Correia, Mayall, O’Grady and Pang: Solutions to Corporate Financial Management, 2e
12 January 2007
2-14
Amount available in 10 years
Value at 18 years of age
= $5 000 x 30/10
= $15 000 (1.06)16
= $38 100
If $5 000 invested at 12% = $5 000 (1.06)36
= $15 000
= $15 000 x 2.540
= R 5 000 x 8.147
= $40 735
The 12% investment would have been better by $2 635
Comprehensive Solution
Bonds for 10 years, then 12% pa for 8 years
Value of bonds after 10 years = 5,000 x
$30
$10
= 15,000
This represents a single sum which will be invested for a further 8 years:
type
cmp
PV
r
n
FV
=
=
=
=
=
=
single sum
semi-annually
15,000
12% pa y 2 = 6% semi-annually = 0.06
8 years x 2 = 16 half years
?
Using formula:
FV
Using tables:
n
=
PV x FVIF16, 6% (Table A)
15,000 x (1.06)16
=
15,000 x 2.540
38,105.28
|
38,100
=
PV(1+r)
=
|
FV
12% pa for 18 years
type
cmp
PV
r
n
FV
=
=
=
=
=
=
single sum
semi-annually
5,000
12% pa y 2 = 6% semi-annually = 0.06
18 years x 2 = 36 half years
?
Using formula:
FV
=
Using tables:
n
FV
PV(1+r)
36
=
PV x FVIF36, 6% (Table A)
=
5,000 x (1.06)
=
5,000 x 8.147
|
40,736.26
|
40,735
Conclusion
It would have been better for the father to invest the original $5,000 immediately in the 12% investment
[Comprehensive solution by Travis Baugh]
Corporate Financial Management: Correia, Mayall, O’Grady and Pang: Solutions
Correia, Mayall, O’Grady and Pang: Solutions to Corporate Financial Management, 2e
12 January 2007
2-15
FV
18 380
FVIF
= P(FVIF)
= 10 000(FVIF)
= 18 380/10 000 = 1.838
Look up Table A, across 9 periods,
= 7%
Alternatively,
r = (1.838)(1/9) -1 = 7%
Using a financial calculator:
N
9
I/YR
7
PV
-10000
PMT
0
FV
18380
2-16
FVIFA
=2
Table A - Check under the 2 percent (per 6 month) column until a factor of 2 is
reached:
Solution:
35 periods = 17.5 years
Using a financial calculator:
N
35
I/YR
4
PV
-1
PMT
0
FV
2
2-17
1.
Future value
FV
140 000
I
= $140 000
= I (FVIFA) FVIFA; 6%, 10 years
= I (13.181)
= 140 000/13.181 = $10 621.35 per annum
2.
FV
140 000
PV
= P(FVIF)
= PV(1.791)
= 140 000/1.791 = $78 168.62
Using a financial calculator or formulae, we will get to slightly more precise figures.
In part 1, using a financial calculator, we enter 140 000 and then FV, enter 6 and then
I/YR, enter 10 and then N and then enter PMT which should give you a solution of
$10 621.51.
In part 2, the FV factor using the formula is (1+0.06)10 = 1.79085 so that the PV is
140 000/1.79085 = $78 175.17. Using a financial calculator, enter 140 000 and then FV,
enter 6 and then I/YR, enter 10 and then N and then enter PV which will give you a
solution of $78 175.27. [Do not worry about the small rounding differences]
Corporate Financial Management: Correia, Mayall, O’Grady and Pang: Solutions
Correia, Mayall, O’Grady and Pang: Solutions to Corporate Financial Management, 2e
12 January 2007
2-18
Loan = $1053.35 PVIFA n = 48, r = 1% (12% pa = 1% per month)
(4 years at monthly compounding = 48 periods)
Loan = $1053.35 * 37.974
Loan = $40,000
Note: Please indicate that the interest rate is 12% per year, interest compounded monthly, as this
is not stated in the question.
Using a financial calculator:
N
48
I/YR
12
PV
40000
PMT
1053.35
FV
0
To use a financial calculator, change the compounding interval from 1 per year to 12 per year.
To do this, enter 12, enter SHIFT and enter PMT (P/YR).
2-19
Amount to be deposited now * (1.10)3=$20,000 – $12,000 * (1.06)3
Amount to be deposited now = $4,288.42
2-20
Alternative = $750 PVIFA n = 10, i = 1.5% (6% pa = 1.5% pqa)
Alternative = $750 * 9.2222
Alternative = $6916.65
Better to pay $6,600 cash as the borrowing costs are higher.
Using a financial calculator:
N
10
I/YR
1.5
PV
6916.64
PMT
750
FV
0
To use a financial calculator, change the compounding interval from 1 per year to 4 per year. To
do this, enter 4, enter SHIFT and enter PMT (P/YR).
2-21
$32,976 = $4,000 (1.08)Ķ
(1.08)Ķ = $32,976 / $4,000 = 8.244 Use logarithms
N = 14 years
Using a financial calculator:
N
14
I/YR
8
PV
-32976
PMT
4000
FV
0
Corporate Financial Management: Correia, Mayall, O’Grady and Pang: Solutions
Correia, Mayall, O’Grady and Pang: Solutions to Corporate Financial Management, 2e
12 January 2007
2-22
$80,000 - $20,000 = $1334.67 PVIFA n = 60, r = ?%
PVIFA n = 60, r = ?% = $60,000 / $1334.67
PVIFA n = 60, r = ?% = 44.955
Using Logarithms, we can solve for n, which is 12% per year or 1% per month.
Using a financial calculator:
N
60
I/YR
12
PV
-60000
PMT
1334.67
FV
0
To use a financial calculator, change the compounding interval from 1 per year to 12 per year.
To do this, enter 12, enter SHIFT and enter PMT (P/YR).
2-23
$2,000,000 = Repayments PVIFA n = 10, i = 9%
Repayments = $2,000,000 / 6.4177
Repayments = $311,638.125
Amount due after 3 years when n = 7
Amount = $311,638.125 PVIFA n = 7, i = 9%
Amount = $311,638.125 * 5.0330
Amount = $1,568,474.68
We can set out an amortisation schedule in Excel as follows;
E
3 Loan
4 Interest
5
6 Term
F
2,000,000.00
9%
10
Year
1
2
3
4
5
6
7
8
9
10
Total
Beg.Bal
2,000,000.00
1,868,359.82
1,724,872.02
1,568,470.33
1,397,992.48
1,212,171.62
1,009,626.89
788,853.12
548,209.73
285,908.42
7
8
9
10
11
12
13
14
15
16
17
18
G
H
I
Payment determination
$F$3/((1-(1/(1+$F$4)^$F$5))/$F$4)
Payment
311,640.18
311,640.18
311,640.18
311,640.18
311,640.18
311,640.18
311,640.18
311,640.18
311,640.18
311,640.18
3,116,401.80
Interest
180,000.00
168,152.38
155,238.48
141,162.33
125,819.32
109,095.45
90,866.42
70,996.78
49,338.88
25,731.76
1,116,401.80
Principal
131,640.18
143,487.80
156,401.70
170,477.85
185,820.86
202,544.73
220,773.76
240,643.40
262,301.30
285,908.42
2,000,000.00
J
Interest
+F10*$F$4
End. Bal.
1,868,359.82
1,724,872.02
1,568,470.33
1,397,992.48
1,212,171.62
1,009,626.89
788,853.12
548,209.73
285,908.42
0.00
[We used the formula, [(1-(1/(1+r)n)]/r to determine the annual payment in Excel but we could have also used the
=PMT function. Note the small rounding differences from using the PV Tables]
Using a financial calculator
N
I/YR
PV
10
9
2000000
PMT
-311640.18
FV
0
Corporate Financial Management: Correia, Mayall, O’Grady and Pang: Solutions