Transcript Study Guide Chapter1 10-11

Study Guide
Chapter1 10-11
Agricultural Economics 330
Instructor: David J. Leatham
Question 1
Suppose you have an opportunity to
purchase an investment for $600 and the
investment promises to return $1,000 in
five years. Does the yield on this
investment increase or decrease if you
can buy this investment for $580 instead
of $600. Circle one.
 Increase
Question 2
 Suppose you have $10,000 in your savings
account and you are investigating the
possibility of investing in bonds. If you believe
that interest rates are going to go up over the
next three years, should you invest in bonds.
Justify your answer.

Probably not. If interest rate go up, the value of the
bonds you purchase will go down. If you wait to buy
the bonds at higher interest rates, the price will be
lower. If you buy them now, you are locked into the
lower interest rate and a decreasing value of the
bond.
Question 3
What does a Net Present Value equal to
0, imply about a project’s rate of return.
 The
rate of return on the investment
(internal rate of return --IRR) is equal to the
required rate of return on the investment
(discount rate).
Question 4
Suppose that you have eight annual
payments of $3,425 left to pay on a loan
with the first payment due in one year.
You can borrow money at 9% and the
bank is willing to sell back the note for
$18,000. Should you buy back this loan?
Assume that you would need to borrow
the $18,000 if you buy back the loan.
0
MV
1
3,425
2
3,425
...
8
r=9%
3,425
Market Value = 3,425 [USPV9%, 8] = 18,957
The market value of this contract is $18,957. You can
buy it for $18,000. Buy it back.
Question 5
Suppose the real price of a tractor in 10
years is $55,000. What is the nominal
price of the tractor if inflation is 3%?

Fn = F*n (1+If)n
F10 = 55,000(1+.03)10 = 73,915.4
Question 6
 Suppose you are considering an investment
that will increase operating receipts by $10,000
and operating expenses by $6,000. Calculate
the after-tax net returns if your marginal tax
rate is 15% and your required rate of return on
investments is 20%.
After-tax net returns = (10,000-6,000)(1-.15)
=4,000(.85) = 3,400
Question 7
 Suppose you are considering an investment
that costs $35,000. You plan on selling the
investment in five years for $10,000. The IRS
will allow you to depreciate this investment
over four years. Calculate the tax savings from
depreciation in the fourth and fifth year if you
use the straight-line method of calculating
depreciation and your marginal tax rate is
15%.
Question 7
Answer
Annual Depreciation for tax purposes = (35,000/4) = 8,750
Tax savings from depreciation = 8,750*.15 = 1,312.5
Tax savings in the fourth year is $1,312.5
Tax savings in the fifth year is 0 because the investment
is depreciated completely (for tax purposes)
over the first four years.
Question 8
Suppose you are considering an
investment that costs $60,000. You plan
on selling the investment in ten years for
$20,000. Calculate the present value of
the after-tax terminal value if
accumulated depreciation is $30,000,
your marginal tax rate is 15%, and your
required rate of return on investments is
10%.
Question 8
Answer
After-tax Terminal Value = 20,000-[20,000-(60,000-30,000)].15
= 21,500
After-tax discount rate = .1(1-.15) = 0.085 or 8.5%
0
V0
10
r = 8.5 %
21,500
V0 = 21,500 (1+.085)-10 = 9,509.14
Question 9
 Suppose that you are considering the purchase
of a bond that matures in 12 years. The bond
has a par value of $1,000, it pays a coupon of 10
percent (annually), and the coupon is paid
semiannually (10s).
Coupon payment every six months = (.10*1,000)/2 = $50
Question 9
Part A
Calculate the market value (price) of the bond
today if the bond’s market rate (yield) is 7%.
0
MV
1
50
2
50
...
24
50
1,000
r = 7/2 %= 3.5 %
Market Value = price = 50[USPV3.5%,24] + 1,000 (1+.035)-24
=$1,240.88
Question 9
Part B
Calculate the market value (price) of the bond
in five years if the bond’s market rate is 4%.
0
MV
1
50
2
50
...
10
50
1,000
r =4/2 %= 2 %
Market Value = price = 50[USPV2%,10] + 1,000 (1+.02)-10
=$1,269.48
Question 9
Part C
 Calculate the Net Present Value and the
Internal Rate of Return on this bond
investment if the current market rate on this
bond is 7%, you expect the market rate to be
4% in 5 years, you plan to sell the bond in five
years, and your required rate of return on this
investment is 8% (4% semiannually). Is this an
acceptable investment?
(hint:
use the
purchase price in part A, and the sell price in
part B)
0
1
50
2
50
...
- 1,240.88
10
50
r =8/2 %= 4 %
1,363.19
NPV = -1,240.88 + 50[USPV4%,10] + 1,363.19 (1+.04)-10
= -1,240.88 + 1,326.47 = 85.59
0
1
50
2
50
...
- 1,240.88
10
50
r =?/2 %= ? %
1,363.19
NPV = 0 = -1,240.88 + 50[USPVr%,10] + 1,363.19 (1+.r)-10
r = IRR = 4.82% (semiannual rate)
r = IRR = 2*4.82 = 9.63%
This is an acceptable investment. NPV > 0 and
the IRR > 8%.
Question 10
.
List the four steps of capital budgeting
discussed in class:
 A.
 B.
 C.
D
Answer 10
.
List the four steps of capital budgeting
discussed in class:
 A.
Identify Alternative Investments
 B. Collect Relevant Information
 C. Layout Cashflows
 D. Analysis
Profitability, risk,
feasibility
sensitivity, and financial
Question 11
Suppose you are considering the
purchase of an investment and your
discount rate is 10%. Also, suppose you
calculate that the net present value of this
investment is equal to zero. What is the
internal rate of return on this
investment?
Answer
 10%
Question 12
Suppose
you have an opportunity to
purchase an investment today for $500.
 A.
Calculate the yield on this investment if
the investment matures in one year and
promises to pay $560 at maturity .
560  500 60
r

 0 .12 or 12%
500
500
Yield = 12%
Question 12
Suppose you have an opportunity to
purchase an investment today for $500.
 B.
Calculate the yield on this investment if
the investment promises to pay $140 at the
end of each year for the next five years.
0
-500
1
2
140
140
V0 = A [USPVr,N]
...
...
5
r=?%
140
Present Value of an Uniform Annuity
500 = 140 [USPVr%, 5]
5
?
-500
140
0
N
i%
PV
PMT
FV
7/16/2015
Agricultural Finance
r = 12.38%
25
Question 13
Suppose the annual cash revenue from an
investment is $9,000 and the annual cash
expenses are $3,000. Calculate the
annual after-tax net returns if the
marginal tax rate is equal to 15%.
Let ATNR=After-tax Net Returns
R= Cash Revenues
E=Cash Expenses
m=marginal tax rate
NR = [R-E]
ATNR
ATNR
= [R-E](1-m)
= [NR](1-m)
= [9,000-3,000](1-.15)
=6,000(.85)
=5,100
Question 14
 Suppose Mr. Agirich is considering the purchase of a
tractor that costs $75,000. He plans on selling the
tractor in 10 years for $10,000. The IRS will allow him
to depreciate the tractor over seven years. Assume that
he uses the straight-line method of calculating
depreciation, the marginal tax rate is 28% and the
required rate of return on investments is 16%.
 A. Calculate the present value of tax savings from
depreciation over the life of the investment.
Annual Depreciation (D) = 75,000/7
= 10,714.29
Annual Tax Savings = mD
= 10,714.29 * .28
= 3,000
After-tax discount rate
= .16(1-.28)
=0.1152 or 11.52%
0
1
2
V0
3,000
3,000
...
...
7
3,000
8
9
10
0
0
0
r = 11.52 %
Present Value of Tax Savings from Depreciation = V0
V0 = A [USPVr,N]
Present Value of an Uniform Annuity
V0 = 3,000 [USPV11.52%, 7]
7
11.52
?
3,000
0
N
i%
PV
PMT
FV
V0 = 13,902.2
Question 14
 Suppose Mr. Agirich is considering the
purchase of a tractor that costs $75,000. He
plans on selling the tractor in 10 years for
$10,000. The IRS will allow him to depreciate
the tractor over seven years. Assume that he
uses the straight-line method of calculating
depreciation, the marginal tax rate is 28% and
the required rate of return on investments is
16%.

B. Calculate the present value of the after-tax
terminal value.
TV
at
N



 TV  TV   cos t   Dn  m


n 1  
TVat = 10,000-[10,000-(75,000-75,000)].28
=10,000-[10,000].28
=10,000-2,800
=7,200
0
10
-V0
r = 11.52% %
7,200
V0 = Present Value of After-tax Terminal Value
V0 = VN (1+r)-N Present Value of a Single Sum
V0 = 7,200 (1+.1152)-10
10
11.52
V0
0
7,200
N
i%
PV
PMT
FV
01/09/80
Agricultural Finance
V0 = 2,419.94
19
Question 15
Suppose Mr. Agirich is considering the purchase of a
center pivot irrigation system. He estimates that the
after-tax net cash flows associated with this investment
are as follows. Assume that the marginal tax rate is 28%.
Component
Net Cash Flow
0
$-85,000
1
$15,000
2
$15,000
Year
3
$15,000
4
$15,000
5
$15,000
6
$59,000
A.
Calculate the net present value (NPV) if the
required rate of return on investments is 18%.
After-tax discount rate = 0.18(1-.28)
= 0.1296 or 12.96%
NPV = -85,000 + 15,000 [USPV12.96%,5] + 59,000(1+.1296)-6
= -85,000 + 52,810 + 28,399
=-3,790.9
NPV = -3,790.9
Question 15
Suppose Mr. Agirich is considering the purchase of a
center pivot irrigation system. He estimates that the
after-tax net cash flows associated with this investment
are as follows. Assume that the marginal tax rate is 28%.
Component
Net Cash Flow
0
$-85,000
1
$15,000
2
$15,000
Year
3
$15,000
4
$15,000
5
$15,000
6
$59,000
B. Explain and show how to calculate the internal rate
of return (IRR) on this investment (estimate
within ½% accuracy).
The internal rate of return (yield) is the rate that makes the
pv(cash inflows) = PV(cash outflows), i.e., NPV=0. Search for
the answer.
NPV = 0 = -85,000 + 15,000 [USPVr%,5]
+ 59,000(1+r)-6
r
NPV
12.96
-3790
11%
1,982
12%
-1,037
11.5%
452
---------------------11.650
The internal rate of return
is between 11.5% and 12%.
If you continue to search
or use a calculator, the IRR
is equal to 11.65%.
Question 15
Suppose Mr. Agirich is considering the purchase of a
center pivot irrigation system. He estimates that the
after-tax net cash flows associated with this investment
are as follows. Assume that the marginal tax rate is 28%.
Component
Net Cash Flow
0
$-85,000
1
$15,000
2
$15,000
Year
3
$15,000
4
$15,000
5
$15,000
6
$59,000
C. Graphically show the relationship between the net
present value (NPV) and the discount rate. Use NPV as
the vertical axis and discount rate as the horizontal axis.
Use at least four data points.
2500
2000
1500
1000
NPV
500
0
-5000.11
0.115
0.12
-1000
-1500
-2000
-2500
-3000
Discount Rate
0.125
Question 15
Suppose Mr. Agirich is considering the purchase of a
center pivot irrigation system. He estimates that the
after-tax net cash flows associated with this investment
are as follows. Assume that the marginal tax rate is 28%.
Component
Net Cash Flow
D.
0
$-85,000
1
$15,000
2
$15,000
Year
3
$15,000
4
$15,000
5
$15,000
Is this an acceptable investment? Why?
6
$59,000
Answer 15.D
This is not an acceptable investment. The
NPV is less than zero which implies that
the rate of return is less than what was
required. In fact, the after-tax required
rate of return was 12.96% but the aftertax rate of return was less than 12%.
Question 16
 Suppose that you are considering the purchase
of a bond that costs $1,060 today and you plan
on selling the bond in four years. Assume that
the bond matures in 11 years, has a par value of
$1,000, pays a coupon of 8 percent (annually),
and the coupon is paid semiannually (8s).

A. Calculate the market value (price) of the bond in
four years if the bond’s market rate is 12%.
0
1
MV
2*7=14
...
...
2
40
r = 12/2 = 6 %
40
1,000
40
Calculate the Market Value (MV). This is an 11 year bond.
In four years there will be 7 years left.
Market rate = 12/2 = 6%
MV = 40 [USPV6%, 14] +1,000(1+.06)-14
14
6
?
40
1000
N
i%
PV
PMT
FV
01/16/97
Agricultural Finance
MV=814.10
28
Question 15
 Suppose that you are considering the purchase
of a bond that costs $1,060 today and you plan
on selling the bond in four years. Assume that
the bond matures in 11 years, has a par value of
$1,000, pays a coupon of 8 percent (annually),
and the coupon is paid semiannually (8s).
 B. Calculate the yield on this bond
investment if you sell the bond in four years
from today and the bond’s market rate is
12%.
0
1
-1060
40
...
... 40
2
2*4=8
40
r = i/2 = ? %
814.1
Calculate the Yield (r), Convert to Annual Rate (i)
Purchase Price = 1,060, Sale price = $814.1 (see 7.A)
1,060 = 40 [USPVr%, 8] +814.1(1+r)-8
8
?
-1,060
40
814.1
N
i%
PV
PMT
FV
01/16/97
Agricultural Finance
r=0.97% & i=1.9%
34
Question 16
Is an investment profitable if the the total
cash inflows are greater than the total cash
outflows? Explain
Answer 16
.
Not always. This measure and rule
ignores the time value of money. If you
paid $100 for an investment today and
received $101 10 years from now, total
cash inflows would be greater than total
cash outflows. It may not be profitable in
the sense that you probably have other
investment opportunities that pay more
money i.e., have a higher rate of return.
Question 17
Does the Net Present Value (NPV)
increase or decrease when the yield of an
investment increases? Explain.
Answer 17
Neither. By definition the yield is the rate
that makes the NPV=0. Thus, NPV is
always zero when the discount rate is
equal to the yield. The NPV is dependent
on the discount rate used, not the yield of
an investment.
Question 18
 Suppose
that you have just graduated from
TAMU and you have a job paying $38,000
per year. You would like to save $20,000 so
that you can make a downpayment on a
house in 5 years. How much would you have
to put in the bank each month if the bank
pays 6 percent on savings accounts (assume
you put the money in the bank at the end of
the month and interest is compounded
monthly)?
0
1
-A
2
-A
...
5*12=60
-A r =6/12=0.5%
20,000
V0 = A [USPVr,N]
Present Value of an Uniform Annuity
20,000 = A [USFV0.5%, 60]
60
0.5
0
?
20,000
N
i%
PV
PMT
FV
A = $286.66
Question 19
 Suppose
that you have an opportunity to buy a
house for $100,000. You have enough money
in your bank account to make a $20,000
downpayment. Suppose you borrow $80,000 to
buy the house and will repay the loan over 30
years. The annual interest on the loan is eight
percent. The bank requires equal monthly
payments.
A.
Calculate the monthly payments.
0
80,000
1
-A
2
-A
V0 = A [USPVr,N]
...
30*12=360
-A r =8/12=0.67%
Present Value of an Uniform Annuity
80,000 = A [USPV0.67%, 360]
360
0.67
80,000
?
0
N
i%
PV
PMT
FV
A = $587.01
Question 19 Conintued
 Suppose
that you have an opportunity to buy a
house for $100,000. You have enough money
in your bank account to make a $20,000
downpayment. Suppose you borrow $80,000 to
buy the house and will repay the loan over 30
years. The annual interest on the loan is eight
percent. The bank requires equal monthly
payments.
B.
How much interest will you pay on this loan if
you keep the loan for 30 years?
Interest
Total Payments=587.01*360 =
 211,324
Total Interest = 211,324-80,000 =
 131,324.2
Question 20
 Suppose
that you have an opportunity to start a
computer business in the shadow of TAMU.
You are sure it will be a successful business but
you don’t have any money to get it started.
Your parents have agreed to lend you $100,000
today so that you can start the business. They
will charge you six-percent interest and require
that you pay the loan back, principal and
interest, at the end of five years.
A.
How much money will you owe your parents in
five years?
0
5
100,000
r = 6%
-V5
VN = V0 (1+r)N Future Value of a Single Sum
V5 = 100,000
(1+.06)5
5
6
100,000
0
V5
N
i%
PV
PMT
FV
V5 = 133,822.56
Question 20 Continued
Part B
 Suppose at the end of five years you don’t have
the money to pay your parents the money you
owe them (Part A.). A friendly bank will lend
you the money. The annual interest rate is 12
percent. The bank will lend you the money for
10 years and requires equal annual payments.
Calculate the annual payments.
0
1
-A
2
-A
10
...
-A
r =12%
133,822.56
V0 = A [USPVr,N]
Present Value of an Uniform Annuity
133,822.56 = A [USPV12%, 10]
10
12
133,822
?
0
N
i%
PV
PMT
FV
A = $23,684.47
Question 20 Continued
Part C
 Suppose at the end of five years you don’t have
the money to pay your parents the money you
owe them (Part A.). You agree to take out a
loan with the local bank to pay your parents as
much as you can. The annual interest rate is 12
percent. The bank will lend you the money for
10 years and requires equal annual payments.
The maximum annual payment you can make is
$10,000. What is the maximum amount of
money that you can borrow from the bank?
0
1
-10k
2
-10k
10
...
-10k
r =12%
V0
V0 = A [USPVr,N]
Present Value of an Uniform Annuity
V0 = 10,000 [USPV12%, 10]
10
12
V0
10,000
0
N
i%
PV
PMT
FV
V0=56,502.23
Question 21
Suppose
you have received permission to sell
“Snow Cones” on TAMU campus for four years.
You can buy a Snow Cone machine for $2,000
and can sell it for $500 in four years. The IRS
will allow this machine to be depreciated using
straight-line for seven years. You anticipate that
you can sell 5,000 Snow Cones per year. You can
sell the cones at $0.50 per cone and it will cost
you $0.35 per cone to make (including labor).
Assume that you require a 14 percent return to
capital and your are in the 15 percent tax
bracket.
 A.
Layout the cash flows.
Period
Component
Cost
0
1
-2,000
Initial Cost
2
...
4
Period
Component
Cost
NR(1-m)
0
1
2
...
4
-2,000
637.5
637.5 ...
637.5
Operating Revenue = 5,000 * .5 = 2,500
Operating Expense = 5,000 * .35 = 1,750
Net Returns = 2,500 - 1,750 = 750
After-tax Net Returns = 750(1-.15) = 637.50
Period
Component
Cost
NR(1-m)
mD
0
1
2
...
4
-2,000
637.5
42.9
637.5 ...
42.9 ...
637.5
42.9
Annual Depreciation = 2,000/7 = 285.71
Tax Savings: Depreciation = 285.71*.15 = 42.86
Period
Component
Cost
NR(1-m)
0
2
...
4
-2,000
mD
Tvat
NCF
1
-2,000
637.5
42.9
637.5 ...
42/9 ...
637.5
42.9
553.6
680.36
680.36
1,233.93
After-Tax Terminal Value=
500-[500-(2,000-(285.71*4))].15 = 553.57
Question 21 Continued
B. Calculate the Net Present Value and
indicate whether not this is an acceptable
investment
Period
Component
Cost
NR(1-m)
0
2
...
4
-2,000
mD
Tvat
NCF
1
-2,000
637.5
42.9
637.5 ...
42.9 ...
637.5
42.9
553.6
680.36
680.36
1,233.93
After-tax discount rate = 0.14(1-.15) = 0.119 or 11.9%
NPV = -2,000 + 637.5[USPV11.9%,4] + 42.9 [USPV11.9%,4]
+553.6(1+.119)-4
= -2,000 +1,940.4 + 130.45 +353.06
=423.91 Acceptable
Problem 21 Continued
Explain and show how to calculate the
internal rate of return (IRR) on this
investment (estimate within ½% accuracy if
time permits).
NPV = -2,000 + 637.5[USPV11.9%,4] + 42.9 [USPV11.9%,4]
+553.6(1+.119)-4
Set NPV = 0 and solve for r
NPV = 0 = -2,000 + 637.5[USPVr%,4] + 42.9 [USPVr%,4]
+553.6(1+r)-4
r
NPV
0.119423.91
0.215
-27.67
0.205
6.03
----------------------0.2068
0
IRR = 20.68%
This is an after-tax
Internal Rate of
Return
Question 22
An increase in the general price level is
called __________________.
Inflation
Question 23
Explain why the yield on bonds issued by
Microsoft is higher than the yield on
comparable bonds issued by the U.S.
government.
Microsoft
Bonds are more risky than U.S.
Treasury bonds. That is, there is a greater
likelihood that Microsoft will default on bonds
than the U.S. Government. Because of the
greater risk, investors demand a greater profit,
thus, a higher yield.
Question 24
When choosing a discount rate, what is
the lower bound (the lowest acceptable
discount rate)?
The
discount rate must be at least as high as the
cost of capital. Thus the cost of capital forms a
lower bound. If the discount rate was set any
lower, investments would be taken that would not
recover the cost of capital.
Question 25
Suppose that new tractors are selling for
$85,000 today but you decide to wait five
years before buying a new tractor. If the
real price of tractors do not change but
the inflation rate is 10% per year, how
much will you pay for a new tractor in
five years? Show all your work.
Question 25
Answer

Fn = F*n (1+If)n
F5 = 85,000(1+.1) 5
= $136,893
Question 26
Calculate the present value of the after-
tax net returns to land in the 7th year if
the real pre-tax net returns to land today
are $100, real net returns to land are
assumed to increase by 4% each year, the
inflation rate is 5%, the marginal tax rate
is 30%, and the pretax risk adjusted
discount rate is 10%. Show all your
work.
Question 26
Answer
F*n = F*0 (1+g)n
g=real growth rate = 4%
n=7
F*7 = 100 (1+.04)7 = 131.59
Continued
Question 26 Answer Continued
Real
Nominal
Net Returns
After-tax
Nominal NR
“n”
F*n
Fn = F*n (1+If)n
Fn (1-m)
7
131.59
F1 = 131.59(1+.05)7
= 185.16
185.16(1-.3) =
129.62
Period Net Returns
After-tax, risk adjusted discount rate = .1(1-.3) = 0.07 ot 7%
PV(after-tax net return in 7th year = 129.62 (1+.07)-7 = 80.72
Question 27
Suppose that you borrow $80,000 to buy
a tractor and the loan is fully amortized
at 12% over eight years. Calculate the
tax savings from claiming interest as an
expense in the second year. Assume that
the pretax discount rate is 14%, the
marginal tax rate is 30.3% and inflation
is expected to be 6%. Show all your
work.
Question 27 -- Answer
Annual Payment =A
80,000 = A [USPV12%,8]
A = 16,104.23
Marginal tax Rate = m =30.3%
Continued
Question 27 -- Answer Continued
Loan Amortization Schedule
Interest
Rate
(1)
Beginning Total
Period
(2)
Interest Principal Loan
Tax
Principal Payment Payment Payment Balance Savings
(5)=(1)*(3) (6)=(4)-(5) (7)=(3)-(6)
(8)=(5)*m
(3)
(4)
0
80,000
.12
1
80,000
16,104
9,600
6,504
73,496
2,909
.12
2
73,496
16,104
8,819.49
7,285
66,211
2,672.31
Tax Savings from Claiming Interest
in the 2nd year = $2,672.31
Investment Description
Sanderson Farms, Inc., a major poultry producer, has established a major poultry
operation in the Brazos Valley. The facility includes a hatchery, a feed mill, and a
poultry processing plant with a capacity to process approximately 625,000 birds
per week.
Sanderson Farms will contract independent growers to support the
poultry facility. Growers finance and build their own poultry houses to supply
pullets (young breeder hens), hatching eggs, and broilers to Sanderson Farms.
Suppose Mr. Agirich, of Aggie Farms, wants to diversify and is
considering the construction and operation of two breeder hen houses. The
estimated cost of two fully-equipped hen houses is $310,000. Annual revenue is
expected to be $88,400. Annual expenses is expected to be $22,100. Mr. Agirich
plans on selling the hen houses in three years and expects that he can sell them for
$255,000. Mr. Agirich anticipates that his marginal tax rate over the next four
years will be 28%. The IRS will allow Aggie Farms to depreciate the hen houses
using straight-line over 20 years.
Investment Description
Mr. Agirich has calculated the after-tax cash flows as follows:
Component:
Cost
0
1
2
3
($310,000.00)
After-tax Net
Returns
$0.00
$47,736.00
$47,736.00
$47,736.00
Tax Savings:
Depreciation
$0.00
$4,340.00
$4,340.00
$4,340.00
After-tax
Terminal Value
$0.00
$0.00
$0.00
$257,380.00
($310,000.00)
$52,076.00
$52,076.00
$309,456.00
Net Cash Flow
from Investment
Question 1
Mr. Agirich can save $4,340 in taxes in
the third year because depreciation is tax
deductible. Is the $4,340 real or
nominal?
Answer
 Nominal
Question 2.A
Suppose Mr. Agirich requires at least a
10% pre-tax, risk-free return on capital
investments and a 6% risk premium on
projects of comparable risk to the hen
houses.
 A.
Calculate the investment’s Net Present
Value.
Discount Rate:
After-tax risk-adjusted rate
r = [ rbt + PREM ] (1-m)
 r = after-tax, risk-adjusted discount rate
 rbt = before-tax, risk-free discount rate
 PREM = risk premium -- adjustment for
risk
 m = marginal tax rate
r = [.10 + .06 ] (1-.28)
r = 0.16 (1-.28)
r = .1152 or 11.52%
7/16/2015
Agricultural Finance
86
Calculate NPV
NPV = -C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N
NPV = -310,000 + 47,7360[USPV11.52%,3] + 4,340 [USPV11.52%,3]
+ 257,380 (1+.1152)-3
NPV = -310,000 +115,606.19 +10,510.53 + 185,573.74
= 1,690.46
NPV = $ 1,690.46
Question 2.B
Suppose Mr. Agirich requires at least a
10% pre-tax, risk-free return on capital
investments and a 6% risk premium on
projects of comparable risk to the hen
houses.
 B.
Calculate the minimum after-tax net
return that can be earned on this investment
per year and still have this investment be an
acceptable investment, holding everything
else constant.
Break-Even
NPV = -310,000 + 47,7360[USPV11.52%,3] + 4,340 [USPV11.52%,3]
+ 257,380 (1+.1152)-3
Set NPV = 0 and Solve for the After-tax Net Return (ATNR)
0 = -310,000 + ATNR [USPV11.52%,3] + 4,340 [USPV11.52%,3]
+ 257,380 (1+.1152)-3
0 = -310,000 + ATNR [USPV11.52%,3] +10,510.53 + 185,573.74
Break-Even
0 = -310,000 + ATNR [USPV11.52%,3] +10,510.53 + 185,573.74
Note:
V0 = 1 [USPV11.52%,3]
2.4218 = [USPV11.52%,3]
0 = -310,000 + ATNR (2.4218) +10,510.53 + 185,573.74
ATNR = 47,038
If the after-tax net returns per year are below $47,038, the
NPV<0, thus this investment would be unacceptable.
Question 2.C
Suppose Mr. Agirich requires at least a
10% pre-tax, risk-free return on capital
investments and a 6% risk premium on
projects of comparable risk to the hen
houses.
 C.
Graphically show the relationship
between the after-tax net return and the Net
Present Value. Use at least three points on
the graph (hint: use information from
problems 2.A and 2.B for two of the points).
Sensitivity Analysis
NPV = -310,000 + ATNR (2.4218) +10,510.53 + 185,573.74
NPV = ATNR (2.4218) - 113,915.73
ATNR
46,750
47,038
47,736
NPV
(696)
0
1,690
Sensitivity Analysis
1500
1000
500
NPV
0
46500
46750
47000
-500
-1000
-1500
ATNR
47250
47,500
Question 2.D
Suppose Mr. Agirich requires at least a
10% pre-tax, risk-free return on capital
investments and a 6% risk premium on
projects of comparable risk to the hen
houses.

D. Suppose that Mr. Agirich made a mistake when calculating
the after-tax net returns. Suppose that the projected annual
revenues of $88,400 and annual expenses of $22,100 are
estimated as real dollars. Assume that Mr. Agirich expects that
inflation will be 3% and the annual revenue and annual
expenses will increase at the rate of inflation over the life of the
investment. Calculate the present value of the after-tax net
returns over the three year life of the investment.
Real Net Returns = 88,400 - 22,100 = 66,300
Real
Period Net Returns
Nominal
Net Returns
After-tax
Nominal NR
“n”
F*n
Fn = F*n (1+If)n
Fn(1-m)
1
66,300
68,289(1-.28) =
49,168
2
66,300
3
66,300
F1 = 66,300 (1+.03)1
= 68,289
F2= 66,300 (1+.03)2
= 70,337
F3 = 66,300 (1+.03)3
= 72,447
7/16/2015
Agricultural Finance
70,337 (1-.28) =
50,643
72,447 (1-.28) =
52,162
95
Present Value of
After-Tax Net Returns
PV(ATNR) = 49,168 (1.1152)-1 +50,643 (1,1152)-2 +52,162(1.1152)-3
= 44,088.95 + 40,720.57 + 37,609.36
= 122,418
Question 3.A
Suppose a bank has offered to lend Mr.
Agirich $248,000. The loan will be fully
amortized at a 10% interest rate over five
years (annual payments).
 A.
Calculate the annual loan payment.
0
1
-A
2
5
-A
...
-A
r = 10 %
248,000
V0= A [USPVr,N]
Present Value of an Uniform Annuity
75,000= A [USPV10%,5]
5
10
248,000
N
i%
PV
7/16/2015
where A = loan payment
-A
PMT
Agricultural Finance
0
AA=65,421.78
FV
98
Question 3.B
Suppose a bank has offered to lend Mr.
Agirich $248,000. The loan will be fully
amortized at a 10% interest rate over five
years (annual payments).
 B.
Calculate the annual tax savings from
claiming interest as a tax deduction in each
of the first three years.
Interest
Rate
(1)
Beginning
Principal
(3)
Loan Amortization Schedule
Total
Interest
Principal
Payment
Payment
Payment
(4)
(5)=(1)*(3) (6)=(4)-(5)
10.00%
10.00%
Period
(2)
0
1
2
$248,000.00
$207,378.22
Loan
Tax
Balance
Savings
(7)=(3)-(6)
(8)=(5)*tax
$248,000.00
$65,421.78 $24,800.00 $40,621.78
$207,378.22
$6,944.00
$65,421.78 $20,737.82 $44,683.95
$162,694.27
$5,806.59
10.00%
3
$162,694.27
$65,421.78 $16,269.43 $49,152.35
$113,541.92
$4,555.44
Question 3.C
Suppose a bank has offered to lend Mr.
Agirich $248,000. The loan will be fully
amortized at a 10% interest rate over five
years (annual payments).
)
C. Calculate the net cash flow after debt
for this investment.
Financial Feasibility
Component:
Cash Flow from investment
Loan Amount
0
-310000.00
52076.00
52076.00
309456.00
-65421.78
-65421.78
-65421.78
6944.00
5806.59
4555.44
248000.00
Loan Payment
Tax Savings from Interest
0.00
Balloon Payment of Loan Principal
Net Cash Flows after debt flows
3
2
1
-62000.00
-6401.78
0.00 -113541.92
-7539.18
135047.74
Question 3.D
Suppose a bank has offered to lend Mr.
Agirich $248,000. The loan will be fully
amortized at a 10% interest rate over five
years (annual payments).
 D.
Is there a potential liquidity problem if
Mr. Agirich invests in the hen houses?
Explain..
Potential Liquidity Problem
Must have $62,000 in cash for the down payment
Must be able to generate $6,402 in the first year and
$7,539 the second year from other parts of the business.
If not, the investment is financially infeasible.
Question 3.E
Suppose a bank has offered to lend Mr.
Agirich $248,000. The loan will be fully
amortized at a 10% interest rate over five
years (annual payments).
 E.
How can Mr. Agirich determine if this
investment is financially feasible?
Financially Feasible
A Projected Cash Flow Statement can be
used to determine if enough surplus cash
can be generated from other parts of the
business to meet the cash deficits caused
by the purchase of the hen houses. If so,
the investment is financially feasible. If
not, Mr. Agirich will not be able to invest
in the hen houses even though it would be
profitable.
Question 4
Suppose Mr. Agirich decides to keep the
hen houses 10 years before selling them.
Also suppose that a bank will lend him
$248,000.
The loan will be fully
amortized at a 11% interest rate over 12
years (annual payment). Calculate the
loan balance at the end of the tenth year
after the scheduled annual payment.
0
1
-A
2
12
-A
...
-A
r = 11 %
248,000
V0= A [USPVr,N]
Present Value of an Uniform Annuity
75,000= A [USPV11%,12]
12
11
248,000
N
i%
PV
7/16/2015
where A = loan payment
-A
PMT
Agricultural Finance
0
AA=38,198.8
FV
108
0
1
2
-38,198.8
3
0
- 38,198.8
r = 11 %
BV
V0= A [USPVr,N]
Present Value of an Uniform Annuity
Book Value= 38,198.8 [USPV11%,2]
2
11
BV
N
i%
PV
7/16/2015
-38,198.8
PMT
Agricultural Finance
where BV = Loan Balance
0
BV = 65,416.3
FV
109
Investment Description
Yield monitoring systems, which are installed on combines, use the Global
Positioning System (GPS) and a mechanical yield monitor to link crop
yield to a given location in a field. Many farmers have purchased monitorequipped combines ($8,000) but do not have the knowledge or desire to
create yield maps from the data collected. It is estimated that a farmer can
increase net returns per acre by $10-$15 per acre by using yield maps
correctly via increased yields and reduced input costs.
Suppose Mr. Agirich of Aggie Farms is an expert in using yield
monitoring systems and using yield maps to enhance farm income. Mr.
Agirich believe he can make money if he sets up a consulting firm that
helps other farmers make yield maps and provides instruction on how to
use the yield maps. Securing a good customer base will be essential for this
to be a profitable venture. Mr. Agirich believes that farmers will pay $3.00
per acre for this service and he believes that he can obtain a clientele base
that will pay him to process 31,000 acres.
Investment Description (cont.)
Mr. Agirich estimates that he will have to produce an
average of five different maps per thousand acres per year. With the
yield mapping software Aglink it takes less than 30 minutes to
produce one map. The initial cost of starting this business is $11,000
that includes yield mapping software, computer equipment, legal
fees, and office supplies. Mr. Agirich anticipates that his marginal
tax rate over the next four years will be 28%. The IRS will allow
Aggie Farms to depreciate the start-up cost using straight-line over
four years.
Annual expenses are expected to be $91,000 including
salaries, office rental, utilities, internet services, mail, advertising
and travel costs. Mr. Agirich plans on selling this business to his son
in three years for $20,000.
Investment Description
Mr. Agirich has calculated the after-tax cash flows as follows:
Component:
Cost
0
1
2
3
($11,000.00)
After-tax Net
Returns
$0.00
$1,440.00
$1,440.00
$1,440.00
Tax Savings:
Depreciation
$0.00
$770.00
$770.00
$770.00
After-tax
Terminal Value
$0.00
$0.00
$0.00
$15,170.00
($11,000.00)
$2,210.00
$2,210.00
$17,380.00
Net Cash Flow
from Investment
Question 1
 Suppose
Mr. Agirich expects inflation to be
4% over the next three years and requires a
10% return on investments. Calculate the
real tax savings from depreciation in the
third year.
Answer
 Fn*=Fn(1+If)n
 Fn*=770(1+.04)3 = 684.53
Question 2.A
Suppose Mr. Agirich requires at least a
5% pre-tax, risk-free return on capital
investments and a 20% risk premium on
projects of comparable risk to the yieldmapping business. The interest rate on
loans is 15%.
A. Calculate the investment’s Net
Present Value.
Discount Rate:
After-tax risk-adjusted rate
r = [ rbt + PREM ] (1-m)
 r = after-tax, risk-adjusted discount rate
 rbt = before-tax, risk-free discount rate
 PREM = risk premium -- adjustment for
risk
 m = marginal tax rate
r = [.05 + .20 ] (1-.28)
r = 0.25 (1-.28)
r = .18 or 18%
7/16/2015
Agricultural Finance
115
Calculate NPV
NPV = -C0 +NR(1-m)[USPVr,N] +mD [USPVr,N] + TVat (1+r)-N
NPV = -11,000 + 1,440[USPV18%,3] + 770 [USPV18%,3]
+ 15,170 (1+.18)-3
NPV = -11,000 +3,130.95 +1,674.19 + 9,232.93
= 3,038.07
NPV = $ 3,3038.07
Question 2.B
 Suppose
Mr. Agirich requires at least a 5%
pre-tax, risk-free return on capital
investments and a 20% risk premium on
projects of comparable risk to the yieldmapping business. The interest rate on loans
is 15%.
B. As
stated above, Mr. Agirich expects to process
31,000 acres for clients and get paid $3 per acre.
Calculate the least number of acres that can be
processed and still have this investment be an
acceptable investment, holding everything else
constant.
Break-Even
NPV = -11,000 + 1,440[USPV18%,3] + 770 [USPV18%,3]
+ 15,170 (1+.18)-3
Set NPV = 0 and Solve for the After-tax Net Return (ATNR)
0 = -11,000 + NR(1-.28) [USPV18%,3] + 770 [USPV18%,3]
+ 15,170 (1+.18)-3
0 = -11,000 + NR(1-.28) [USPV18%,3] +1,674.19 + 9,232.93
Break-Even
0 = -11,000 + NR(1-.28) [USPV18%,3] +1,674.19 + 9,232.93
Note:
V0 = 1 [USPV11.52%,3]
2.1743 = [USPV11.52%,3]
0 = -11,000 + NR(1-.28) [2.1743] +1,674.19 + 9,232.93
NR = 59.34
Break-Even
NR=Price per Acre * Acres Processed
59.33 = ($3 *AP)-91,000
AP = 91,059.33/3
AP = 30,353
If the number of acres processed (AP) per year are below
30,353, the NPV<0, thus this investment would be
unacceptable.
Question 2.C
 Suppose
Mr. Agirich requires at least a 5%
pre-tax, risk-free return on capital
investments and a 20% risk premium on
projects of comparable risk to the yieldmapping business. The interest rate on loans
is 15%.
C.
Graphically show the relationship between the
acres processed and the Net Present Value. Use
at least three points on the graph.
Sensitivity Analysis
(hint: use information from problems 2.A and 2.B for
two of the points).
NPV = -11,000 + [(3*AP)-91,000](1-.28) [2.1743] +1,674.19 + 9,232.93
NPV = 4.6965*AP - 142,553
ATNR
30,000
30,353
31,000
NPV
(1,658)
0
3,038
Sensitivity Analysis
4000
3000
2000
NPV 1000
0
30000
30500
-1000
-2000
Processed Acres
31000
Question 2.D
Suppose
Mr. Agirich requires at least a 5% pretax, risk-free return on capital investments and a
20% risk premium on projects of comparable
risk to the yield-mapping business. The interest
rate on loans is 15%.
 D.
Suppose that Mr. Agirich made a mistake when
calculating the after-tax net returns. Suppose that the
projected revenue per acre of $3 and annual expenses
of $91,000 are estimated as real dollars. Assume that
Mr. Agirich expects that inflation will be 4% and the
annual revenue and annual expenses will increase at
the rate of inflation over the life of the investment.
Calculate the present value of the after-tax net returns
over the three-year life of the investment.
Real Net Returns = (3*31,000) -91,000 = 2,000
Real
Period Net Returns
Nominal
Net Returns
After-tax
Nominal NR
“n”
F*n
Fn = F*n (1+If)n
Fn(1-m)
1
2,000
2080 (1-.28) =
1,497.6
2
2,000
3
2,000
F1 = 2,000 (1+.04)1
= 2080
F2= 2,000 (1+.04)2
= 2163
F3 = 2,000 (1+.04)3
= 2,249
7/16/2015
Agricultural Finance
2163 (1-.28) =
1,557.5
72,447 (1-.28) =
1,619.8
125
Present Value of
After-Tax Net Returns
PV(ATNR) = 1,497.6 (1.18)-1 +1,557.5 (1.18)-2 +1,619.8(1.18)-3
= 1,269.15 + 1,118.57 + 985.86
= 3,373.58
Question 3.A
Suppose a bank has offered to lend Mr.
Agirich $10,000. The loan will be fully
amortized at a 15% interest rate over two
years (annual payments).
 A.
Calculate the annual loan payment.
0
1
-A
2
5
-A
...
-A
r = 15 %
10,000
V0= A [USPVr,N]
Present Value of an Uniform Annuity
10,000= A [USPV15%,2]
2
15
10,000
N
i%
PV
7/16/2015
where A = loan payment
-A
PMT
Agricultural Finance
0
AA=6,151.16
FV
128
Question 3.B
Suppose a bank has offered to lend Mr.
Agirich $10,000. The loan will be fully
amortized at a 15% interest rate over two
years (annual payments).
 B.
Show a complete amortization schedule
for this loan.
Loan Amortization Schedule
Interest
Rate
(1)
15.00%
15.00%
Period
(2)
0
1
2
Beginning
Principal
(3)
$10,000.00
$5,348.84
Total
Interest Principal
Loan
Tax
Payment Payment Payment Balance Savings
(4)
(5)=(1)*(3) (6)=(4)-(5) (7)=(3)-(6) (8)=(5)*tax
$10,000.00
$6,151.16 $1,500.00 $4,651.16 $5,348.84 $225.00
$6,151.16 $802.33 $5,348.84
$0.00 $120.35
Question 3.C
Suppose a bank has offered to lend Mr.
Agirich $10,000. The loan will be fully
amortized at a 15% interest rate over two
years (annual payments).
)
C. Calculate the net cash flow after debt
for this investment.
Financial Feasibility
Component:
0
Cash Flow from investment
-11000.00
Loan Amount
10000.00
Loan Payment
Tax Savings from Interest
Balloon Payment of Loan Principal
Net Cash Flows after debt flows
-1000.00
1
2
3
2210.00
2210.00
17380.00
-6151.16
-6151.16
0.00
420.00
224.65
0.00
0.00
0.00
0.00
-3521.16
-3716.51
17380.00
Question 3.D
Suppose a bank has offered to lend Mr.
Agirich $10,000. The loan will be fully
amortized at a 15% interest rate over two
years (annual payments).
 D.
Is there a potential liquidity problem if
Mr. Agirich invests in yield-mapping
business? Explain.
Potential Liquidity Problem
Must have $1,000 in cash for the down payment
Must be able to generate $3,521 in the first year and
$3,716 the second year from other parts of the business.
If not, the investment is financially infeasible.
Question 3.E
Suppose a bank has offered to lend Mr.
Agirich $10,000. The loan will be fully
amortized at a 15% interest rate over two
years (annual payments).
 E.
Suppose it is projected that the net cash
flows after debt are negative in the first and
second year. How can Mr. Agirich determine
if this investment is financially feasible?
Financially Feasible
 A Projected
Cash Flow Statement can be
used to determine if enough surplus cash can
be generated from other parts of the
business to meet the cash deficits caused by
the purchase of the yield-mapping business.
If so, the investment is financially feasible. If
not, Mr. Agirich will not be able to invest in
the yield-mapping business even though it
would be profitable.
Question 4
 Suppose
Mr. Agirich decides to keep the
yield-mapping business 12 years before
selling it. Also suppose that a bank will lend
him $10,000. The loan will be fully
amortized at a 15% interest rate over 20
years (annual payment). Calculate the loan
balance at the end of the twelfth year after
the scheduled annual payment.
0
1
-A
2
20
-A
...
-A
r = 15 %
10,000
V0= A [USPVr,N]
Present Value of an Uniform Annuity
10,000= A [USPV15%,20]
20
15
10,000
N
i%
PV
7/16/2015
where A = loan payment
-A
PMT
Agricultural Finance
0
AA=1,597.61
FV
138
0
1
2
- 1,597.61
r = 15 %
Present Value of an Uniform Annuity
Book Value= 1,597.61[USPV15%,8]
8
15
BV
N
i%
PV
7/16/2015
8
- 1,597.61 ... 1,597.61
BV
V0= A [USPVr,N]
...
- 1,597.61
PMT
Agricultural Finance
where BV = Loan Balance
0
BV = 7,169
FV
139