡 𝑃𝑀𝑇 = 17,000 (
. 061 )
1 − (1 + . 06
1 )− (1)(4)
𝑃𝑀𝑇 = 17,000 (0.06)
1 − (1.06)− 4
𝑃𝑀𝑇 =1020
1 − 0.792093663 𝑃𝑀𝑇 =
1020
0.207906337 𝑃𝑀𝑇 = $4,906.06
2. John 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 payment
𝑃𝑀𝑇 = 200,000 (
. 05512 )
1 − (1 + . 055
12 )− (12)(30)
𝑃𝑀𝑇 =200,000 (0.004583333)
1 − (1.004583333)− 360
𝑃𝑀𝑇 = 916.66
1 − 0.192775275 𝑃𝑀𝑇 =
916.666
0.807224725 𝑃𝑀𝑇 = $1,135.58
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.3 KEY
3. Ethan 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?
c. 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 payment
𝑃𝑀𝑇 = 3,000 (
. 1812 )
1 − (1 + . 1812 )
−(12)(4) 𝑃𝑀𝑇 =
3,000 (0.015)
1 − 1.015)− 48 𝑃𝑀𝑇 =
45
1 − 0.48936169
𝑃𝑀𝑇 = $88.13
d. Solve for total cost of TV:
Total cost of TV and finance charges
= $ 88.13 x 48 = $4230.24
4. 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 payment
𝑃𝑀𝑇 = 150,000 (
. 05252 )
1 − (1 + . 0525
2 )−(2)(7)
𝑃𝑀𝑇 = 3,000 (0.02625)
1 − (1.02625)−14 𝑃𝑀𝑇 =
3.937.5
1 − 0.69575385
𝑃𝑀𝑇 = 3937.5
0.30424615 𝑃𝑀𝑇 = $12,941.82
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.4
Future Value of a Dollar Per Period Practice
1. Linda 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 payment
i = 6%, or .06 Interest
n = 12 (monthly)
t = 4 years
FV = $ ? Future Value at end of 4 years
2. John 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 Interest
n = 12 (monthly)
t = 20 years
FV = $ ? Future Value in 20 years
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.4
3. Sara’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 payment
i = 6%, or .06 Interest
n = 12 (monthly)
t = 12 years
FV = $ ? Future Value end of 12 years
4. An 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 Interest
n = 1 (annual)
t = 10 years
FV = $ ? Future Value at end of 10 years
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.4 KEY
Future Value of a Dollar Per Period Practice
1. Linda 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 payment
i = 6%, or .06
n = 12 (monthly)
t = 4 years
FV = $ ? Future Value at end of 4 years
𝐹𝑉 = 𝑃𝑀𝑇 [(1 +
𝑖𝑛
)𝑛𝑡
− 1
𝑖𝑛
] 𝐹𝑉 = 100 [(1 +
. 0612
)(12)(4)
− 1
. 0612
]
𝐹𝑉 = 100 [(1.005)48 − 1
0.005] 𝐹𝑉 = 100 [
0.27048916
0.005 ] 𝐹𝑉 = 100[54.097832]
𝐹𝑉 = $5,409.78
2. John 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 years
𝐹𝑉 = 600 [(1 +
. 052512 )
(12)(20)
− 1
. 052512
] 𝐹𝑉 = 600 [(1.004375)240 − 1
0.004375]
𝐹𝑉 = 600 [2.851114 − 1
0.004375 ] 𝐹𝑉 = 600 [
1.851114
0.004375] 𝐹𝑉 = 600[423.11177]
𝐹𝑉 = $253,867.06
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.4 KEY
3. Sara’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 payment
i = 6%, or .06
n = 12 (monthly)
t = 12 years
FV = $ ? Future Value end of 12 years
𝐹𝑉 = 500 [(1 +
. 0612 )
(12)(12)
− 1
. 0612
] 𝐹𝑉 = 500 [(1.005)144 − 1
0.005]
𝐹𝑉 = 500 [2.0507508 − 1
0.005] 𝐹𝑉 = 500 [
1.0507508
0.005] 𝐹𝑉 = 500[210.150163]
𝐹𝑉 = $105,075.08
4. An 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 years
𝐹𝑉 = 25,000 [(1 +
. 071 )
(1)(10)
− 1
. 071
] 𝐹𝑉 = 25,000 [(1 .07)10 − 1
0.07]
𝐹𝑉 = 25,000 [1.967151357 − 1
0.07] 𝐹𝑉 = 25,000 [
0.967151357
0.07]
𝐹𝑉 = 25,000[13.81644796] 𝐹𝑉 = $345,411.20
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.5
Future Value of a Dollar Practice
1. Jill 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 Investment
i = 5%, or .05 (interest)
n = 2 (semi-annual)
t = 5 years
FV = $ ? Future Value at maturity
2. A 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 Investment
i = 6%, or .06 (appreciation rate)
n = 1 (annual)
t = 10 years
FV = $ ? Future Value in 10 years
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.5
3. Kevin 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 Deposit
i = 4%, or .04 (interest)
n = 12 (monthly)
t = 30 years
FV = $ ? Future Value in 30 years
4. Nathan 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 years
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.5 KEY
Future Value of a Dollar Practice
1. Jill 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 Investment
i = 5%, or .05 (interest)
n = 2 (semi-annual)
t = 5 years
FV = $ ? Future Value at maturity
𝐹𝑉 = 𝑃𝑉 (1 + 𝑖
𝑛)
𝑛𝑡
𝐹𝑉 = 5,000 (1 + . 05
2)
(2)(5)
𝐹𝑉 = 5,000(1.025)10
𝐹𝑉 = 5,000 𝑋 1.28008454 𝐹𝑉 = $6,400.42
2. A 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 Investment
i = 6%, or .06 (appreciation rate)
n = 1 (annual)
t = 10 years
FV = $ ? Future Value in 10 years
𝐹𝑉 = 75,000 (1 + . 06
1)
(1)(10)
𝐹𝑉 = 75,000(1.06)10 𝐹𝑉 = 75,000 𝑋 1.79084769
𝐹𝑉 = $134,313.58
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.5 KEY
3. Kevin 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 Deposit
i = 4%, or .04 (interest)
n = 12 (monthly)
t = 30 years
FV = $ ? Future Value in 30 years
𝐹𝑉 = 30,000 (1 + . 04
12)
(12)(30)
𝐹𝑉 = 30,000(1.003333333)360
𝐹𝑉 = 30,000 𝑋 3.313498014 𝐹𝑉 = $99,404.94
4. Nathan 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 years
𝐹𝑉 = 800,000 (1 + . 07
1)
(1)(5)
𝐹𝑉 = 800,000(1.07)5 𝐹𝑉 = 800,000 𝑋 1.402551731
𝐹𝑉 = $1,122,041.39
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.6
Present Value of a Dollar Practice
1. Jill 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?
a) Problem for Car:
FV = $ 15,000 Value at maturity
i = 6 %, or .06 rate
n = 12 (monthly)
t = 6 years
PV = $ ? Required deposit
b) Problem for down payment:
FV = $ 40,000 Value at maturity
i = 6%, or .06 interest rate
n = 12 (monthly)
t = 6 years
PV = $ ? Required deposit
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.6
2. You 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 maturity
i = 5 %, or .05 rate
n = 12 (monthly)
t = 5 years
PV = $ ? Required deposit
3. Your 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 cost
i = 5.75 %, or .0575 rate
n = 2 (semi-annual)
t = 5 years
PV = $ ? Required deposit
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.6 KEY
Present Value of a Dollar Practice
1. Jill 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?
c) Problem for Car:
FV = $ 15,000 Value at maturity
i = 6 %, or .06 rate
n = 12 (monthly)
t = 6 years
PV = $ ? Required deposit
𝑃𝑉 = 𝐹𝑉
(1 + 𝑖𝑛)
𝑛𝑡 𝑃𝑉 = 15,000
(1 + . 0612 )
(12)(6) 𝑃𝑉 =
15,000
(1.005)72 𝑃𝑉 =
15,000
1.432044278
𝑃𝑉 = $10,474.54
d) Problem for down payment:
FV = $ 40,000 Value at maturity
i = 6%, or .06 interest rate
n = 12 (monthly)
t = 6 years
PV = $ ? Required deposit
𝑃𝑉 = 40,000
(1 + . 0612 )
(12)(6) 𝑃𝑉 =
40,000
(1.005)72 𝑃𝑉 =
40,000
1.432044279 𝑃𝑉 = $27,932.10
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.6 KEY
2. You 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 maturity
i = 5 %, or .05 rate
n = 12 (monthly)
t = 5 years
PV = $ ? Required deposit
𝑃𝑉 = 20,000
(1 + . 0512 )
(12)(5) 𝑃𝑉 =
20,000
(1.004166667)60 𝑃𝑉 =
20,000
1.283358678 𝑃𝑉 = $15,584.11
3. Your 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 cost
i = 5.75 %, or .0575 rate
n = 2 (semi-annual)
t = 5 years
PV = $ ? Required deposit
𝑃𝑉 = 400,000
(1 + . 0575
2 )(2)(5)
𝑃𝑉 =400,000
(1.02875)10 𝑃𝑉 =
400,000
1.327695497 𝑃𝑉 = $301,273.90
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.7
Present Value of a Dollar Per Period Practice
1. A 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?
a) Solve for present value of the note.
PMT = $ 1,000 per period
i = 5%, or .05 interest
n = 12 (monthly)
t = 15 years
PV = $ ? Solve for Present Value
b) 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 = $
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.7
2. 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 period
i = 8%, or .08 interest
n = 1 (annual)
t = 20 years
PV = $ ? Present Value of Rental property
3. A 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 period
i = 6%, or .06 interest
n = 1 (annual)
t = 10 years
PV = $ ? Present Value of 10 yr. contract
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.7
4. An 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?
a) Solve for today’s value of 10 year cash flow:
PMT = $ 12,500 payment
i = 10%, or .10 interest
n = 1 (annual)
t = 10 years
PV = $ Today’s current Value
b) 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 payment
i = 5%, or .05% interest
n = 1 (annual)
t = 10 years
PV = $ ? Today’s current value
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.7 KEY
Present Value of a Dollar Per Period Practice
1. A 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?
c) Solve for present value of the note.
PMT = $ 1,000 per period
i = 5%, or .05 interest
n = 12 (monthly)
t = 15 years
PV = $ ? Solve for Present Value
𝑃𝑉 = 𝑃𝑀𝑇 [(1 +
𝑖𝑛)
𝑛𝑡
− 1]
(1 + 𝑖𝑛)
𝑛𝑡
∗ (𝑖𝑛)
𝑃𝑉 = 1,000
[(1 + . 0512 )
(12)(15)
− 1]
(1 + . 0512 )
(12)(15)
∗ (. 0512 )
𝑃𝑉 =1,000 [(1.004166667)180 − 1]
(1.004166667)180 ∗ (. 004166667) 𝑃𝑉 =
1,000 [1.113704059]
2.113704059 ∗ .00416666
𝑃𝑉 =1113.704059
0.008807101 𝑃𝑉 = $126,455.21
d) 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 = $ 53,545
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.7 KEY
2. 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 period
i = 8%, or .08 interest
n = 1 (annual)
t = 20 years
PV = $ ? Present Value of Rental property
𝑃𝑉 = 10,000
[(1 + . 08
1 )(1)(20)
− 1]
(1 + . 08
1 )(1)(20)
∗ (. 08
1 )
𝑃𝑉 = 10,000 [(1.08)20 − 1]
(1.08)20 ∗ (0.08)
𝑃𝑉 = 10,000 [3.660957144]
4.6600957144 ∗ 0.08 𝑃𝑉 =
36609.57144
0.37287657 𝑃𝑉 = $98,181.47
3. A 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 period
i = 6%, or .06 interest
n = 1 (annual)
t = 10 years
PV = $ ? Present Value of 10 yr. contract
𝑃𝑉 = 50,000
[(1 + . 06
1 )(1)(10)
− 1]
(1 + . 06
1 )(1)(10)
∗ (. 06
1 )
𝑃𝑉 = 50,000 [(1.06)10 − 1]
(1.06)10 ∗ (0.06)
𝑃𝑉 = 50,000 [0.790847697]
1.790847697 ∗ 0.06 𝑃𝑉 =
39542.38
0.10745 𝑃𝑉 = $368,008.26
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.7 KEY
4. An 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?
c) Solve for today’s value of 10 year cash flow:
PMT = $ 12,500 payment
i = 10%, or .10 interest
n = 1 (annual)
t = 10 years
PV = $ Today’s current Value
𝑃𝑉 = 12,500
[(1 + . 10
1 )(1)(10)
− 1]
(1 + . 10
1 )(1)(10)
∗ (. 10
1 )
𝑃𝑉 = 12,500 [(1.10)10 − 1]
(1.10)10 ∗ (0.10)
𝑃𝑉 = 12,500 [1.59374246]
0.259374246 𝑃𝑉 =
19921.78075
0.259374246 𝑃𝑉 = $76,807.09
d) 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 payment
i = 5%, or .05% interest
n = 1 (annual)
t = 10 years
PV = $ ? Today’s current value
𝑃𝑃𝑉 = 12,500
[(1 + . 05
1 )(1)(10)
− 1]
(1 + . 05
1 )(1)(10)
∗ (. 05
1 )
𝑃𝑉 = 12,500 [(1.05)10 − 1]
(1.05)10 ∗ (0.05)
𝑃𝑉 = 12,500 [0.628894627]
0.081444731 𝑃𝑉 =
7861.18
0.081444731 𝑃𝑉 = $96,521.65
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.8
Sinking Funds Factor Practice
1. A 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 years
i = 6%, or .06 interest
n = 4 (quarterly)
t = 10 years
Pmt = $ ? Quarterly deposit
2. Jill 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 years
i = 7%, or .07 interest
n = 4 (quarterly)
t = 5 years
Pmt = $ ? Quarterly deposit
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.8
3. A 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 years
i = 4%, or .04 interest
n = 1 (annual)
t = 7 years
Pmt = $ ? Annual deposit
4. Jack 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 interest
n = 12 (monthly)
t = 5 years
Pmt = $ ? Monthly deposit
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.8 KEY
Sinking Funds Factor Practice
1. A 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 years
i = 6%, or .06 interest
n = 4 (quarterly)
t = 10 years
Pmt = $ ? Quarterly deposit
𝑃𝑀𝑇 = 𝐹𝑉 ∗
𝑖𝑛
(1 + 𝑖𝑛)
𝑛𝑡
− 1
𝑃𝑀𝑇 = 20,000 ∗
. 064
(1 + . 06
4 )(4)(10)
− 1
𝑃𝑀𝑇 = 20,000 ∗ 0.015
(1.015)40 − 1
𝑃𝑀𝑇 = 300
0.8140184𝑃𝑀𝑇 = $368.54
2. Jill 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 years
i = 7%, or .07 interest
n = 4 (quarterly)
t = 5 years
Pmt = $ ? Quarterly deposit
𝑃𝑀𝑇 = 75,000 ∗
. 074
(1 + . 07
4 )(4)(5)
− 1
𝑃𝑀𝑇 = 75,000 ∗ 0.0175
(1.0175)20 − 1𝑃𝑀𝑇 =
1312.5
0.414778196
𝑃𝑀𝑇 = $3,164.34
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.8 KEY
3. A 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 years
i = 4%, or .04 interest
n = 1 (annual)
t = 7 years
Pmt = $ ? Annual deposit
𝑃𝑀𝑇 = 200,000 ∗
. 041
(1 + . 04
1 )(1)(7)
− 1
𝑃𝑀𝑇 = 200,000 ∗ 0.04
(1.04)7 − 1𝑃𝑀𝑇 =
8,000
0.315931779
𝑃𝑀𝑇 = $25,321.92
4. Jack 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 interest
n = 12 (monthly)
t = 5 years
Pmt = $ ? Monthly deposit
𝑃𝑀𝑇 = 75,000 ∗
. 0512
(1 + . 0512 )
(12)(5)
− 1
𝑃𝑀𝑇 = 75,000 ∗
0.004166667𝑛
(1.004166667)60 − 1
𝑃𝑀𝑇 =312.50
0.283358704𝑃𝑀𝑇 = $1,102.84
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.9
Time Value of Money Blog Evaluation
Locate 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.
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.9
Insurance Blog Evaluation Rubric
20 points 15 points 10 points 5 points
Con
ten
t
Blog 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.
Vie
wp
oin
t C
reate
d Blog 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.
Cre
ati
vit
y i
n
Wri
tin
g
Blog 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.
Cit
ati
on
s
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.
Qu
ali
ty o
f
Wri
tin
g
Writing 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.
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
Time Value of Money Alternative Evaluation
Amortization
1. A 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 payment
2. High 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 payment
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
Future Value of a Dollar Per Period
3. Courtney 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 payment
i = 5%, or .05 Interest
n = 12 (monthly)
t = 10 years
FV = $ ? Future Value in 10 years
4. A 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 payment
i = 6%, or .06 Interest
n = 12 (monthly)
t = 5 years
FV = $ ? Future Value in 5 years
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
Future Value of a Dollar
5. Joe 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
6. 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 5
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
Present Value of a Dollar
7. 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 rate
n = 12 (monthly)
t = 15 years
PV = $ ? Present Value of bond
8. Calculate 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 rate
n = 1 (annual)
t = 5 years
PV = $ ? Present Value of Property
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
Present Value of a Dollar Per Period
9. The 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).
a) Solve for present value of the annuity:
PMT = $ 2500 (payment)
i = 4%, or .04 interest
n = 12 (monthly)
t = 20 years
PV = $ ? Present Value of Annuity
b) Calculate 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 = $
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
Sinking Funds Factor
10. A 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:
a. How much down payment will be needed in 10 years (Future Value)?
b. 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 rate
n = 2 (semi - annual)
t = 10 years
Pmt = $ ? Semi-Annual deposit
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10
11. A 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:
a. How much is needed to complete the purchase at the end of 3 years?
b. 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 rate
n = 4 (quarterly)
t = 3 years
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
Time Value of Money Alternative Evaluation
Amortization
1. A 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 payment
PMT = PV (
in)
1 − (1 + in)
− nt PMT = 500,000 (
. 06254 )
1 − (1 + . 0625
4 )− (4)(10)
PMT = 500,000 (0.015625)
1 − (1.015625)− 40
PMT = 7812.5
1 − 0.53785436 PMT =
7812.5
0.46214564 PMT = $16,904.84
2. High 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 payment
PMT = PV (
in)
1 − (1 + in)
− nt PMT = 5,000,000 (
. 0522 )
1 − (1 + . 052
2 )− (2)(25)
PMT = 130,000
1 − 0.277097088
PMT = 130,000
0.722902912 PMT = $179,830.51
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
Future Value of a Dollar Per Period
3. Courtney 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 payment
i = 5%, or .05 Interest
n = 12 (monthly)
t = 10 years
FV = $ ? Future Value in 10 years
FV = PMT [(1 +
in)
nt
− 1
in
] FV = 4,000 [(1 +
. 0512 )
(12)(10)
− 1
. 0512
]
FV = 4,000 [(1.004166667)120 − 1
0.004166667] FV = 4,000 [
1.647009498 − 1
0.004166667]
FV = 4,000 [0.647009498
0.004166667] FV = 4,000[155.2822671] FV = $621,129.13
4. A 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 payment
i = 6%, or .06 Interest
n = 12 (monthly)
t = 5 years
FV = $ ? Future Value in 5 years
FV = 2,500 [(1 +
. 0612 )
(12)(5)
− 1
. 0612
] FV = 2,500 [(1.005)60 − 1
0.005]
FV = 2,500 [1.348850 − 1
0.005] FV = 2,500 [
0.3488501
0.005] FV = 2,500[69.77002]
FV = $174,425.05
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
Future Value of a Dollar
5. Joe 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 = PV (1 + i
n)
nt
FV = 3,000 (1 + . 04
1)
(1)(15)
FV = 3,000(1.04)15
FV = 3,000 X 1.800943506 FV = $5,402.83
6. 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 5
FV = PV (1 + i
n)
nt
FV = 200,000 (1 + . 03
1)
(1)(5)
FV = 200,000(1.03)5
FV = 200,000 X 1.15927402 FV = $231,854.81
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
Present Value of a Dollar
7. 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 rate
n = 12 (monthly)
t = 15 years
PV = $ ? Present Value of bond
PV = FV
(1 + in)
nt PV = 30,000
(1 + . 045
12 )(12)(15)
PV = 30,000
(1.00375)180 PV =
30,000
1.961555008
PV = $15,293.98
8. Calculate 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 rate
n = 1 (annual)
t = 5 years
PV = $ ? Present Value of Property
PV = 400,000
(1 + . 04
1 )(1)(5)
PV = 400,000
(1.04)5 PV =
400,000
1.216652902 PV = $328,770.84
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
Present Value of a Dollar Per Period
9. The 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).
c) Solve for present value of the annuity:
PMT = $ 2500 (payment)
i = 4%, or .04 interest
n = 12 (monthly)
t = 20 years
PV = $ ? Present Value of Annuity
PV = PMT [(1 +
in)
nt
− 1]
(1 + in)
nt
∗ (in)
PV = 2,500
[(1 + . 0412
)(12)(20)
− 1]
(1 + . 0412 )
(12)(20)
∗ (. 0412 )
PV = 2,500 [(1.00333333)240 − 1]
(1.00333333)240 ∗ (0.00333333) PV =
2,500 [1.222580315]
2.222580315 ∗ 0.00333333
PV =3056.450787
0.007408594 PV = $412,554.77
d) Calculate the difference between the cash settlement and present value of the annuity.
Which is higher?
PV of Annuity (from part a) = $ ? 412,555
Cash settlement = $ 375,000 - 375,000
Net Difference = $ $37,555
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
Sinking Funds Factor
10. A 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:
a. 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 payment
b. 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 rate
n = 2 (semi - annual)
t = 10 years
Pmt = $ ? Semi-Annual deposit
PMT = FV ∗
in
(1 + in)
nt
− 1
PMT = 175,000 ∗
. 03752
(1 + . 0375
2 )(2)(10)
− 1
PMT = 175,000 ∗ 0.01875
(1.01875)20 − 1
PMT = 3,281.25
0.449948026 PMT = $7,292.51
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money EP6.10 KEY
11. A 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:
a. How much is needed to complete the purchase at the end of 3 years?
4 x 25,000 = $100,000
b. 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 rate
n = 4 (quarterly)
t = 3 years
PMT = 100,000 ∗
. 04754
(1 + . 0475
4 )(4)(3)
− 1
PMT = 100,000 ∗ 0.011875
(1.011875)12 − 1
PMT =1187.50
0.15218546 PMT = $7,802.98
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money Teacher Note
Note to Teachers for Problem Solving
The 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 Problems
1. Review calculators following functions:
a. Exponent ^ carrot key is used to raise to the power
b. ANS [ ANS ] provides answer for the calculation
c. Negative sign [ ( -- ) ] use to enter a negative number and then press =. In
the six functions formula, only amortization uses the negative sign.
d. Enter [ Enter ] Be sure to hit enter after each calculation!
e. Clear Button CLEAR Make sure to clear before all calculations.
2. Read the questions more than once. Go back; write down what is given in the problem.
3. 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.
4. Calculate parenthesis first for both the numerator and denominators in the formula.
5. Next calculate the Exponent for numerator and denominators in the formula.
6. 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.
7. Next calculate the brackets, if in the problem
8. Follow progression of calculations left to right, reducing factors to decimal form for a
multiplying factor to arrive at desired answer.
9. Recommend practice of calculating the following calculations:
a. 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 ( 𝑖
𝑛) = (
.06
𝟏) = 0.06
b. Parenthesis calculation plus 1: Same example above, plus
Economic Principles in Agribusiness EP6 Time Value of Money
Economic Principles in Agribusiness: Time Value of Money Teacher Note
(1 + 𝑖
𝑛) = (1 +
.06
1) = (1 + 0.06) = 1.06
c. Parenthesis 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 years
Same example above, plus exponent of 5 represents time and 1 represents number
of compound periods (annual):
(1 + 𝑖
𝑛)
(𝑛)∗(𝑡)
= (1 + .06
1)
(1)∗(𝟓)
= (1 + 0.06)𝟓 = (1.06)𝟓 = 1.338225578
In the above formula, from left to right one would follow these steps:
Step one: Write the formula
Step 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.