Principles of Finance: IRR, NPV, Bond Pricing, Cash Flow, Savage Value, and NPV Calculation

This article covers topics related to Principles of Finance such as IRR, NPV, Bond Pricing, Cash Flow, Savage Value, and NPV Calculation. It includes solved examples and calculations for better understanding.

PRINCIPLES OF FINANCE

Table of Contents
SECTION A.....................................................................................................................................3
Question 1....................................................................................................................................3
(a) calculation of IRR..................................................................................................................3
(b) calculation of NPV.................................................................................................................5
Question 2....................................................................................................................................6
Question 3....................................................................................................................................7
Question 4....................................................................................................................................7
a....................................................................................................................................................7
Question 4.b.................................................................................................................................7
Question 4.c.................................................................................................................................7
Question 5....................................................................................................................................8
Question 6....................................................................................................................................8
a)..................................................................................................................................................8
b)..................................................................................................................................................9
c)..................................................................................................................................................9
d)..................................................................................................................................................9
Question 7..................................................................................................................................10
Question 8..................................................................................................................................10
SECTION B...................................................................................................................................12
Question 1..................................................................................................................................12
Question 3..................................................................................................................................12
REFERENCES................................................................................................................................1

SECTION A
Question 1
(a) calculation of IRR
Project 1
Discount rate (r) 35%
Year (t)
Project 1
cash flow Present value factor
Present value of cash
flow
(1/1+r)^t
(cash flow* present
value factor)
0 -20000 0
1 10000 0.7407407407 7407.4074074074
2 10000 0.548696845 5486.9684499314
3 10000 0.4064421074 4064.4210740233
4 10000 0.3010682277 3010.6822770543
Total 19969.4792084164
NPV -30.5207915836
IRR
Discount rate (t) 34.00%
present value factor present value
Year (t)
Project 1
cash flow (1/1+r)^t
(cash flow* present
value factor)
0 -20000 0
1 10000 0.7462686567 7462.6865671642
2 10000 0.556916908 5569.1690799733
3 10000 0.4156096328 4156.0963283383
4 10000 0.3101564424 3101.564424133

20289.5163996087
NPV 289.5163996087
The value of NPV is calculated by taking the difference of present value of cash inflow and cash-
outflow. So at the rate of 35% (discount rate), the value of NPV is negative. IRR is existed where
NPV is zero. Which means that IRR is existed between 34% and 35%. Moreover, the rate of IRR
is 34.90%.
project 2
Discount rate (r) 31.00%
Year (t) Cash flow Present value factor Present value
(1/1+r)^t
(cash flow* present
value factor)
0 -20000 0 -0
1 0 0.7633587786 0
2 0 0.5827166249 0
3 0 0.4448218511 0
4 60000 0.3395586649 20373.519896462
20373.519896462
NPV 373.5198
Discount rate 32.00%
year Project 2 present value factor present value
0 -20000 0 -0
1 0 0.7575757576 0
2 0 0.5739210285 0

3 0 0.4347886579 0
4 60000 0.3293853469 19763.1208149615
Total 19763.1208149615
NPV -236.8791850385
From the above analysis it can be interpreted that when discount rate is 31%, the value of NPV is
positive. Moreover, as it is increased to 32% the value of NPV becomes negative. The rate of
IRR lies at the place where the value of NPV becomes ZERO. Therefore, the rate of IRR lies
between 31% and 32%. So the rate of IRR is 31.61%.
(b) calculation of NPV
Project 1
Discount rate (r) 10.00%
Year (t)
Project 1
cash flow present value factor present value
(1/1+r)^t
(cash flow* present
value factor)
0 -20000 0
1 10000 0.9090909091 9090.9090909091
2 10000 0.826446281 8264.4628099174
3 10000 0.7513148009 7513.1480090158
4 10000 0.6830134554 6830.1345536507
Total 31698.6544634929
NPV 11698.6544634929
NPV =31698.6544 – 20000
=11698.65 (positive is favourable)
Project 2
Discount rate (r) 10.00%
Year (t) Cash flow present value factor present value
(1/1+r)^t (cash flow* present

value factor)
0 -20000 0 -0
1 0 0.9090909091 0
2 0 0.826446281 0
3 0 0.7513148009 0
4 60000 0.6830134554 40980.8073219042
40980.8073219042
NPV 20980.8073219042
NPV= 40980.807 – 20000
=20980.80 (Positive is favourable)
When company select the project on the basis of positive and higher NPV. Moreover, NPV
shows how much return company is getting back a positive NPV shows favourable project. In
order to decide which project is more favourable( in terms of return ). Out of these two project,
project 2 is providing higher return because it has better NPV then project A.
Question 2
6%
Risk
Rf
10%
20%
Exp. Return
30%
11%

Question 3
a)
Bond price = Coupon 1 / (1 + YTM / 2)1 + Coupon 2 / (1 + YTM / 2)2 +........Coupon 40 / (1 +
YTM / 2)40 + Face value / (1 + YTM)20
Coupon = 1000 * 5% = 50 / 2 = 25 every half year
YTM = 6% / 2 = 3%
= 25 / (1 + 3%)1 + 25 / (1 + 3%)2......25 / (1 + 3%)40 + 1000 / (1 + 6%)20
= 884.43 would be the bond price at issuance.
b) The price of the bond at this point where coupon rate is equivalent to yield to maturity would
be equals to its par or face value that is, 1000.
Question 4
a
Interest = 1000 * 8%
= 800
Price of bond: interest / risk rate
= 800 / 10%
= 800
Question 4.b
5.548%
Question 4.c
(1)
Bond C
6% = [80 + {(1000 – price) / 2 }] / [{1000 + Price} / 2]
.06 = 160 + 1000 – price / 1000 + price
= 785
Bond D
6% = [80 + {(1000 – price) / 8}] / [{1000 + Price} / 2]
6% = 640 + 1000 – Price / 4 (1000 + price)
= 280
(2)
7

Bond C
10% = [80 + {(1000 – price) / 2 }] / [{1000 + Price} / 2]
= 963
Bond D
10% = [80 + {(1000 – price) / 8}] / [{1000 + Price} / 2]
= 308
(3)
The above stated calculation clearly indicate that yield to maturity certainly increases or
decreases the value of the bond. If it is increased than the value of bond will also improve and in
case it is decreased than the value of bond of reduce. The bond D has a greater risk element as
the maturity is more which also reflect in the price of bond. The risk also depict in the prices of
the bond.
Question 5
Expected future cash flow:
40000 / 11%
= 363636
Question 6
a)
Calculation of Savage value of fixed assets
The expenditure of the fixed assets at the beginning of the project which is also known as the
actual cost of fixed assets would be = $1000.
The depreciation on fixed assets in year 1 = $280, year 2 = $280 and year 3 = $280.
So, the total depreciation on fixed asset over the three years = $280 + $280 + $280 = 840.
Formula to calculate the carrying value of the fixed assets after three years = Original cost –
Depreciation
= $1000 - $840 = $160
Market value of the retired assets = $500 which is also known as salvage value before tax.
The after-tax savage value of the fixed assets = market value of the retired assets * (1 – tax rate)
= $500* (1 – 0.3) = $500* 0.7
= $350
8

The after-tax savage value of the fixed assets is $350.
b)
Calculation of operating cash flow of each year of the project
Particulars Year 1 Year 2 Year 3
Operating income 540 540 540
Add Depreciation 280 280 280
Less investment in net
working capital
-500 -100 -100
Add recovered from
net working capital
- - 700
Less Income tax -162 -162 -162
Operating cash flow 158 558 1258
c)
Calculation of Cash flow from assets or financing activities in each year of the projects
Particulars Year 1 Year 2 Year 3
Purchase of assets -1000 0 0
Sale of assets 0 0 500
Cash flow from assets -1000 0 500
d)
Calculation of NPV
Years Cash flow Discounting factor
@10%
Present value of cash
flow
0 -1500 0 -1500
9

1 658 – 100 = 558 0.9 502.2
2 658 – 100 = 558 0.82 457.56
3 658 – 100 + 350 + 500
= 1408
0.75 1056
Present value of cash inflow – Initial investment = 2015.76 – 1500 = 515.76.
If the required rate of return of this project is 10%, then it is advisable to the company to accept
this project because at 10% return the company will earn profit. It is because the net present
value of the three-year project is positive.
Question 7
Date Cipl
a
Rt Idea Rt Won
derla
Rt PVR Rt Alke
m
Rt Cipla Idea Won
derla
PVR Alke
m
21-
02-17
593.
1
0.06
%
108.
35
-
0.09
%
374.1
5
0.32
%
1268 -
0.04
%
2000
.05
-
1.73
%
0.00% -
0.66
%
0.26
%
-
0.19
%
-
2.02%
22-
02-17
589.
25
-
0.65
%
112.
6
3.92
%
374.4
5
0.08
%
1263.
35
-
0.37
%
2022
.55
1.12
%
-
0.71%
3.36
%
0.02
%
-
0.52
%
0.84%
23-
02-17
592.
4
0.53
%
119.
6
6.22
%
373.4 -
0.28
%
1260.
1
-
0.26
%
2076
.85
2.68
%
0.47% 5.65
%
-
0.34
%
-
0.41
%
2.40%
27-
02-17
585.
25
-
1.21
%
114.
55
-
4.22
%
373.8
5
0.12
%
1278.
1
1.43
%
2154
.75
3.75
%
-
1.27%
-
4.79
%
0.06
%
1.27
%
3.46%
28-
02-17
583.
7
-
0.26
%
115.
85
1.13
%
372.4 -
0.39
%
1295.
55
1.37
%
2141
.55
-
0.61
%
-
0.33%
0.57
%
-
0.45
%
1.21
%
-
0.90%
1-03- 586. 0.45 113. - 373.8 0.38 1296. 0.05 2144 0.12 0.38% - 0.32 - -
10

17 3 % 25 2.24
%
% 25 % .15 % 2.81
%
% 0.10
%
0.17%
2-03-
17
589.
25
0.50
%
109.
6
-
3.22
%
375.3 0.40
%
1303.
65
0.57
%
2142
.1
-
0.10
%
0.44% -
3.79
%
0.34
%
0.42
%
-
0.38%
3-03-
17
588.
6
-
0.11
%
110.
55
0.87
%
378.2
5
0.79
%
1310.
05
0.49
%
2138.95[
-0.15%]
-
0.17%
0.30
%
0.73
%
0.34%1=K1
28-$K$131
6-03-
17
590.
1
0.25
%
109.
75
·0.7
2%
380.2 0.52
%
1331.
9
1.67
%
2110.2
·1.34%
0.19% ·1.2
9%
0.46
%
1.51%
·1.63%
7-03-
17
588.
05
·0.3
5%
108.
6
·l.05
%
381.2 0.26
%
1344.
6
0.95
%
2048.6
·2.92%
·0.41
%
·l.61
%
0.21
%
0.80%
·3.21%
Avera
ge
daily
rate
0.06
%
0.57
%
0.06
%
0.15
%
0.
29
%
X = Excess Retun matrix
Alkem Rt cieta Idea Wonderl
a
PVR Alkem
1569.85
1636.5 4.25
%
-
0.27%
0.39% -0.23% 7.27
%
3.96%
1644.75 0.50
%
0.05% -
0.09%
-0.78% -
1.13
%
0.22%
11

1616.9 -
1.69
%
0.31% -
1.92%
-0.30% -
1.69
%
-
1.98%
I Ciola Idea Wonderla PVR Alkem
TRANSPOSE{LS:P130),LS:P130)
Idea Wonderla PVR
Alkem
1635.9 1.18% 2.42% 0.39% -0.06% -0.46% =MMULT{TR
1602.. 85 ·2.02% ·2.52% ·1.63% ·0.32% ·1.62% ·2.31%
1616.35 0.84% ·1.85% ·1.52% ·1.06% ·3.47" 0.55%
1624.3 0.49% 1.24% 0.58% ·0.12% ·0.63% 0.20%
1622.35 ·0.12% 1.31% 0.33% ·0.21% ·1.43% ·0.41%
X transpose multipied by X
Cipla Cipla
0.02788
Idea
0.00679
Wonderla
0.00425
PVR
0.00515
Alkem
0.00804
Idea 0.00679 0.14084 0.00497 0.00289 0.00475
Wonderla 0.00425 0.00497 0.03055 0.00500 0.00351
PVR 0.00515 0.00289 0.00500 0.05109 0.00338
Alkem 0.00804 0.00475 0.00351 0.00338 0.04310
transpose multipied by X
Cipla Cipla
0.02788
Idea
0.00679
Wonderla
0.00425
PVR
0.00515
Alkem
0.00804
Idea 0.00679 0.14084 0.00497 0.00289 0.00475
12

Wonderla 0.00425 0.00497 0.03055 0.00500 0.00351
PVR 0.00515 0.00289 0.00500 0.05109 0.00338
Alkem 0.00804 0.00475 0.00351 0.00338 0.04310
n 127
Variance Covariance matrix
Cipla Cipla
0.0002195
Idea
0.0000535
Wonderla
0.0000335
PVR
0.0000405
Alkem
0.0000633
Idea 0.0000535 0.0011090 0.0000391 0.0000227 0.0000374
Wonderla 0.0000335 0.0000391 0.0002405 0.0000394 0.0000277
PVR 0.0000405 0.0000227 0.0000394 0.0004022 0.0000266
Alkem 0.0000633 0.0000374 0.0000277 0.0000266 0.0003393
Question 8
a)
Weight of equity = 140 / (140 + 380) = 0.2692 or 26.92%
Weight of equity = 380 / (140 + 380) = 0.7308 or 73.08%
WACC = 0.2692 * (0.06) (1 – 0.38) + 0.7308 * 0.11 = 0.904 = 9.04%
Times in years T0 T1 T2 T3 T4 T5 T6
EBIT 12.5 13.75 15.125 16.638 18.301 20.131 20.735
Tax @ 38% 4.75 5.225 5.7475 6.322 6.954 7.650 7.879
EAT 7.75 8.525 9.3775 10.315 11.347 12.481 12.856
Depreciation – 8% of
EBIT 1.00 1.10 1.21 1.33 1.46 1.61 1.66
Capital Spending – 15%
of EBIT -1.875 -2.0625 -2.269 -2.496 -2.745 -3.020 -3.110
13

Working capital – 9% of
EBIT -1.125 -1.2375 -1.361 -1.497 -1.647 -1.812 -1.866
Net Cash Inflow 5.75 6.33 6.96 7.65 8.42 9.26 9.54
WACC – 9.04% 1 0.917 0.841 0.771 0.707 0.649
PV of Cash flow 5.75 5.80 5.85 5.90 5.96 6.01
Present value of cash in year 6 = CF5 / (WACC – g)
= $8,418,575(1 + .03) / (.0904 – .03)
= $143,561,792
discounting cash flows and terminal value in terms of their present value. By Doing so, we find:
V0 = $5,750,000 / 1.0904 + $6,325,000 / 1.09042 + $6,957,500 / 1.09043
+ $7,653,250 / 1.09044 + ($8,418,575 + 143,561,792) / 1.09045
V0 = $119,969,144
Market value of equity = Market value of firm – market value of debt
S = $119,969,144 – 30,500,000
S =$89,469,144
Maximum share price = market value of equity / no. of shares outstanding
Share price = $89,469,144 / 1,850,000
Share price = $48.36
b)
EV/EBITDA multiple = 8
Calculation of Terminal Value using EV/EBITDA multiple = Present EBITDA X 8
= ($12.60 + $ 1.01)million X 8
= $13.61 million X 8
= $ 108.86 million
Therefore maximum share price can be offered = $108.86 million / 1.85 million = $58.84 per
share
14

SECTION B
Question 1
The internal rate of return technique do not provide the clearly picture of future. It ignore
the overall size of project. It ignores future cost with calculation . Mutually exclusive projects
got ignored while calculating the internal rate of return. Different term of project is not
considered while evaluating the internal rate of return technique. In case the later cash inflow are
not sufficient than the IRR is not possible to calculate in the project. Also the wealth of the
project is not possible to measure with the support of internal rate of return method or technique.
It does not account for investment. It suggests to keep match up with multiple cash (Kim, Kim
and Yook, 2021). The disadvantage of the Internal rate of return technique can be solved with the
use of other method or techniques like net present value and the payback period and other
relevant techniques. To overcome the challenges of IRR time horizon can cut down to deal with
the time related issues. Also the management can use this technique only for the projects contain
only a shirt time duration.
Question 3
Beta is a measure of a stock volatility in relation to the overall market. The Beta is one of the
most popular indicator with the help of which investors can measure the risk of the securities.
Beta is a concept that measures the expected move in a stock relative to movements in the
overall market. A beta greater than 1.0 suggest that the particular stock and security is more
volatile than the broader market. While in the case, when Beta is less than 1.0 indicate a stock
with lower volatile. Beta is basically and probably a better indicator of the short-term risk not for
the long term risk (Xiang and et.al., 2019). In order to calculate and estimate the beta of the
securities, the two factors is need to be used. The two factors likely to determine its value is the
risk free return rate and the other one is stocks rate of return.
Beta = Covariance/ variance.
Covariance = measure of a stocks return relative to that of the market
Variance = measure of how the market moves relative to its mean
15

16

REFERENCES
Books and journals
Kim, K., Kim, J. and Yook, D., 2021. Analysis of Features Affecting Contracted Rate of Return
of Korean PPP Projects. Sustainability. 13(6). p.3311.
Xiang, J. and et.al., 2019. Hydroxycinnamic acid amide (HCAA) derivatives, flavonoid C-
glycosides, phenolic acids and antioxidant properties of foxtail millet. Food
chemistry. 295. pp.214-223.
1