Solutions To Problem
Solutions To Problem
Chapter 8
TIME VALUE OF MONEY
1.
(i)
A x PVIFA (12%, 5) = 15,000,000
A x 3.605 = 15,000,000
15,000,000
A = = 4,160,888
3.605
(ii)
2,961,498
The required proportion = = 0.71
4,160,888
2.
69
0.35 +
r
69
= 0.35 + = 5.66 years
13
3.
1,000,000
Annual installment = = 298,329
3.352
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5.
Rs.32,000 / Rs. 2,000 = 16 = 24
6.
In 14 years Rs.5, 000 grows to Rs.20, 000 or 4 times. This is 2 2 times the initial
deposit. Hence doubling takes place in 14 / 2 = 7 years.
According to the Rule of 69, the doubling period is .35 + 69 / Interest rate
We therefore have
0.35 + 69 / Interest rate = 7
Interest rate = 69/(7-0.35) = 10.38 %
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7.
In 18 years Rs.10, 000 grows to Rs.80, 000 or 8 times. This is 2 3 times the initial
deposit. Hence doubling takes place in 18 / 3 = 6 years.
According to the Rule of 69, the doubling period is 0.35 + 69 / Interest rate. We
therefore have
0.35 + 69 / Interest rate = 6
8.
Saving Rs.5000 a year for 3 years and Rs.7000 a year for 7 years thereafter is
equivalent to saving Rs.5000 a year for 10 years and Rs.2000 a year for the years 4
through 10.
Hence the savings will cumulate to:
5000 x FVIFA (8%, 10 years) + 2000 x FVIFA (8%, 7 years)
= 5000 x 14.487 + 2000 x 8.923 = Rs.90281
9.
Let A be the annual savings.
10.
The present value of an annual pension of Rs.120, 000 for 20 years when r =
10% is:
120,000 x PVIFA (10%, 20 years)
= 120,000 x 8.514 = Rs.1, 021,680
Rahul will be better off with the annual pension amount of Rs.120,000.
11.
The present value of an annual payment of Rs.10,000 for 10 years when r = 9%
is:
10,000 x PVIFA ( 9 %, 10 years)
= 10,000 x 6.418 = Rs.64, 180
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12.
The present value of the income stream is:
30,000 x PVIF (9%, 1 year) + 50,000 x PVIF (9%, 3 years)
+ 100,000 x PVIFA (9 %, 7 years) x PVIF (9%, 3 years)
= 30,000 x 0.917 + 50,000 x 0.772 + 100,000 x 5.033 x 0.772 =
Rs.454, 658...352 x 0.658 = Rs.152, 395.
13.
The present value of the income stream is:
1,000 x PVIFA (12%, 3 years) + (5,000/ 0.12) x PVIF (12%, 3 years)
= 1,000 x 2.402 + (5000/0.12) x 0.712
= Rs.32,069
14.
To earn an annual income of Rs.240,000 forever , beginning from the end of 6
years from now, if the deposit earns 12% per year a sum of Rs.240,000 / 0.12 =
Rs.2,000,000 is required at the end of 5 years. The amount that must be
deposited to get this sum is:
Rs.2, 000,000 PVIF (12%, 5 years) = Rs.2, 000,000 x 0.567
= Rs. 1,134,000
15.
PV( Stream X) = 500 PV( 18%, 1yr) +550 PV( 18%, 2yrs) + 600 PV( 18%,
3yrs) + 650 PV( 18%, 4yrs) + 700 PV( 18%, 5yrs) + 750 PV( 18%, 6yrs)
= 500 x 0.847 +550 x 0.718 + 600 x 0.609 + 650 x 0.516 + 700 x 0.437 + 750 x
0.370 = 2102.6
PV( Stream Y) = 750 PV( 18%, 1yr) +700 PV( 18%, 2yrs) + 650 PV( 18%,
3yrs) + 600 PV( 18%, 4yrs) + 550 PV( 18%, 5yrs) + 500 PV( 18%, 6yrs)
= 750 x 0.847 +700 x 0.718 + 650 x 0.609 + 600 x 0.516 + 550 x 0.437 + 500 x
0.370 = 2268.65
16.
FV10 = Rs.200,000 [1 + (0.12 / 6)]10x6
= Rs.200,000 (1.02)60
= Rs.200,000 x 3.281
= Rs.656,200
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17.
A B C
18. The interest rate implicit in the offer of Rs.600,000 after 8 years in lieu of
Rs.200,000 now is the value of r in the following equation:
Rs.200,000 x FVIF (r,8 years) = Rs.600,000
Rs.600,000
FVIF (r,8 years) = = 3.000
Rs.200,000
19.
FV5 = Rs.500,000 [1 + (0.09 / 4)]5x4
= Rs.500,000 (1.0225)20
= Rs.500,000 x 1.5605
= Rs.780,250
If the inflation rate is 3 % per year, the value of Rs.780,250, 5 years from
now, in terms of the current rupees is:
Rs.780,250 x PVIF (3%, 5 years)
= Rs.780,250 x 0. 863 = Rs.673,356
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20.
The discounted value of Rs.100,000 receivable at the beginning of each year
from 2015 to 2019, evaluated as at the beginning of 2014 (or end of 2013)
is:
= Rs.100,000 x PVIFA (10%, 5 years)
= Rs.100,000 x 3.791= Rs.379,100
If A is the amount deposited at the end of each year from 2007 to 2011 then
A x FVIFA (10%, 5 years) = Rs.313,137
A x 6.105 = Rs.313,137
A = Rs.313,137/ 6.105 = Rs.51,292
21.
The discounted value of the annuity of Rs.120,000 receivable for 20 years,
evaluated as at the end of 7th year is:
22.
40 per cent of the pension amount is
0.40 x Rs.10,000 = Rs.4,000
Assuming that the monthly interest rate corresponding to an annual interest rate
of 12% is 1%, the discounted value of an annuity of Rs.4,000 receivable at the
end of each month for 240 months (20 years) is:
(1.01)240 - 1
Rs.4,000 x = Rs.363,278
.01 (1.01)240
If Mr. Tiwari borrows Rs.P today on which the monthly interest rate is 1%
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Rs. 363,278
P = = Rs.139,722
2.60
23.
The discounted value of the debentures to be redeemed between 6 to 8 years
evaluated at the end of the 5th year is:
If A is the annual deposit to be made in the sinking fund for the years 1 to 5,
then
A x FVIFA (10%, 5 years) = Rs.49.74 million
A x 6.105 = Rs.49.74 million
A = Rs.8,147,420
24.
Equated annual installment = 2,000,000 / PVIFA(12%,5)
= 2,000,000 / 3.605
= Rs.554,785
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Chapter 9
VALUATION OF SECURITIES
1.
(i)
Value = 60 x PVIFA (8%, 10) + 1000 x PVIF (8%, 10)
= 60 x 6.710 + 1000 x 0. 463
= 402.60 + 463 = 865.60
(ii)
60 + (1000 – 965) /10
YTM = = 0.0649 % per semi annum or 12.98 p.a
0.4 x 1000 + 0.6 x 965
2.
D1
g = r -
P0
20
= 0.25 - = 17.86%
280
3.
D1
g = r -
P0
10
= 0.20 - = 17.85 %
465
4.
Approximate YTM
C + (M - P) /n
=
0.4 M + 0.6 P
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90 + (1000 – 1050) / 5
= 7.77%
0.6 x 1,050 + 0.4 x 1,000
6.
D1 8 (1.12)
P0 = = = Rs.149.33
r–g 0.18 – 0.12
7.
(i)
Value = 70 x PVIFA (10%, 3) + 1000 x PVIF (10% , 3)
= 70 x 2.487 + 1000 x 0.751
= 174 + 751 = 925
(ii)
70 + (1000 – 985) / 3
YTM = = 7.57%
0.4 x 1000 + 0.6 x 985
8.
(i)
9 + (100 – 108)/6
= 7.32%
0.6 x 108 + 0.4 x 100
(ii)
D0 (1 + g) 2.40 (1.10)
rE = +g= + 0.10
P0 60
= 14.4%
9.
Po = D1/ (r – g) = Do (1+g) / (r – g)
Do = Rs.2.00, g = -0.05, Po = Rs.10
So
10 = 2.00 (1- .05) / (r-(-.05)) = 1.90 / (r + .05)
r +0.05 =1.90/10 = 0.19
r = 0.19 – 0.05 = 0.14
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Chapter 11
TECHNIQUES OF CAPITAL BUDGETING
1.
(i)
18% 19%
PVIF PV PVIF PV
150,000 0.847 127,050 0.840 126,000
180,000 0.718 129,240 0.706 127,080
240,000 0.609 146,160 0.593 142,320
250,000 0.516 129,000 0.499 124,750
531,450 520,150
531,450 – 530,000
18% + x 1%
531,450 – 520,150
= 18.13%
(iii)
PVB
BCR =
I
567,500
= = 1.071
530,000
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2.
(i)
100,000 200,000
NPV = - 500 000 + +
(1.10) (1.10)2
300,000 100,000
+ +
(1.10)3 (1.10)4
(ii)
14 % 15 %
100,000 .877 87,700 .870 87,000
200,000 .769 153,800 .756 151,200
300,000 .675 202,500 .658 197,400
100,000 .529 59,200 .572 57,200
503,200 492,800
3200
14 % + = 14.31 %
10,400
(iii)
Depends on the COC
If the COC is 10 %
549893
= 1.0998
500000
500
+
(1.10) (1.12) (1.14) (1.16)
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Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating
in this range we get an approximate DPB of 2.64 years.
Project N
Cost of capital =
15 % p.a
Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating
in this range we get an approximate DPB of 2.89 years.
5 Project N
Cost of capital =
15 % p.a
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Discounted pay back period (DPB) lies between 2 and 3 years. Interpolating
in this range we get an approximate DPB of 2.89 years.
5.
The details for the two alternatives are shown below:
6.
(1.14) (1.14)2
= - 44837
(ii)
NPV of the project at time varying discount rates
= - 1,000,000
+ 100,000
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(1.12)
+ 200,000
(1.12) (1.13)
+ 300,000
+ 600,000
+ 300,000
7.
Investment A
Investment B
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d) BCR = PVB / I
= 194,661 / 300,000 = 0.65
Investment C
Investment D
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8 + (1 x 100,000 / 200,000)
Comparative Table
Investment A B C D
a) Payback period
(in years) 5 9 2.88 8.5
Highest NPV
Highest IRR
Highest BCR
8.
IRR (r) can be calculated by solving the following equations for the value of r.
16
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Through a process of trial and error it can be verified that r = 9.20% pa.
9.
Define NCF as the minimum constant annual net cashflow that justifies the purchase
of the given equipment. The value of NCF can be obtained from the equation
10.
. a) (i) The IRR (r ) of project P can be obtained by solving the following
equation for `r’.
-1000 -1200 x PVIF (r,1) – 600 x PVIF (r,2) – 250 x PVIF (r,3)
+ 2000 x PVIF (r,4) + 4000 x PVIF (r,5) = 0
-1600 + 200 x PVIF (r',1) + 400 x PVIF (r',2) + 600 x PVIF (r',3)
+ 800 x PVIF (r',4) + 100 x PVIF (r',5) = 0
11.
(a) Project A
Project B
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IRR (r'') of the differential project can be obtained from the equation
12 x PVIFA (r'', 6) = 50
i.e., r'' = 11.53%
12.
(i) Project M
The pay back period of the project lies between 2 and 3 years. Interpolating in
this range we get an approximate pay back period of 2.63 years/
Project N
The pay back period lies between 1 and 2 years. Interpolating in this range we
get an approximate pay back period of 1.55 years.
(ii) Project M
Cost of capital =
12% p.a
Discounted pay back period (DPB) lies between 3 and 4 years. Interpolating
in this range we get an approximate DPB of 3.1 years.
Project N
Cost of capital =
12% per annum
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2 22 17.54 51.47
(iii) Project M
Cost of capital = 12% per annum
NPV = - 50 + 11 x PVIFA (12,1)
+ 19 x PVIF (12,2) + 32 x PVIF (12,3)
+ 37 x PVIF (12,4)
= Rs.21.26 million
Project N
Cost of capital = 12% per annum
NPV = Rs.20.63 million
Since the two projects are independent and the NPV of each project is (+) ve,
both the projects can be accepted. This assumes that there is no capital
constraint.
(iv) Project M
Cost of capital = 10% per annum
NPV = Rs.25.02 million
Project N
Cost of capital = 10% per annum
NPV = Rs.23.08 million
Since the two projects are mutually exclusive, we need to choose the project
with the higher NPV i.e., choose project M.
(v) Project M
Cost of capital = 15% per annum
NPV = 16.13 million
Project N
Cost of capital: 15% per annum
NPV = Rs.17.23 million
Again the two projects are mutually exclusive. So we choose the project with
the higher NPV, i.e., choose project N.
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