Winter 1, 2013
7/2 /2012
Chapter 4.
Ch 04 P35 Build a Model
Except for charts and answers that must be writ en, only Excel formulas that use cel references or functions wil be accepted for credit.
Numeric answers in cel s wil not be accepted.
To get the dialog box, click on fx, then Financial, then FV, then OK.
Inputs:
PV
=
10 0
I/YR
=
10%
N
=
5
Formula:
FV = PV(1+I)^N =
Wizard (FV):
Experiment by changing the input values to se how quickly the output values change.
Years (D10):
Interest Rate (D9)
$-
0%
5%
20%
0
$0.0
$0.0
$0.0
1
$0.0
$0.0
$0.0
2
$0.0
$0.0
$0.0
3
$0.0
$0.0
$0.0
4
$0.0
$0.0
$0.0
5
$0.0
$0.0
$0.0
Inputs:
FV
=
10 0
I/YR
=
10%
N
=
5
Formula:
PV = FV/(1+I)^N =
Wizard (PV):
d.
A security has a cost of $1,0 0 and wil return $2,0 0 after 5 years.
What rate of return does the
security provide?
Inputs:
PV
=
-10 0
FV
=
20 0
I/YR
=
?
N
=
5
Wizard (Rate):
Inputs:
PV
=
-30
FV
=
60
I/YR
=
growth rate
2%
N
=
?
Wizard (NPER):
= Years to double.
Inputs:
PMT =
$1,0 0
N =
5
I/YR
=
15%
PV:
Use function wizard (PV)
PV
=
FV:
Use function wizard (FV)
FV
=
g.
How would the PV and FV of the above an uity change if it were an an uity due rather than an
ordinary an uity?
PV an uity due
=
x
=
Exactly the same adjustment is made to find the FV of the an uity due.
FV an uity due
=
x
=
h.
What would the FV and the PV for parts a and c be if the interest rate were 10% with
Part a.
FV with semian ual compounding:
Orig. Inputs
New Inputs
Inputs:
PV
=
10 0
10 0
I/YR
=
10%
5%
N
=
5
10
Formula:
FV = PV(1+I)^N =
Wizard (FV):
Part c.
PV with semian ual compounding:
Orig. Inputs
New Inputs
Inputs:
FV
=
10 0
10 0
I/YR
=
10%
5%
N
=
5
10
Formula:
PV = FV/(1+I)^N =
Wizard (PV):
i.
Find the PV and FV of an investment that makes the fol owing end-of-year payments.
The
interest rate is 8%.
Year
Payment
1
10
2
20
3
40
Rate
=
8%
To find the PV, use the NPV function:
PV
=
Year
Payment
x
(1 + I )^(N-t)
=
FV
1
10
1.17
1 6.64
2
20
1.08
216.0
3
40
1.0
40 .0
Sum
=
An alternative procedure for finding the FV would be to find the PV of the series using the NPV
function, then compound that amount, as is done below:
PV
=
FV of PV
=
Original amount of mortgage:
50 0
Term of mortgage:
10
Interest rate:
0.085
An ual payment (use PMT function):
Year
Beg. Amt.
Pmt
Interest
Principal
End. Bal.
1
$0.0
$0.0
$0.0
$0.0
2
$0.0
$0.0
$0.0
$0.0
$0.0
3
$0.0
$0.0
$0.0
$0.0
$0.0
4
$0.0
$0.0
$0.0
$0.0
$0.0
5
$0.0
$0.0
$0.0
$0.0
$0.0
6
$0.0
$0.0
$0.0
$0.0
$0.0
7
$0.0
$0.0
$0.0
$0.0
$0.0
8
$0.0
$0.0
$0.0
$0.0
$0.0
9
$0.0
$0.0
$0.0
$0.0
$0.0
10
$0.0
$0.0
$0.0
$0.0
$0.0
(1)
Create a graph that shows how the payments are divided betwe n interest and
principal repayment over time.
(2)
Sup ose the loan cal ed for 10 years of monthly payments, 120 payments in al , with
the same original amount and the same nominal interest rate.
What would the
amortization schedule show now?
The monthly payment would be:
Month
Beg. Amt.
Pmt
Interest
Principal
End. Bal.
1
$0.0
$0.0
$0.0
$0.0
2
$0.0
$0.0
$0.0
$0.0
$0.0
3
$0.0
$0.0
$0.0
$0.0
$0.0
4
$0.0
$0.0
$0.0
$0.0
$0.0
5
$0.0
$0.0
$0.0
$0.0
$0.0
6
$0.0
$0.0
$0.0
$0.0
$0.0
7
$0.0
$0.0
$0.0
$0.0
$0.0
8
$0.0
$0.0
$0.0
$0.0
$0.0
9
$0.0
$0.0
$0.0
$0.0
$0.0
10
$0.0
$0.0
$0.0
$0.0
$0.0
1
$0.0
$0.0
$0.0
$0.0
$0.0
12
$0.0
$0.0
$0.0
$0.0
$0.0
13
$0.0
$0.0
$0.0
$0.0
$0.0
14
$0.0
$0.0
$0.0
$0.0
$0.0
15
$0.0
$0.0
$0.0
$0.0
$0.0
16
$0.0
$0.0
$0.0
$0.0
$0.0
17
$0.0
$0.0
$0.0
$0.0
$0.0
18
$0.0
$0.0
$0.0
$0.0
$0.0
19
$0.0
$0.0
$0.0
$0.0
$0.0
20
$0.0
$0.0
$0.0
$0.0
$0.0
21
$0.0
$0.0
$0.0
$0.0
$0.0
2
$0.0
$0.0
$0.0
$0.0
$0.0
23
$0.0
$0.0
$0.0
$0.0
$0.0
24
$0.0
$0.0
$0.0
$0.0
$0.0
25
$0.0
$0.0
$0.0
$0.0
$0.0
26
$0.0
$0.0
$0.0
$0.0
$0.0
27
$0.0
$0.0
$0.0
$0.0
$0.0
28
$0.0
$0.0
$0.0
$0.0
$0.0
29
$0.0
$0.0
$0.0
$0.0
$0.0
30
$0.0
$0.0
$0.0
$0.0
$0.0
31
$0.0
$0.0
$0.0
$0.0
$0.0
32
$0.0
$0.0
$0.0
$0.0
$0.0
3
$0.0
$0.0
$0.0
$0.0
$0.0
34
$0.0
$0.0
$0.0
$0.0
$0.0
35
$0.0
$0.0
$0.0
$0.0
$0.0
36
$0.0
$0.0
$0.0
$0.0
$0.0
37
$0.0
$0.0
$0.0
$0.0
$0.0
38
$0.0
$0.0
$0.0
$0.0
$0.0
39
$0.0
$0.0
$0.0
$0.0
$0.0
40
$0.0
$0.0
$0.0
$0.0
$0.0
41
$0.0
$0.0
$0.0
$0.0
$0.0
42
$0.0
$0.0
$0.0
$0.0
$0.0
43
$0.0
$0.0
$0.0
$0.0
$0.0
44
$0.0
$0.0
$0.0
$0.0
$0.0
45
$0.0
$0.0
$0.0
$0.0
$0.0
46
$0.0
$0.0
$0.0
$0.0
$0.0
47
$0.0
$0.0
$0.0
$0.0
$0.0
48
$0.0
$0.0
$0.0
$0.0
$0.0
49
$0.0
$0.0
$0.0
$0.0
$0.0
50
$0.0
$0.0
$0.0
$0.0
$0.0
51
$0.0
$0.0
$0.0
$0.0
$0.0
52
$0.0
$0.0
$0.0
$0.0
$0.0
53
$0.0
$0.0
$0.0
$0.0
$0.0
54
$0.0
$0.0
$0.0
$0.0
$0.0
5
$0.0
$0.0
$0.0
$0.0
$0.0
56
$0.0
$0.0
$0.0
$0.0
$0.0
57
$0.0
$0.0
$0.0
$0.0
$0.0
58
$0.0
$0.0
$0.0
$0.0
$0.0
59
$0.0
$0.0
$0.0
$0.0
$0.0
60
$0.0
$0.0
$0.0
$0.0
$0.0
61
$0.0
$0.0
$0.0
$0.0
$0.0
62
$0.0
$0.0
$0.0
$0.0
$0.0
63
$0.0
$0.0
$0.0
$0.0
$0.0
64
$0.0
$0.0
$0.0
$0.0
$0.0
65
$0.0
$0.0
$0.0
$0.0
$0.0
6
$0.0
$0.0
$0.0
$0.0
$0.0
67
$0.0
$0.0
$0.0
$0.0
$0.0
68
$0.0
$0.0
$0.0
$0.0
$0.0
69
$0.0
$0.0
$0.0
$0.0
$0.0
70
$0.0
$0.0
$0.0
$0.0
$0.0
71
$0.0
$0.0
$0.0
$0.0
$0.0
72
$0.0
$0.0
$0.0
$0.0
$0.0
73
$0.0
$0.0
$0.0
$0.0
$0.0
74
$0.0
$0.0
$0.0
$0.0
$0.0
75
$0.0
$0.0
$0.0
$0.0
$0.0
76
$0.0
$0.0
$0.0
$0.0
$0.0
7
$0.0
$0.0
$0.0
$0.0
$0.0
78
$0.0
$0.0
$0.0
$0.0
$0.0
79
$0.0
$0.0
$0.0
$0.0
$0.0
80
$0.0
$0.0
$0.0
$0.0
$0.0
81
$0.0
$0.0
$0.0
$0.0
$0.0
82
$0.0
$0.0
$0.0
$0.0
$0.0
83
$0.0
$0.0
$0.0
$0.0
$0.0
84
$0.0
$0.0
$0.0
$0.0
$0.0
85
$0.0
$0.0
$0.0
$0.0
$0.0
86
$0.0
$0.0
$0.0
$0.0
$0.0
87
$0.0
$0.0
$0.0
$0.0
$0.0
8
$0.0
$0.0
$0.0
$0.0
$0.0
89
$0.0
$0.0
$0.0
$0.0
$0.0
90
$0.0
$0.0
$0.0
$0.0
$0.0
91
$0.0
$0.0
$0.0
$0.0
$0.0
92
$0.0
$0.0
$0.0
$0.0
$0.0
93
$0.0
$0.0
$0.0
$0.0
$0.0
94
$0.0
$0.0
$0.0
$0.0
$0.0
95
$0.0
$0.0
$0.0
$0.0
$0.0
96
$0.0
$0.0
$0.0
$0.0
$0.0
97
$0.0
$0.0
$0.0
$0.0
$0.0
98
$0.0
$0.0
$0.0
$0.0
$0.0
9
$0.0
$0.0
$0.0
$0.0
$0.0
10
$0.0
$0.0
$0.0
$0.0
$0.0
101
$0.0
$0.0
$0.0
$0.0
$0.0
102
$0.0
$0.0
$0.0
$0.0
$0.0
103
$0.0
$0.0
$0.0
$0.0
$0.0
104
$0.0
$0.0
$0.0
$0.0
$0.0
105
$0.0
$0.0
$0.0
$0.0
$0.0
106
$0.0
$0.0
$0.0
$0.0
$0.0
107
$0.0
$0.0
$0.0
$0.0
$0.0
108
$0.0
$0.0
$0.0
$0.0
$0.0
109
$0.0
$0.0
$0.0
$0.0
$0.0
1 0
$0.0
$0.0
$0.0
$0.0
$0.0
1 1
$0.0
$0.0
$0.0
$0.0
$0.0
1 2
$0.0
$0.0
$0.0
$0.0
$0.0
1 3
$0.0
$0.0
$0.0
$0.0
$0.0
1 4
$0.0
$0.0
$0.0
$0.0
$0.0
1 5
$0.0
$0.0
$0.0
$0.0
$0.0
1 6
$0.0
$0.0
$0.0
$0.0
$0.0
1 7
$0.0
$0.0
$0.0
$0.0
$0.0
1 8
$0.0
$0.0
$0.0
$0.0
$0.0
1 9
$0.0
$0.0
$0.0
$0.0
$0.0
120
$0.0
$0.0
$0.0
$0.0
$0.0
a.
Find the FV of $1,0 0 invested to earn 10% annual y 5 years from now.
Answer this question by using
a
math formula and also by using the
Excel
function wizard.
Note:
When you use the wizard and fil in the menu items, the result is the formula you se on the formula line
if you click on cel E12.
Put the pointer on E12 and then click the function wizard (fx) to se the completed
menu.
Also, it is general y easiest to fil in the wizard menus by clicking on one of the menu slots to activate the
cursor and then clicking on the cel where the item is given.
Then, hit the tab key to move down to the next
menu slot to continue fil ing out the dialog box.
b.
Now create a table that shows the FV at 0%, 5%, and 20% for 0, 1, 2, 3, 4, and 5 years.
Then create a
graph with years on the horizontal axis and FV on the vertical axis to display your results.
Begin by typing in the row and column labels as shown below. We could fil in the table by inserting formulas in
al the cel s, but a bet er way is to use an Excel data table as described in the 20 7 Excel tutorial (Tab 4 - Data
Tables Graphs).
We used the data table procedure.
Note that the Row Input Cel is D9 and the Column Input
Cel is D10, and we set Cel B32 equal to Cel E1 .
Then, we selected (highlighted) the range B32:E38, then
clicked Data, Table, and fil ed in the menu items to complete the table.
To create the graph, first select the range C3 :E38.
Then click the chart wizard.
Then fol ow the menu. It is
easy to make a chart, but a lot of detailed steps are involved to format it so that it's "pret y."
Pret y charts are
general y not neces ary to get the picture, though. Note that as the last item in the chart menu you are asked if
you want to put the chart on the workshe t or on a separate tab.
This is a mat er of taste.
We put the chart
below on the spreadshe t so we could se how changes in the data lead to changes in the graph.
Note that the inputs to the data table, hence to the graph, are now in the row and column heads.
Change the 20%
in Cel E32 to .3 (or 30%), then to .4, then to .5, etc., to se how the table and the chart changes.
c.
Find the PV of $1,0 0 due in 5 years if the discount rate is 10% per year.
Again, work the problem
with
a formula and also by using the function wizard.
Note:
In the wizard's menu, use zero for Pmt because there are no periodic payments.
Also, set the FV with a
negative sign so that the PV wil ap ear as a positive number.
Note:
Use zero for Pmt since there are no periodic payments.
Note that the PV is given a negative sign because
it is an outflow (cost to buy the security).
Also, note that you must scrol down the menu to complete the inputs.
e.
Sup ose California’s population is 30 mil ion people, and its population is expected to grow by 2%
per
year.
How long would it take for the population to double?
f.
Find the PV of an ordinary annuity that pays $1,0 0 at the end of each of the next 5 years if the
interest rate is 15%.
Then find the FV of that same annuity.
For the PV, each payment would be received one period so ner, hence would be discounted back one les year.
This would make the PV larger.
We can find the PV of the an uity due by finding the PV of an ordinary an uity
and then multiplying it by (1 + I).
semian ual
compounding rather than 10% with annual compounding?
Excel does not have a function for the sum of the future values for a set of uneven payments. Therefore, we must
find this FV by some other method.
Probably the easiest procedure is to simply compound each payment, then
sum them, as is done below.
Note that since the payments are received at the end of each year, the first payment
is compounded for 2 years, the second for 1 year, and the third for 0 years.
j.
Suppose you bought a house and to k out a mortgage for $50,0 0.
The interest rate is 8.5%, and
you
must amortize the loan over 10 years with equal end-of-year payments.
Set up an amortization
schedule
that shows the annual payments and the amount of each payment that repays the
principal and the
amount that constitutes interest expense to the bor ower and interest income to
the lender.
Go back to cel s D184 and D185, and change the interest rate and the term to maturity to se
how the payments would change.
Now we would have a 12
×
10 = 120-payment loan at a monthly rate of .085/12 = 0.0 7083 3 %.