Chapter 7 TIME VALUE OF MONEY 1. Value five years hence of a deposit of Rs.1,000 at various interest rates is as follows: r = 8% FV 5 = Rs.1469 r = 10% FV 5 = Rs.1611 r = 12% FV 5 = Rs.1762 r = 15% FV 5 = Rs.2011 2. 30 years 3. In 12 years Rs.1000 grows to Rs.8000 or 8 times. This is 2 3 times the initial deposit. Hence doubling takes place in 12 / 3 = 4 years. According to the Rule of 69, the doubling period is: 0.35 + 69 / Interest rate Equating this to 4 and solving for interest rate, we get Interest rate = 18.9%. 4. Saving Rs.2000 a year for 5 years and Rs.3000 a year for 10 years thereafter is equivalent to saving Rs.2000 a year for 15 years and Rs.1000 a year for the years 6 through 15. Hence the savings will cumulate to: 2000 x FVIFA (10%, 15 years) + 1000 x FVIFA (10%, 10 years) = 2000 x 31.772 + 1000 x 15.937 = Rs.79481. 1
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Chapter 7TIME VALUE OF MONEY
1. Value five years hence of a deposit of Rs.1,000 at various interest rates is as follows:
r = 8% FV5 = Rs.1469
r = 10% FV5 = Rs.1611
r = 12% FV5 = Rs.1762
r = 15% FV5 = Rs.2011
2. 30 years
3. In 12 years Rs.1000 grows to Rs.8000 or 8 times. This is 23 times the initial deposit. Hence doubling takes place in 12 / 3 = 4 years.
According to the Rule of 69, the doubling period is:
0.35 + 69 / Interest rate
Equating this to 4 and solving for interest rate, we get
Interest rate = 18.9%.
4. Saving Rs.2000 a year for 5 years and Rs.3000 a year for 10 years thereafter is equivalent to saving Rs.2000 a year for 15 years and Rs.1000 a year for the years 6 through 15.Hence the savings will cumulate to:2000 x FVIFA (10%, 15 years) + 1000 x FVIFA (10%, 10 years)= 2000 x 31.772 + 1000 x 15.937 = Rs.79481.
5. Let A be the annual savings.
A x FVIFA (12%, 10 years) = 1,000,000A x 17.549 = 1,000,000
So, A = 1,000,000 / 17.549 = Rs.56,983.
6. 1,000 x FVIFA (r, 6 years) = 10,000
FVIFA (r, 6 years) = 10,000 / 1000 = 10
1
From the tables we find thatFVIFA (20%, 6 years) = 9.930FVIFA (24%, 6 years) = 10.980
Using linear interpolation in the interval, we get:
20% + (10.000 – 9.930) r = x 4% = 20.3% (10.980 – 9.930)
12. The present value of the income stream is:1,000 x PVIF (12%, 1 year) + 2,500 x PVIF (12%, 2 years)+ 5,000 x PVIFA (12%, 8 years) x PVIF(12%, 2 years)
= 1,000 x 0.893 + 2,500 x 0.797 + 5,000 x 4.968 x 0.797 = Rs.22,683.
13. The present value of the income stream is:2,000 x PVIFA (10%, 5 years) + 3000/0.10 x PVIF (10%, 5 years)= 2,000 x 3.791 + 3000/0.10 x 0.621= Rs.26,212
14. To earn an annual income of Rs.5,000 beginning from the end of 15 years from now, if the deposit earns 10% per year a sum of
Rs.5,000 / 0.10 = Rs.50,000is required at the end of 14 years. The amount that must be deposited to get this sum is:
From the tables we find that:PVIFA (15%, 10 years) = 5.019PVIFA (18%, 10 years) = 4.494
Using linear interpolation we get:5.019 – 5.00
r = 15% + ---------------- x 3%5.019 – 4.494
= 15.1%
16. PV (Stream A) = Rs.100 x PVIF (12%, 1 year) + Rs.200 xPVIF (12%, 2 years) + Rs.300 x PVIF(12%, 3 years) + Rs.400 x
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PVIF (12%, 4 years) + Rs.500 x PVIF (12%, 5 years) +Rs.600 x PVIF (12%, 6 years) + Rs.700 x PVIF (12%, 7 years) +Rs.800 x PVIF (12%, 8 years) + Rs.900 x PVIF (12%, 9 years) +Rs.1,000 x PVIF (12%, 10 years)
= Rs.100 x 0.893 + Rs.200 x 0.797 + Rs.300 x 0.712 + Rs.400 x 0.636 + Rs.500 x 0.567 + Rs.600 x 0.507 + Rs.700 x 0.452 + Rs.800 x 0.404 + Rs.900 x 0.361 + Rs.1,000 x 0.322
= Rs.2590.9
Similarly,PV (Stream B) = Rs.3,625.2PV (Stream C) = Rs.2,851.1
Difference between theeffective rate and statedrate (%) 0.6 2.2 2.8
20. Investment required at the end of 8th year to yield an income of Rs.12,000 per year from the end of 9th year (beginning of 10th year) for ever:
Rs.12,000 x PVIFA(12%, ∞ )
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= Rs.12,000 / 0.12 = Rs.100,000
To have a sum of Rs.100,000 at the end of 8th year , the amount to be deposited now is: Rs.100,000 Rs.100,000
= = Rs.40,388PVIF(12%, 8 years) 2.476
21. The interest rate implicit in the offer of Rs.20,000 after 10 years in lieu of Rs.5,000 now is:Rs.5,000 x FVIF (r,10 years) = Rs.20,000
Rs.20,000 FVIF (r,10 years) = = 4.000
Rs.5,000
From the tables we find thatFVIF (15%, 10 years) = 4.046
This means that the implied interest rate is nearly 15%.I would choose Rs.20,000 for 10 years from now because I find a return of 15% quite
acceptable.
22. FV10 = Rs.10,000 [1 + (0.10 / 2)]10x2
= Rs.10,000 (1.05)20
= Rs.10,000 x 2.653= Rs.26,530
If the inflation rate is 8% per year, the value of Rs.26,530 10 years from now, in terms of the current rupees is:
Rs.26,530 x PVIF (8%,10 years)= Rs.26,530 x 0.463 = Rs.12,283
23. A constant deposit at the beginning of each year represents an annuity due.PVIFA of an annuity due is equal to : PVIFA of an ordinary annuity x (1 + r)To provide a sum of Rs.50,000 at the end of 10 years the annual deposit should
be
Rs.50,000 A = FVIFA(12%, 10 years) x (1.12)
Rs.50,000 = = Rs.2544
17.549 x 1.12
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24. The discounted value of Rs.20,000 receivable at the beginning of each year from 2005 to 2009, evaluated as at the beginning of 2004 (or end of 2003) is:
Rs.20,000 x PVIFA (12%, 5 years)= Rs.20,000 x 3.605 = Rs.72,100.
The discounted value of Rs.72,100 evaluated at the end of 2000 isRs.72,100 x PVIF (12%, 3 years)
= Rs.72,100 x 0.712 = Rs.51,335
If A is the amount deposited at the end of each year from 1995 to 2000 thenA x FVIFA (12%, 6 years) = Rs.51,335A x 8.115 = Rs.51,335A = Rs.51,335 / 8.115 = Rs.6326
25. The discounted value of the annuity of Rs.2000 receivable for 30 years, evaluated as at the end of 9th year is:
Rs.2,000 x PVIFA (10%, 30 years) = Rs.2,000 x 9.427 = Rs.18,854The present value of Rs.18,854 is:
Rs.18,854 x PVIF (10%, 9 years)= Rs.18,854 x 0.424= Rs.7,994
26. 30 per cent of the pension amount is 0.30 x Rs.600 = Rs.180
Assuming that the monthly interest rate corresponding to an annual interest rate of 12% is 1%, the discounted value of an annuity of Rs.180 receivable at the end of each month for 180 months (15 years) is:
Rs.180 x PVIFA (1%, 180)
(1.01)180 - 1Rs.180 x ---------------- = Rs.14,998
.01 (1.01)180
If Mr. Ramesh borrows Rs.P today on which the monthly interest rate is 1%
From the tables we find that:PVIFA(1%,24) = 21.244
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PVIFA (2%, 24) = 18.914
Using a linear interpolation21.244 – 20.000
r = 1% + ---------------------- x 1% 21.244 – 18,914
= 1.53%
Thus, the bank charges an interest rate of 1.53% per month.The corresponding effective rate of interest per annum is
[ (1.0153)12 – 1 ] x 100 = 20%
28. The discounted value of the debentures to be redeemed between 8 to 10 years evaluated at the end of the 5th year is:
Rs.10 million x PVIF (8%, 3 years) + Rs.10 million x PVIF (8%, 4 years) + Rs.10 million x PVIF (8%, 5 years)
= Rs.10 million (0.794 + 0.735 + 0.681) = Rs.2.21 million
If A is the annual deposit to be made in the sinking fund for the years 1 to 5, thenA x FVIFA (8%, 5 years) = Rs.2.21 millionA x 5.867 = Rs.2.21 millionA = 5.867 = Rs.2.21 millionA = Rs.2.21 million / 5.867 = Rs.0.377 million
29. Let `n’ be the number of years for which a sum of Rs.20,000 can be withdrawn annually.
31. Define n as the maturity period of the loan. The value of n can be obtained from the equation.
200,000 x PVIFA(13%, n) = 1,500,000PVIFA (13%, n) = 7.500
From the tables or otherwise it can be verified that PVIFA(13,30) = 7.500Hence the maturity period of the loan is 30 years.
32. Expected value of iron ore mined during year 1 = Rs.300 million
Expected present value of the iron ore that can be mined over the next 15 years assuming a price escalation of 6% per annum in the price per tonne of iron
1 – (1 + g)n / (1 + i)n
= Rs.300 million x ------------------------ i - g
= Rs.300 million x 1 – (1.06) 15 / (1.16) 15 0.16 – 0.06
= Rs.300 million x (0.74135 / 0.10)= Rs.2224 million
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MINICASE
Solution:
1. How much money would Ramesh need 15 years from now?
500,000 x PVIFA (10%, 15years)+ 1,000,000 x PVIF (10%, 15years)= 500,000 x 7.606 + 1,000,000 x 0.239= 3,803,000 x 239,000 = Rs.4,042,000
2. How much money should Ramesh save each year for the next 15 years to be able to meet his investment objective?
Ramesh’s current capital of Rs.600,000 will grow to :
600,000 (1.10)15 = 600,000 x 4.177 = Rs 2,506,200
This means that his savings in the next 15 years must grow to :
4,042,000 – 2,506,200 = Rs 1,535,800
So, the annual savings must be : 1,535,800 1,535,800
= = Rs.48,338FVIFA (10%, 15 years) 31.772
3. How much money would Ramesh need when he reaches the age of 60 to meet his donation objective?
200,000 x PVIFA (10% , 3yrs) x PVIF (10%, 11yrs)
= 200,000 x 2.487 x 0.317 = 157,676
4. What is the present value of Ramesh’s life time earnings?
400,000 400,000(1.12) 400,000(1.12)14
46 1 2 15
9
1.12 15
1 – 1.08
= 400,000 0.08 – 0.12
= Rs.7,254,962
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Chapter 8
VALUATION OF BONDS AND STOCKS
1. 5 11 100P = +
t=1 (1.15) (1.15)5
= Rs.11 x PVIFA(15%, 5 years) + Rs.100 x PVIF (15%, 5 years)= Rs.11 x 3.352 + Rs.100 x 0.497= Rs.86.7
2.(i) When the discount rate is 14%7 12 100
P = +t=1 (1.14) t (1.14)7
= Rs.12 x PVIFA (14%, 7 years) + Rs.100 x PVIF (14%, 7 years)= Rs.12 x 4.288 + Rs.100 x 0.4= Rs.91.46
(ii) When the discount rate is 12%7 12 100
P = + = Rs.100t=1 (1.12) t (1.12)7
Note that when the discount rate and the coupon rate are the same the value is equal to par value.
3. The yield to maturity is the value of r that satisfies the following equality. 7 120 1,000
Rs.750 = + = Rs.100 t=1 (1+r) t (1+r)7
Try r = 18%. The right hand side (RHS) of the above equation is:Rs.120 x PVIFA (18%, 7 years) + Rs.1,000 x PVIF (18%, 7 years)= Rs.120 x 3.812 + Rs.1,000 x 0.314= Rs.771.44
Try r = 20%. The right hand side (RHS) of the above equation is:Rs.120 x PVIFA (20%, 7 years) + Rs.1,000 x PVIF (20%, 7 years)= Rs.120 x 3.605 + Rs.1,000 x 0.279= Rs.711.60Thus the value of r at which the RHS becomes equal to Rs.750 lies between 18% and 20%.
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Using linear interpolation in this range, we get
771.44 – 750.00Yield to maturity = 18% + 771.44 – 711.60 x 2%
= 18.7%4.
10 14 100 80 = +
t=1 (1+r) t (1+r)10
Try r = 18%. The RHS of the above equation is
Rs.14 x PVIFA (18%, 10 years) + Rs.100 x PVIF (18%, 10 years)= Rs.14 x 4.494 + Rs.100 x 0.191 = Rs.82
Try r = 20%. The RHS of the above equation isRs.14 x PVIFA(20%, 10 years) + Rs.100 x PVIF (20%, 10 years)= Rs.14 x 4.193 + Rs.100 x 0.162= Rs.74.9
Using interpolation in the range 18% and 20% we get:
82 - 80Yield to maturity = 18% + ----------- x 2%
82 – 74.9
= 18.56%
5.12 6 100
P = +t=1 (1.08) t (1.08)12
= Rs.6 x PVIFA (8%, 12 years) + Rs.100 x PVIF (8%, 12 years)= Rs.6 x 7.536 + Rs.100 x 0.397= Rs.84.92
6. The post-tax interest and maturity value are calculated below:
12. The market price per share of Commonwealth Corporation will be the sum of three components:
A: Present value of the dividend stream for the first 4 yearsB: Present value of the dividend stream for the next 4 yearsC: Present value of the market price expected at the end of 8 years.
(c ) The standard deviation of rate of return is : σ = pi (Ri – R)2
The σ of the rate of return on MVM’s stock is calculated below:--------------------------------------------------------------------------------------------------- Ri pi pI ri (Ri-R) (R i- R)2 pi (Ri-R)2
2 (a) For Rs.1,000, 20 shares of Alpha’s stock can be acquired. The probability distribution of the return on 20 shares is
Economic Condition Return (Rs) ProbabilityHigh Growth 20 x 55 = 1,100 0.3Low Growth 20 x 50 = 1,000 0.3Stagnation 20 x 60 = 1,200 0.2Recession 20 x 70 = 1,400 0.2
Expected return = (1,100 x 0.3) + (1,000 x 0.3) + (1,200 x 0.2) + (1,400 x 0.2)
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= 330 + 300 + 240 + 280= Rs.1,150
Standard deviation of the return = [(1,100 – 1,150)2 x 0.3 + (1,000 – 1,150)2 x
0.3 + (1,200 – 1,150)2 x 0.2 + (1,400 – 1,150)2 x 0.2]1/2
= Rs.143.18
(b) For Rs.1,000, 20 shares of Beta’s stock can be acquired. The probability distribution of the return on 20 shares is:
Economic condition Return (Rs) Probability
High growth 20 x 75 = 1,500 0.3Low growth 20 x 65 = 1,300 0.3Stagnation 20 x 50 = 1,000 0.2Recession 20 x 40 = 800 0.2
Expected return = (1,500 x 0.3) + (1,300 x 0.3) + (1,000 x 0.2) + (800 x 0.2) = Rs.1,200
Standard deviation of the return = [(1,500 – 1,200)2 x .3 + (1,300 – 1,200)2 x .3 + (1,000 – 1,200)2 x .2 + (800 – 1,200)2 x .2]1/2 = Rs.264.58
(c ) For Rs.500, 10 shares of Alpha’s stock can be acquired; likewise for Rs.500, 10 shares of Beta’s stock can be acquired. The probability distribution of this option is:
Return (Rs) Probability(10 x 55) + (10 x 75) = 1,300 0.3(10 x 50) + (10 x 65) = 1,150 0.3(10 x 60) + (10 x 50) = 1,100 0.2(10 x 70) + (10 x 40) = 1,100 0.2
Expected return = (1,300 x 0.3) + (1,150 x 0.3) + (1,100 x 0.2) + (1,100 x 0.2)
= Rs.1,175Standard deviation = [(1,300 –1,175)2 x 0.3 + (1,150 – 1,175)2 x 0.3 +
(1,100 – 1,175)2 x 0.2 + (1,100 – 1,175)2 x 0.2 ]1/2
= Rs.84.41d. For Rs.700, 14 shares of Alpha’s stock can be acquired; likewise for Rs.300, 6 shares of Beta’s stock can be acquired. The probability distribution of this
option is:
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Return (Rs) Probability
(14 x 55) + (6 x 75) = 1,220 0.3(14 x 50) + (6 x 65) = 1,090 0.3(14 x 60) + (6 x 50) = 1,140 0.2(14 x 70) + (6 x 40) = 1,220 0.2
Expected return = (1,220 x 0.3) + (1,090 x 0.3) + (1,140 x 0.2) + (1,220 x 0.2) = Rs.1,165
Standard deviation = [(1,220 – 1,165)2 x 0.3 + (1,090 – 1,165)2 x 0.3 + (1,140 – 1,165)2 x 0.2 + (1,220 – 1,165)2 x 0.2]1/2
= Rs.57.66
The expected return to standard deviation of various options are as follows :
(a) Return on portfolio consisting of stock A = 7.83%
(b) Return on portfolio consisting of stock A and B in equalproportions = 0.5 (0.0783) + 0.5 (0.0917)
= 0.085 = 8.5%
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(c ) Return on portfolio consisting of stocks A, B and C in equalproportions = 1/3(0.0783 ) + 1/3(0.0917) + 1/3 (0.090)
= 0.0867 = 8.67%
(d) Return on portfolio consisting of stocks A, B, C and D in equalproportions = 0.25(0.0783) + 0.25(0.0917) + 0.25(0.0900) +
0.25(0.095)= 0.08875 = 8.88%
4. Define RA and RM as the returns on the equity stock of Auto Electricals Limited a and Market portfolio respectively. The calculations relevant for calculating the beta of the stock are shown below:
Year RA RM RA-RA RM-RM (RA-RA) (RM-RM) RA-RA/RM-RM
Intrinsic value of share = D1 / (r- g) = Do (1+g) / ( r – g)
Given Do = Rs.2.00, g = 0.08, r = 0.175 2.00 (1.08)
Intrinsic value per share of stock A = 0.175 – 0.08
= Rs.22.74
6. The SML equation is RA = RF + βA (RM – RF)
Given RA = 15%. RF = 8%, RM = 12%, we have
0.15 = .08 + βA (0.12 – 0.08)
0.07i.e.βA = = 1.75
0.04
Beta of stock A = 1.75
7. The SML equation is: RX = RF + βX (RM – RF)
We are given 0.15 = 0.09 + 1.5 (RM – 0.09) i.e., 1.5 RM = 0.195or RM = 0.13%
Therefore return on market portfolio = 13%
8. RM = 12% βX = 2.0 RX =18% g = 5% Po = Rs.30
Po = D1 / (r - g)
Rs.30 = D1 / (0.18 - .05)
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So D1 = Rs.39 and Do = D1 / (1+g) = 3.9 /(1.05) = Rs.3.71
Rx = Rf + βx (RM – Rf)
0.18 = Rf + 2.0 (0.12 – Rf)
So Rf = 0.06 or 6%.
Original Revised
Rf 6% 8%RM – Rf 6% 4%g 5% 4%βx 2.0 1.8
Revised Rx = 8% + 1.8 (4%) = 15.2%
Price per share of stock X, given the above changes is
3.71 (1.04)= Rs.34.45
0.152 – 0.04
Chapter 10OPTIONS AND THEIR VALUATION
1. S = 100 u = 1.5 d = 0.8
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E = 105 r = 0.12 R = 1.12
The values of ∆ (hedge ratio) and B (amount borrowed) can be obtained as follows:
Cu – Cd
∆ =(u – d) S
Cu = Max (150 – 105, 0) = 45
Cd = Max (80 – 105, 0) = 0
45 – 0 45 9∆ = = = = 0.6429
0.7 x 100 70 14
u.Cd – d.Cu
B =(u-d) R
(1.5 x 0) – (0.8 x 45)=
0.7 x 1.12
-36= = - 45.92
0.784
C = ∆ S + B= 0.6429 x 100 – 45.92= Rs.18.37
Value of the call option = Rs.18.37
2. S = 40 u = ? d = 0.8R = 1.10 E = 45 C = 8
We will assume that the current market price of the call is equal to the pair value of the call as per the Binomial model.
Given the above data
Cd = Max (32 – 45, 0) = 0
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∆ Cu – Cd R= x
B u Cd – d Cu S
∆ Cu – 0 1.10= x
B -0.8Cu 40
= (-) 0.034375
∆ = - 0.34375 B (1)C = ∆ S + B8 = ∆ x 40 + B (2)
Substituting (1) in (2) we get
8 = (-0.034365 x 40) B + B8 = -0.375 Bor B = - 21.33
∆ = - 0.034375 (-21.33) = 0.7332
The portfolio consists of 0.7332 of a share plus a borrowing of Rs.21.33 (entailing a repayment of Rs.21.33 (1.10) = Rs.23.46 after one year). It follows that when u occurs either u x 40 x 0.7332 – 23.46 = u x 40 – 45
-10.672 u = -21.54 u = 2.02
or
u x 40 x 0.7332 – 23.46 = 0u = 0.8
Since u > d, it follows that u = 2.02.Put differently the stock price is expected to rise by 1.02 x 100 = 102%.
3. Using the standard notations of the Black-Scholes model we get the following results:ln (S/E) + rt + σ2 t/2
d1 = t
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= ln (120 / 110) + 0.14 + 0.4 2 /2 0.4
= 0.08701 + 0.14 + 0.08 0.4
= 0.7675
d2 = d1 - t= 0.7675 – 0.4= 0.3675
N(d1) = N (0.7675) ~ N (0.77) = 0.80785N (d2) = N (0.3675) ~ N (0.37) = 0.64431
C = So N(d1) – E. e-rt. N(d2)= 120 x 0.80785 – 110 x e-0.14 x 0.64431= (120 x 0.80785) – (110 x 0.86936 x 0.64431)= 35.33
Value of the call as per the Black and Scholes model is Rs.35.33.
4. t = 0.2 x 1 = 0.2
Ratio of the stock price to the present value of the exercise price 80
= ------------------------- 82 x PVIF (15.03,1)
80= ----------------------
82 x 0.8693= 1.122
From table A6 we find the percentage relationship between the value of the call option and stock price to be 14.1 per cent. Hence the value of the call option is
0.141 x 80 = Rs.11,28.
5. Value of put option = Value of the call option+ Present value of the exercise price- Stock price ……… (A)
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The value of the call option gives an exercise price of Rs.85 can be obtained as follows:
t = 0.2 1 = 0.2
Ratio of the stock price to the present value of the exercise price
80= ---------------------
85 x PVIF (15.03,1)
= 80 / 73.89 = 1.083
From Table A.6, we find the percentage relationship between the value of the call option and the stock price to be 11.9%
Hence the value of the call option = 0.119 x 80 = Rs.9.52
Plugging in this value and the other relevant values in (A), we get
b) NP V = 40,000 x PVIFA (12,5)+ 30,000 x PVIFA (12,2) x PVIF (12,5)+ 20,000 x PVIFA (12,3) x PVIF (12,7)- 300,000
= (40,000 x 3.605) + (30,000 x 1.690 x 0.567)+ (20,000 x 2.402 x 0.452) – 300,000
= - 105339
c) IRR (r ) can be obtained by solving the equation 40,000 x PVIFA (r, 5) + 30,000 x PVIFA (r, 2) x PVIF (r,5) +20,000 x PVIFA (r, 3) x PVIF (r, 7) = 300,000
Through the process of trial and error we find thatr = 1.37%
d) BCR = PVB / I= 194,661 / 300,000 = 0.65
Investment C
a) Payback period lies between 2 years and 3 years. Linear interpolation in this range provides an approximate payback period of 2.88 years.
b) NPV = 80.000 x PVIF (12,1) + 60,000 x PVIF (12,2) + 80,000 x PVIF (12,3) + 60,000 x PVIF (12,4)
+ 80,000 x PVIF (12,5) + 60,000 x PVIF (12,6)+ 40,000 x PVIFA (12,4) x PVIF (12.6)- 210,000
= 111,371
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c) IRR (r) is obtained by solving the equation80,000 x PVIF (r,1) + 60,000 x PVIF (r,2) + 80,000 x PVIF (r,3) + 60,000 x PVIF (r,4) + 80,000 x PVIF (r,5) + 60,000 x PVIF (r,6)+ 40000 x PVIFA (r,4) x PVIF (r,6) = 210000
Through the process of trial and error we get r = 29.29%
d) BCR = PVB / I = 321,371 / 210,000 = 1.53
Investment D
a) Payback period lies between 8 years and 9 years. A linear interpolation in this range provides an approximate payback period of 8.5 years.
8 + (1 x 100,000 / 200,000)
b) NPV = 200,000 x PVIF (12,1)+ 20,000 x PVIF (12,2) + 200,000 x PVIF (12,9)+ 50,000 x PVIF (12,10) - 320,000
= - 37,160
c) IRR (r ) can be obtained by solving the equation200,000 x PVIF (r,1) + 200,000 x PVIF (r,2) + 200,000 x PVIF (r,9) + 50,000 x PVIF (r,10)
= 320000
Through the process of trial and error we get r = 8.45%
d) BCR = PVB / I = 282,840 / 320,000 = 0.88
Comparative Table
Investment A B C D
a) Payback period (in years) 5 9 2.88 8.5
b) NPV @ 12% pa 26000 -105339 111371 -37160
c) IRR (%) 15.14 1.37 29.29 8.45
d) BCR 1.13 0.65 1.53 0.88
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Among the four alternative investments, the investment to be chosen is ‘C’because it has the Lowest payback period
Highest NPVHighest IRRHighest BCR
3. IRR (r) can be calculated by solving the following equations for the value of r. 60000 x PVIFA (r,7) = 300,000
i.e., PVIFA (r,7) = 5.000
Through a process of trial and error it can be verified that r = 9.20% pa.
4. The IRR (r) for the given cashflow stream can be obtained by solving the following equation for the value of r.
-3000 + 9000 / (1+r) – 3000 / (1+r) = 0
Simplifying the above equation we get
r = 1.61, -0.61; (or) 161%, (-)61%
NOTE: Given two changes in the signs of cashflow, we get two values for the IRR of the cashflow stream. In such cases, the IRR rule breaks down.
5. 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
NCF x PVIFA (10,8) = 500000NCF = 500000 / 5.335
= 93271
6. Define I as the initial investment that is justified in relation to a net annual cashinflow of 25000 for 10 years at a discount rate of 12% per annum. The value of I can be obtained from the following equation
25000 x PVIFA (12,10) = Ii.e., I = 141256
7. PV of benefits (PVB) = 25000 x PVIF (15,1)+ 40000 x PVIF (15,2)+ 50000 x PVIF (15,3)+ 40000 x PVIF (15,4)+ 30000 x PVIF (15,5)
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= 122646 (A)
Investment = 100,000 (B)
Benefit cost ratio = 1.23 [= (A) / (B)]
8. The NPV’s of the three projects are as follows:
Project P Q R
Discount rate
0% 400 500 6005% 223 251 312
10% 69 40 7015% - 66 - 142 - 135
25% - 291 - 435 - 46130% - 386 - 555 - 591
9. NPV profiles for Projects P and Q for selected discount rates are as follows:(a)
NPV at a cost of capital of 12%= - 100 + 25 x PVIFA (12,6)= Rs.2.79 million
IRR (r ) can be obtained by solving the following equation for r.25 x PVIFA (r,6) = 100i.e., r = 12,98%
Project B
NPV at a cost of capital of 12%= - 50 + 13 x PVIFA (12,6)= Rs.3.45 million
IRR (r') can be obtained by solving the equation13 x PVIFA (r',6) = 50i.e., r' = 14.40% [determined through a process of trial and error]
(b) Difference in capital outlays between projects A and B is Rs.50 millionDifference in net annual cash flow between projects A and B is Rs.12 million.NPV of the differential project at 12%
= -50 + 12 x PVIFA (12,6)= Rs.3.15 million
IRR (r'') of the differential project can be obtained from the equation12 x PVIFA (r'', 6) = 50i.e., r'' = 11.53%
11(a) 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 NThe pay back period lies between 1 and 2 years. Interpolating in this range we get an approximate pay back period of 1.55 years.
(b) Project M
34
Cost of capital = 12% p.aPV of cash flows up to the end of year 2 = 24.97PV of cash flows up to the end of year 3 = 47.75PV of cash flows up to the end of year 4 = 71.26
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 NCost of capital = 12% per annumPV of cash flows up to the end of year 1 = 33.93PV of cash flows up to the end of year 2 = 51.47
DPB lies between 1 and 2 years. Interpolating in this range we get an approximate DPB of 1.92 years.
(c ) Project MCost of capital = 12% per annumNPV = - 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 NCost of capital = 12% per annumNPV = Rs.20.63 millionSince 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.
(d) Project MCost of capital = 10% per annumNPV = Rs.25.02 million
Project NCost of capital = 10% per annumNPV = 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.NOTE: The MIRR can also be used as a criterion of merit for choosing between the two projects because their initial outlays are equal.
(e) Project MCost of capital = 15% per annumNPV = 16.13 million
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Project NCost of capital: 15% per annumNPV = Rs.17.23 millionAgain the two projects are mutually exclusive. So we choose the project with the higher NPV, i.e., choose project N.
(f) Project M Terminal value of the cash inflows: 114.47MIRR of the project is given by the equation
50 (1 + MIRR)4 = 114.47i.e., MIRR = 23.01%
Project NTerminal value of the cash inflows: 115.41MIRR of the project is given by the equation
(b) NPV of the net cash flow stream @ 15% per discount rate
= -140 + 10.20 x PVIF(15,1) + 20.55 x PVIF (15,2)+ 31.46 x PVIF (15,3) + 62.80 x PVIF (15,4) + 49.25 x PVIF (15,5)+ 35.94 x PVIF (15,6) + 55 x PVIF (15,7)
= Rs.1.70 million
3.(a) A. Initial outlay (Time 0)
38
i. Cost of new machine Rs. 3,000,000ii. Salvage value of old machine 900,000iii Incremental working capital requirement 500,000iv. Total net investment (=i – ii + iii) 2,600,000
B. Operating cash flow (years 1 through 5)
Year 1 2 3 4 5
i. Post-tax savings in manufacturing costs 455,000 455,000 455,000 455,000 455,000
ii. Incremental depreciation 550,000 412,500 309,375 232,031 174,023
iii. Tax shield on incremental dep. 165,000 123,750 92,813 69,609 52,207iv. Operating cash flow ( i + iii) 620,000 578,750 547,813 524,609 507,207
C. Terminal cash flow (year 5)
i. Salvage value of new machine Rs. 1,500,000ii. Salvage value of old machine 200,000iii. Recovery of incremental working capital 500,000iv. Terminal cash flow ( i – ii + iii) 1,800,000
D. Net cash flows associated with the replacement project (in Rs)
Assumptions: (1) The useful life is assumed to be 10 years under all three scenarios. It is also assumed that the salvage value of the
investment after ten years is zero.
(2) The investment is assumed to be depreciated at 10% per annum; and it is also assumed that this method and rate of depreciation are acceptable to the IT (income tax) authorities.
(3) The tax rate has been calculated from the given table i.e. 10 / 35 x 100 = 28.57%.
(4) It is assumed that only loss on this project can be offset against the taxable profit on other projects of the company; and thus the company can claim a tax shield on the loss in the same year.
(c) Accounting break even point (under ‘expected’ scenario)Fixed costs + depreciation = Rs. 45 million
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Contribution margin ratio = 60 / 200 = 0.3Break even level of sales = 45 / 0.3 = Rs.150 million
Financial break even point (under ‘xpected’ scenario)
i. Annual net cash flow = 0.7143 [ 0.3 x sales – 45 ] + 25= 0.2143 sales – 7.14
ii. PV (net cash flows) = [0.2143 sales – 7.14 ] x PVIFA (13,10)= 1.1628 sales – 38.74
iii. Initial investment = 200
iv. Financial break even levelof sales = 238.74 / 1.1628 = Rs.205.31 million
2.(a) Sensitivity of NPV with respect to quantity manufactured and sold:
(in Rs)Pessimistic Expected Optimistic
Initial investment 30000 30000 30000Sale revenue 24000 42000 54000Variable costs 16000 28000 36000Fixed costs 3000 3000 3000Depreciation 2000 2000 2000Profit before tax 3000 9000 13000Tax 1500 4500 6500Profit after tax 1500 4500 6500Net cash flow 3500 6500 8500NPV at a cost of capital of 10% p.aand useful life of 5 years -16732 - 5360 2222
(b) Sensitivity of NPV with respect to variations in unit price.
Exhibit 1 presents the correspondence between the values of exogenous variables and the two digit random number. Exhibit 2 shows the results of the simulation.
Exhibit 1 Correspondence between values of exogenous variables and
7. To carry out a sensitivity analysis, we have to define the range and the most likely values of the variables in the NPV Model. These values are defined below
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Variable Range Most likely value
I Rs.30,000 – Rs.30,000 Rs.30,000k 10% - 10% 10%F Rs.3,000 – Rs.3,000 Rs.3,000D Rs.2,000 – Rs.2,000 Rs.2,000T 0.5 – 0.5 0.5N 5 – 5 5S 0 – 0 0Q Can assume any one of the values - 1,400*
800, 1,000, 1,200, 1,400, 1,600 and 1,800P Can assume any of the values 20, 30, 30**
40 and 50V Can assume any one of the values 20*
15,20 and 40---------------------------------------------------------------------------------------- * The most likely values in the case of Q, P and V are the values that have the
highest probability associated with them
** In the case of price, 20 and 30 have the same probability of occurrence viz 0.4. We have chosen 30 as the most likely value because the expected value of the distribution is closer to 30
Sensitivity Analysis with Reference to Q
The relationship between Q and NPV given the most likely values of other variables is given by
The standard deviation of P1 is .1075 for the given investment with an expected PI of 1.24. The maximum standard deviation of PI acceptable to the company for an investment with an expected PI of 1.25 is 0.30.
Since the risk associated with the investment is much less than the maximum risk acceptable to the company for the given level of expected PI, the company must should accept the investment.
9. The NPVs of the two projects calculated at their risk adjusted discount rates are as follows: 6 3,000
Project A: NPV = - 10,000 = Rs.2,333t=1 (1.12)t
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5 11,000Project B: NPV = - 30,000 = Rs.7,763
t=1 (1.14)t
PI and IRR for the two projects are as follows:
Project A B
PI 1.23 1.26IRR 20% 24.3%
B is superior to A in terms of NPV, PI, and IRR. Hence the company must choose B.
10. The certainty equivalent co-efficients for the five years are as follows
Year Certainty equivalent coefficient
t = 1 – 0.06 t
1 1 = 0.942 2 = 0.883 3 = 0.82 4 = 0.76 5 = 0.70
The present value of the project calculated at the risk-free rate of return is : 5 (1 – 0.06 t) At
t=1 (1.08)t
7,000 x 0.94 8,000 x 0.88 9,000 x 0.82 10,000 x 0.76 8,000 x 0.70 + + + +
(1.08) (1.08)2 (1.08)3 (1.08)4 (1.08)5
6,580 7,040 7,380 7,600 5,600 + + + +
(1.08) (1.08)2 (1.08)3 (1.08)4 (1.08)5
= 27,386
Net present value of the Project = (27,386 – 30,000 = Rs. –2,614
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MINICASE
Solution:1. The expected NPV of the turboprop aircraft
2. If Southern Airways buys the piston engine aircraft and the demand in year 1 turns out to be high, a further decision has to be made with respect to capacity expansion. To evaluate the piston engine aircraft, proceed as follows:
First, calculate the NPV of the two options viz., ‘expand’ and ‘do not expand’ at decision point D2:
0.8 (15000) + 0.2 (1600)Expand : NPV = - 4400 +
1.12
= 6600
0.8 (6500) + 0.2 (2400)Do not expand : NPV =
1.12= 5071
Second, truncate the ‘do not expand’ option as it is inferior to the ‘expand’ option. This means that the NPV at decision point D2 will be 6600
Third, calculate the NPV of the piston engine aircraft option.
0.65 (2500+6600) + 0.35 (800)NPV = – 5500 +
1.12
55
0.35 [0.2 (6500) + 0.8 (2400)] +
(1.12)2
= – 5500 + 5531 + 898 = 929
3. The value of the option to expand in the case of piston engine aircraftIf Southern Airways does not have the option of expanding capacity at the end of year 1, the NPV of the piston engine aircraft would be:
2. Define rp as the cost of preference capital. Using the approximate yield formula rp can be calculated as follows:
9 + (100 – 92)/6rp = --------------------
0.4 x100 + 0.6x92
= 0.1085 (or) 10.85%
3. WACC = 0.4 x 13% x (1 – 0.35)+ 0.6 x 18%
= 14.18%
4. Cost of equity = 10% + 1.2 x 7% = 18.4%(using SML equation)
Pre-tax cost of debt = 14%
After-tax cost of debt = 14% x (1 – 0.35) = 9.1%
Debt equity ratio = 2 : 3
WACC = 2/5 x 9.1% + 3/5 x 18.4%
= 14.68%
5. Given0.5 x 14% x (1 – 0.35) + 0.5 x rE = 12%
where rE is the cost of equity capital.
Therefore rE – 14.9%
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Using the SML equation we get
11% + 8% x β = 14.9%
where β denotes the beta of Azeez’s equity.
Solving this equation we get β = 0.4875.
6(a) The cost of debt of 12% represents the historical interest rate at the time the debt was originally issued. But we need to calculate the marginal cost of debt (cost of raising new debt); and for this purpose we need to calculate the yield to maturity of the debt as on the balance sheet date. The yield to maturity will not be equal to12% unless the book value of debt is equal to the market value of debt on the balance sheet date.
(b) The cost of equity has been taken as D1/P0 ( = 6/100) whereas the cost of equity is (D1/P0) + g where g represents the expected constant growth rate in dividend per share.
7. The book value and market values of the different sources of finance are provided in the following table. The book value weights and the market value weights are provided within parenthesis in the table.
(Rs. in million)Source Book value Market valueEquity 800 (0.54) 2400 (0.78)Debentures – first series 300 (0.20) 270 (0.09)Debentures – second series 200 (0.13) 204 (0.06)Bank loan 200 (0.13) 200 (0.07)Total 1500 (1.00) 3074 (1.00)
Given a hurdle rate of 18% (the firm’s cost of capital), projects P, Q and R would have been rejected because the expected returns on these projects are below 18%. Project S would be accepted because the expected return on this project exceeds 18%.An appropriate basis for
59
accepting or rejecting the projects would be to compare the expected rate of return and the required rate of return for each project. Based on this comparison, we find that all the four projects need to be rejected.
9.(a) Given
rD x (1 – 0.3) x 4/9 + 20% x 5/9 = 15%rD = 12.5%,where rD represents the pre-tax cost of debt.
(b) Given13% x (1 – 0.3) x 4/9 + rE x 5/9 = 15%rE = 19.72%, where rE represents the cost of equity.
10. Cost of equity = D1/P0 + g = 3.00 / 30.00 + 0.05 = 15%
(a) The first chunk of financing will comprise of Rs.5 million of retained earnings costing 15 percent and Rs.25 million of debt costing 14 (1-.3) = 9.8 per centThe second chunk of financing will comprise of Rs.5 million of additional equity costing 15 per cent and Rs.2.5 million of debt costing 15 (1-.3) = 10.5 per cent
(b) The marginal cost of capital in the first chunk will be :5/7.5 x 15% + 2.5/7.5 x 9.8% = 13.27%
The marginal cost of capital in the second chunk will be: 5/7.5 x 15% + 2.5/7.5 x 10.5% = 13.50%
Note : We have assumed that(i) The net realisation per share will be Rs.25, after floatation costs, and(ii) The planned investment of Rs.15 million is inclusive of floatation costs
11. The cost of equity and retained earningsrE = D1/PO + g
= 1.50 / 20.00 + 0.07 = 14.5%The cost of preference capital, using the approximate formula, is :
11 + (100-75)/10rE = = 15.9%
0.6 x 75 + 0.4 x 100
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The pre-tax cost of debentures, using the approximate formula, is :
13.5 + (100-80)/6rD = = 19.1%
0.6x80 + 0.4x100
The post-tax cost of debentures is 19.1 (1-tax rate) = 19.1 (1 – 0.5)
= 9.6%
The post-tax cost of term loans is 12 (1-tax rate) = 12 (1 – 0.5)
= 6.0%
The average cost of capital using book value proportions is calculated below :
Source of capital Component Book value Book value Product of Cost Rs. in million proportion (1) & (3) (1) (2) (3)
3. Po = Rs.220 S = Rs.150 N = 4a. The theoretical value per share of the cum-rights stock would simply be
Rs.220
b. The theoretical value per share of the ex-rights stock is :
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NPo+S 4 x 220 +150 = = Rs.206
N+1 4+1
c. The theoretical value of each right is :Po – S 220 – 150
= = Rs.14 N+1 4+1
The theoretical value of 4 rights which are required to buy 1 share is Rs.14x14=Rs.56.
4. Po = Rs.180 N = 5a. The theoretical value of a right if the subscription price is Rs.150
Po – S 180 – 150 = = Rs.5
N+1 5+1
b. The ex-rights value per share if the subscription price is Rs.160 NPo + S 5 x 180 + 160
= = Rs.176.7 N+1 5+1
c. The theoretical value per share, ex-rights, if the subscription price isRs.180? 100?
5 x 180 + 180 = Rs.180
5+1
5 x 180 + 100 = Rs.166.7
5+1
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Chapter 19CAPITAL STRUCTURE AND FIRM VALUE
1. Net operating income (O) : Rs.30 millionInterest on debt (I) : Rs.10 millionEquity earnings (P) : Rs.20 millionCost of equity (rE) : 15%
Cost of debt (rD) : 10%Market value of equity (E) : Rs.20 million/0.15 =Rs.133 million Market value of debt (D) : Rs.10 million/0.10 =Rs.100 millionMarket value of the firm (V) : Rs.233 million
2. Box Cox
Market value of equity 2,000,000/0.15 2,000,000/0.15 = Rs.13.33 million = Rs.13.33 million
Market value of debt 0 1,000,000/0.10=Rs.10 million
Market value of the firm Rs.13.33million =23.33 million
(a) Average cost of capital for Box Corporation13.33. 0
x 15% + x 10% = 15%13.33 13.33
Average cost of capital for Cox Corporation 13.33 10.00
x 15% + x 10% = 12.86%23.33 23.33
(b) If Box Corporation employs Rs.30 million of debt to finance a project that yields Rs.4 million net operating income, its financials will be as follows.
Net operating income Rs.6,000,000Interest on debt Rs.3,000,000Equity earnings Rs.3,000,000Cost of equity 15%
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Cost of debt 10%Market value of equity Rs.20 millionMarket value of debt Rs.30 millionMarket value of the firm Rs.50 million
Average cost of capital 20 30
15% x + 10% = 12% 50 50
(c) If Cox Corporation sells Rs.10 million of additional equity to retire Rs.10 million of debt , it will become an all-equity company. So its
average cost of capital will simply be equal to its cost of equity, which is 15%.
3. rE = rA + (rA-rD)D/E 20 = 12 + (12-8) D/E So D/E = 2
The optimal debt ratio is 0.10 as it minimises the weighted average cost of capital.
5. (a) If you own Rs.10,000 worth of Bharat Company, the levered company which is valued more, you would sell shares of Bharat Company, resort to personal leverage, and buy the shares of Charat Company.
(b) The arbitrage will cease when Charat Company and Bharat Company are valued alike
70
6. The value of Ashwini Limited according to Modigliani and Miller hypothesis is
Expected operating income 15 = = Rs.125 million Discount rate applicable to the 0.12 risk class to which Aswini belongs7. The average cost of capital(without considering agency and bankruptcy cost) at various leverage ratios is given below.
6. 18 = [ ROI + ( ROI – 8 ) 0.7 ] ( 1 – 0.5) ROI = 24.47 per cent EBIT7. a. Interest coverage ratio =
Interest on debt
150 =
40 = 3.75 EBIT + Depreciation b. Cash flow coverage ratio =
Loan repayment instalment
74
Int.on debt + (1 – Tax rate)
= 150 + 30
40 + 50
= 28. The debt service coverage ratio for Pioneer Automobiles Limited is given by : 5 PAT i + Depi + Inti) i=1 DSCR = 5
Inti + LRIi) i=1
= 133.00 + 49.14 +95.80
95.80 + 72.00
= 277.94 167.80
= 1.66
9. (a) If the entire outlay of Rs. 300 million is raised by way of debt carrying 15 per cent interest, the interest burden will be Rs. 45 million.
Considering the interest burden the net cash flows of the firm duringa recessionary year will have an expected value of Rs. 35 million (Rs.80 million - Rs. 45 million ) and a standard deviation of Rs. 40 million . Since the net cash flow (X) is distributed normally
X – 35
40 has a standard normal deviation Cash flow inadequacy means that X is less than 0. 0.35 Prob(X<0) = Prob (z< ) = Prob (z<- 0.875)
40 = 0.1909
(b) Since µ = Rs.80 million, = Rs.40 million , and the Z value corresponding to the risk tolerance limit of 5 per cent is – 1.645, the cash available from the operations to service the debt is equal to X which is defined as :
X – 80 = - 1.645
75
40 X = Rs.14.2 million
Given 15 per cent interest rate, the debt than be serviced is 14.2
= Rs. 94.67 million 0.15
Chapter 21DIVIDEND POLICY AND FIRM VALUE
1. Payout ratio Price per share
3(0.5)+3(0.5) 0.15 0.5
0.12 = Rs. 28.13
0.12
3(0.7 5)+3(0.25) 0.15 0.12
0.75 = Rs. 26.56 0.12
3(1.00) 1.00 = Rs. 25.00 0.12
2. Payout ratio Price per share
8(0.25)0.25 = undefined
0.12 – 0.16(0.75) 8(0.50)
0.50 = Rs.1000.12 – 0.16(0.50) 8(1.00)
1.0 =Rs.66.7 0.12 – 0.16 (0)
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3.P Q
Next year’s price 80 74 Dividend 0 6 Current price P Q Capital appreciation (80-P) (74-Q) Post-tax capital appreciation 0.9(80-P) 0.9 (74-Q) Post-tax dividend income 0 0.8 x 6 Total return 0.9 (80-P)
P= 14%
0.9 (74-Q) + 4.8Q
=14% Current price (obtained by solving the preceding equation)
P = Rs.69.23 Q = Rs.68.65
77
Chapter 22DIVIDEND DECISION
1. a. Under a pure residual dividend policy, the dividend per share over the 4 year period will be as follows:
b. The external financing required over the 4 year period (under the assumption that the company plans to raise dividends by 10 percents every two years) is given below :
Required Level of External Financing (in Rs.)
Year 1 2 3 4
A . Net income 10,000 12,000 9,000 15,000
B . Targeted DPS 1.00 1.10 1.10 1.21
C . Total dividends 5,000 5,500 5,500 6,050
D . Retained earnings(A-C) 5,000 6,500 3,500 8,950
E . Capital expenditure 8,000 7,000 10,000 8,000
F . External financing
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requirement 3,000 500 6,500 Nil(E-D)if E > D or 0 otherwise
c. Given that the company follows a constant 60 per cent payout ratio, the dividend per share and external financing requirement over the 4 year period are given below
Dividend Per Share and External Financing Requirement(in Rs.)
Year 1 2 3 4
A. Net income 10,000 12,000 9,000 15,00
B. Dividends 6,000 7,200 5,400 9,000
C. Retained earnings 4,000 4,800 3,600 6,000
D. Capital expenditure 8,000 7,000 10,000 8,000
E. External financing(D-C)if D>C, or 0 4,000 2,200 6,400 2,000otherwise
F. Dividends per share 1.20 1.44 1.08 1.80
2. Given the constraints imposed by the management, the dividend per share has tobe between Rs.1.00 (the dividend for the previous year) and Rs.1.60 (80 percent of earnings per share)
Since share holders have a preference for dividend, the dividend should be raised over the previous dividend of Rs.1.00 . However, the firm has substantial
investment requirements and it would be reluctant to issue additional equitybecause of high issue costs ( in the form of underpricing and floatation costs)
Considering the conflicting requirements, it seems to make sense to payRs.1.20 per share by way of dividend. Put differently the pay out ratio may beset at 60 per cent.
3. According to the Lintner modelDt = cr EPSt + (1-c)Dt –1
EPSt =3.00, c= 0.7, r=0.6 , and Dt-1
Hence Dt = 0.7 x 0.6 x 3.00 + (1-0.7)1.20
= Rs.1.62
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4. The bonus ratio (b) must satisfy the following constraints :(R-Sb)≥0.4S (1+b) (1)0.3 PBT ≥0.1 S(1+b) (2)
R = Rs.100 million, S= Rs.60 million, PBT = Rs.60 millionHence the constraints are(100-60 b) ≥ 0.4 x 60 (1+b) (1a) 0.3 x 60≥0.1 x 60 (1+b) (2a)
These simplify tob ≥ 76/84b ≥ 2
The condition b ≥ 76/84 is more restructive than b≥ 2 So the maximum bonus ratio is 76/84 or 19/21
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Chapter 23 Debt Analysis and Management
1. (i) Initial Outlay(a) Cost of calling the old bonds
Face value of the old bonds 250,000,000 Call premium 15,000,000 265,000,000
(b) Net proceeds of the new bondsGross proceeds 250,000,000 Issue costs 10,000,000
240,000,000(c) Tax savings on tax-deductible expenses
Tax rate[Call premium+Unamortised issue cost on the old bonds] 9,200,000 0.4 [ 15,000,000 + 8,000,000]Initial outlay i(a) – i(b) – i(c) 15,800,000
(ii) Annual Net Cash Savings(a) Annual net cash outflow on old bonds
Interest expense 42,500,000- Tax savings on interest expense and amortisation of issue expenses 17,400,0000.4 [42,500,000 + 8,000,000/10]
25,100,000(b) Annual net cash outflow on new bonds
Interest expense 37,500,000- Tax savings on interest expense and amortisation of issue cost 15,500,000
0.4 [ 37,500,000 – 10,000,000/8] 22,000,000
Annual net cash savings : ii(a) – ii(b) 3,100,000
(iii) Present Value of the Annual Cash Savings Present value of an 8-year annuity of 3,100,000 at a discount rate of 9 per cent which is the post –tax cost of new bonds 3,100,000 x 5.535 17,158,500
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(iv) Net Present Value of Refunding the Bonds
(a) Present value of annual cash savings 17,158,500(b) Net initial outlay 15,800,000(c) Net present value of refunding the bonds :
iv(a) – iv(b). 1,358,5002. (i) Initial Outlay
(a) Cost of calling the old bonds Face value of the old bonds 120,000,000 Call premium 4,800,000
124,800,000(b) Net proceeds of the new issue
Gross proceeds 120,000,000Issue costs 2,400,000
117,600,000 (c) Tax savings on tax-deductible expenses 3,120,000
Tax rate[Call premium+Unamortised issue costs onthe old bond issue] 0.4 [ 4,800,000 + 3,000,000]
Initial outlay i(a) – i(b) – i(c) 4,080,000
(ii) Annual Net Cash Savings(a) Annual net cash out flow on old bonds
Interest expense 19,200,000- Tax savings on interest expense and amortisation of issue costs 7,920,000 0.4[19,200,000 + 3,000,000/5]
11,280,000
(b) Annual net cash outflow on new bonds Interest expense 18,000,000- Tax savings on interest expense and amortistion of issue costs 7,392,000
0.4[18,000,000 + 2,400,000/5] 10,608,000
Annual net cash savings : ii(a) – ii(b) 672,000 (iii) Present Value of the Annual Net Cash Savings
Present value of a 5 year annuity of 672,000 at as discount rate of 9 per cent, which is the post-tax 2,614,080 cost of
new bonds
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(iv) Net Present Value of Refunding the Bonds (a) Present value of annual net cash savings 2,614,080
(b) Initial outlay 4,080,000 (c) Net present value of refunding the bonds : - 1,466,000
iv(a) – iv(b)
3. Yield to maturity of bond P 8 160 1000
918.50 = + t=1 (1+r)t (1+r)8
r or yield to maturity is 18 percent
Yield to maturity of bond Q 5 120 1000
761 = + t=1 (1+r)t (1+r)5
r or yield to maturity is 20 per cent
Duration of bond P is calculated below
Year Cash flow Present Value Proportion of Proportion of bond’s at 18% bond’s value Value x Time
1. The product of the standard deviation and square root of time is :t = 0.35 2 = 0.495
The ratio of the stock price to the present value of the exercise price is :
Stock price 40 = = 1.856
PV (Exercise price) 25/(1.16)
The ratio of the value of call option to stock price corresponding to numbers 0.495 and 1.856 can be found out from Table A.6 by interpolation. Note thetable gives values for the following combinations
1.75 2.00
0.45 44.6 50.8
0.50 45.3 51.3
Since we are interested in the combination 0.495 and 1.856 we first interpolatebetween 0.450 and 0.500 and then interpolate between 1.75 and 2.00
Interpolation between 0.450 and 0.500 gives
1.75 2.00
0.450 44.6 50.8
0.495 45.23 51.25
0.500 45.3 51.3
Then, interpolation between 1.75 and 2.00 gives
1.75 1.856 2.00
86
0.495 45.23 47.78 51.25
Chapter 24LEASING, HIRE PURCHASE, AND PROJECT FINANCE
2. The projected cash inflows and outflows for the quarter, January through March, is shown below .
Month December January February March (Rs.) (Rs.) (Rs.) (Rs.)
Inflows : Sales collection 50,000 55,000 60,000
Outflows :Purchases 22,000 20,000 22,000 25,000Payment to sundry creditors 22,000 20,000 22,000Rent 5,000 5,000 5,000Drawings 5,000 5,000 5,000Salaries & other expenses 15,000 18,000 20,000Purchase of furniture - 25,000 -
Total outflows(2to6) 47,000 73,000 52,000
Given an opening cash balance of Rs.5000 and a target cash balance of Rs.8000, the surplus/deficit in relation to the target cash balance is worked out below :
3. The balances in the books of Datta co and the books of the bank are shown below:
(Rs.) 1 2 3 4 5 6 7 8 9 10
Books of Datta Co:
Opening Balance
30,000
46,000
62,000
78,000 94,000
1,10,000
1,26,000
1,42,000
1,58,000
1,74,000
Add: Cheque received
20,000
20,000
20,000
20,000 20,000
20,000
20,000
20,000
20,000
20,000
Less: Cheque issued
4,000
4,000
4,000
4,000 4,000
4,000
4,000
4,000
4,000
4,000
Closing Balance
46,000
62,000
78,000
94,000 1,10,000
1,26,000
1,42,000
1,58,000
1,74,000
1,90,000
Books of the Bank:
Opening Balance
30,000
30,000
30,000
30,000 30,000 30,000 50,000 70,000 90,000
1,06,000
Add: Cheques realised
- - - - - 20,000 20,000 20,000 20,000
20,000
Less: Cheques debited
- - - - - - - - 4,000
4,000
95
Closing Balance
30,000
30,000
30,000
30,000 30,000 50,000 70,000 90,000 1,06,000
1,22,000
From day 9 we find that the balance as per the bank’s books is less than the balance as per Datta Company’s books by a constant sum of Rs.68,000. Hence in the steady situation Datta Company has a negative net float of Rs.68,000.
4. Optimal conversion size is2bT
C = I
b = Rs.1200, T= Rs.2,500,000, I = 5% (10% dividend by two)
So, 2 x 1200 x 2,500,000
C = = Rs.346,4100.05
5. 3 3 b2
RP = + LL 4I
UL = 3 RP – 2 LL
I = 0.12/360 = .00033, b = Rs.1,500, = Rs.6,000, LL = Rs.100,000
3 3 x 1500 x 6,000 x 6,000RP = + 100,000
4 x .00033
= 49,695 + 100,000 = Rs.149,695
UL = 3RP – 2LL = 3 x 149,695 – 2 x 100,000 = Rs.249,085
96
Chapter 28CREDIT MANAGEMENT
1. Δ RI = [ΔS(1-V)- ΔSbn](1-t)- k ΔIΔ S
Δ I = x ACP x V360
Δ S = Rs.10 million, V=0.85, bn =0.08, ACP= 60 days, k=0.15, t = 0.40
Hence, ΔRI = [ 10,000,000(1-0.85)- 10,000,000 x 0.08 ] (1-0.4)
9. Profit when the customer pays = Rs.10,000 - Rs.8,000 = Rs.2000Loss when the customer does not pay = Rs.8000
Expected profit = p1 x 2000 –(1-p1)8000 Setting expected profit equal to zero and solving for p1 gives : p1 x 2000 – (1- p1)8000 = 0 p1 = 0.80 Hence the minimum probability that the customer must pay is 0.80
MINICASE Solution:
Present Data Sales : Rs.800 million Credit period : 30 days to those deemed eligible Cash discount : 1/10, net 30 Proportion of credit sales and cash sales are 0.7 and 0.3. 50 percent of the credit customers
avail of cash discount Contribution margin ratio : 0.20 Tax rate : 30 percent Post-tax cost of capital : 12 percent ACP on credit sales : 20 days
Effect of Relaxing the Credit Standards on Residual Income
Incremental sales : Rs.50 million Bad debt losses on incremental sales: 12 percent ACP remains unchanged at 20 days
100
∆RI = [∆S(1 – V) - ∆Sbn] (1 – t) – R ∆ I
∆Swhere ∆ I = x ACP x V
360
∆ RI = [50,000,000 (1-0.8) – 50,000,000 x 0.12] (1 – 0.3)
50,000,000- 0.12 x x 20 x 0.8
360
= 2,800,000 – 266,667 = 2,533,333
Effect of Extending the Credit Period on Residual Income
1.a. No. of Order Ordering Cost Carrying Cost Total Cost Orders Per Quantity (U/Q x F) Q/2xPxC of Ordering Year (Q) (where and Carrying (U/Q) PxC=Rs.30)
2 UF 2x250x200b. Economic Order Quantity (EOQ) = =
PC 30 2UF = 58 units (approx)
2. a EOQ = PC
U=10,000 , F=Rs.300, PC= Rs.25 x 0.25 =Rs.6.25
2 x 10,000 x 300
102
EOQ = = 9806.25
10000 b. Number of orders that will be placed is = 10.20
980 Note that though fractional orders cannot be placed, the number of orders
relevant for the year will be 10.2 . In practice 11 orders will be placed during the year. However, the 11th order will serve partly(to the extent of 20 percent) the present year and partly(to the extent of 80 per cent) the following year. So only 20 per cent of the ordering cost of the 11th order relates to the present year. Hence the ordering cost for the present year will be 10.2 x Rs.300
c. Total cost of carrying and ordering inventories 980
= [ 10.2 x 300 + x 6.25 ] = Rs.6122.5 2
3. U=6,000, F=Rs.400 , PC =Rs.100 x 0.2 =Rs.20
2 x 6,000 x 400EOQ = = 490 units
20
U U Q’(P-D)C Q* PC Δπ = UD + - F- -
Q* Q’ 2 2
6,000 6,000 = 6000 x .5 + - x 400
490 1,000
1,000 (95)0.2 490 x 100 x 0.2- -
2 2
= 30,000 + 2498 – 4600 = Rs.27898
4. U=5000 , F= Rs.300 , PC= Rs.30 x 0.2 = Rs.6
2 x 5000 x 300EOQ = = 707 units
6 If 1000 units are ordered the discount is : .05 x Rs.30 = Rs.1.5 Change in
103
profit when 1,000 units are ordered is :
5,000 5,000 Δπ = 5000 x 1.5 + - x 300
707 1,000
1000 x 28.5 x 0.2 707 x 30 x 0.2 - - = 7500 + 622-729 =Rs.7393
2 2
If 2000 units are ordered the discount is : .10 x Rs.30 = Rs.3 Change in profit when 2,000 units are ordered is :
5000 5000 2000x27x0.2 707x30x0.2 Δπ = 5000 x 3.0 + - x 300- -
707 2000 2 2
= 15,000 +1372 – 3279 = Rs.13,093
5. The quantities required for different combinations of daily usage rate(DUR)and lead times(LT) along with their probabilities are given in the following
* Note that if the DUR is 4 units with a probability of 0.3 and the LT is 5 days with a probability of 0.6, the requirement for the combination DUR = 4 units and LT = 5 days is 20 units with a probability of 0.3x0.6 = 0.18. We have assumed that the probability distributions of DUR and LT are independent. All other entries in the table are derived similarly.
The normal (expected) consumption during the lead time is :
The Zi scores arranged in an ascending order are shown below
Good(G)Account Number Zi Score or
Bad (B)
24 3.3890 B18 3.8398 B25 4.4097 B23 4.7946 B22 5.1265 B20 5.1571 B17 5.4405 B 5 5.6938 G21 5.7038 B16 5.7090 B19 5.7292 B 4 6.6918 G
113
10 6.7018 G 2 6.7373 G 9 6.8514 G 1 7.1046 G11 7.1426 G 3 7.4720 G13 7.7554 G14 7.8870 G 8 7.9378 G 7 8.0847 G12 8.9231 G15 9.2498 G 6 9.4728 G
From the above table, it is evident that a Zi score which represents the mid-point between the Zi scores of account numbers 19 and 4 results in the minimum number of misclassifications . This Zi
score is :
5.7292 + 6.6918= 6.2105
2Given this cut-off Zi score, there is just one misclassification (Account number 5)
114
Chapter 4ANALYSING FINANCIAL PERFORMANCE
Net profit1. Return on equity =
Equity
= Net profit Net sales Total assets x x
Net sales Total assets Equity
1 = 0.05 x 1.5 x = 0.25 or 25 per cent
0.3
Debt EquityNote : = 0.7 So = 1-0.7 = 0.3
Total assets Total assets
Hence Total assets/Equity = 1/0.3
2. PBT = Rs.40 million PBIT
Times interest covered = = 6 Interest
So PBIT = 6 x InterestPBIT – Interest = PBT = Rs.40 million 6 x Interest = Rs.40 millionHence Interest = Rs.8 million
115
3. Sales = Rs.7,000,000Net profit margin = 6 per centNet profit = Rs.7000000 x 0.06 = 420,000Tax rate = 60 per cent
420,000 So, Profit before tax = = Rs.1,050,000
(1-.6)Interest charge = Rs.150,000
So Profit before interest and taxes = Rs.1,200,000 Hence
1,200,000 Times interest covered ratio = = 8
150,000
4. CA = 1500 CL = 600 Let BB stand for bank borrowingCA+BB
= 1.5CL+BB
1500+BB = 1.5
600+BB
BB = 120
1,000,0005. Average daily credit sales = = 2740
365160000
ACP = = 58.4 2740
If the accounts receivable has to be reduced to 120,000 the ACP must be:120,000
x 58.4 = 43.8days160,000
Current assets
116
6. Current ratio = = 1.5 Current liabilities
Current assets - InventoriesAcid-test ratio = = 1.2
Current liabilities
Current liabilities = 800,000 Sales
Inventory turnover ratio = = 5 InventoriesCurrent assets - Inventories
Acid-test ratio = = 1.2 Current liabilities
Current assets InventoriesThis means - = 1.2
Current liabilities Current liabilities
Inventories1.5 - = 1.2
800,000
Inventories = 0.3
800,000
Inventories = 240,000
Sales = 5 So Sales = 1,200,000
2,40,000
7. Debt/equity = 0.60Equity = 50,000 + 60,000 = 110,000So Debt = 0.6 x 110,000 = 66,000Hence Total assets = 110,000+66,000 = 176,000Total assets turnover ratio = 1.5So Sales = 1.5 x 176,000 = 264,000Gross profit margin = 20 per centSo Cost of goods sold = 0.8 x 264,000 = 211,200Day’s sales outstanding in accounts receivable = 40 days
Sales
117
So Accounts receivable = x 40 360
264,000 = x 40 = 29,333
360
Cost of goods sold 211,200Inventory turnover ratio = = = 5
Inventory Inventory
So Inventory = 42,240
Assuming that the debt of 66,000 represent current liabilitiesCash + Accounts receivable
The comparison of the Omex’s ratios with the standard is given below
Omex StandardCurrent ratio 1.42 1.5Acid-test ratio 0.75 0.80Debt-equity ratio 1.31 1.5Times interest covered ratio 3.02 3.5Inventory turnover ratio 3.6 4.0Average collection period 57.6 days 60 daysTotal assets turnover ratio 1.27 1.0Net profit margin ratio 5.4% 6%Earning power 20.1% 18%Return on equity 15.7% 15%
Note that solutions to problems 10 & 11 are not given
MINICASE
Solution:
(a) Key ratios for 20 X 5 12.4
Current ratio = = 0.93 13.4
8.8 + 6.7Debt-equity ratio = = 0.98
6.5 + 9.3
57.4Total assets turnover ratio = = 1.96
120
[(34 – 6.6) + (38 – 6.7)] / 2
3.0Net profit margin = = 5.2 percent 57.4
5 Earning power = = 17.0 percent
[(34 – 6.6) + (38 – 6.7)] / 2
3.0Return on equity = = 20.2 percent
(13.9 + 15.8) / 2
(b) Dupont Chart for 20 x 5
–
÷
÷
+
121
Return on total assets
10.2%
Net profitmargin5.2%
Total asset turnover
1.96
Net profit3.0
Net sales57.4
Net sales57.4
Average total assets29.35
Net sales +/-Non-op. surplus
deficit 57.8
Total costs54.8
Average fixed assets
21.4
Average net current assets 54.0
+
(c) Common size and common base financial statements
Common Size Financial Statements Profit and Loss Account
Regular (in million) Common Size (%)20 X 4 20 X 5 20 X 4 20 X 5
Total 27.4 31.3 100 114 Net fixed assets 19.6 23.2 100 118 Net current assets 5.1 5.7 100 112 Other assets 2.7 2.4 100 89
Total 27.4 31.3 100 114
123
(d) The financial strengths of the company are:
Asset productivity appears to be good. Earning power and return on equity are quite satisfactory Revenues have grown impressively over 20 x 4 – 20 x 5
The financial weaknesses of the company are:
Current ratio is unusually low While revenues grew impressively, costs rose even faster: As a result profit margins
declined The company did not have any tax liability in the last two years. If the company has to
bear the burden of regular taxes, its return on equity will be adversely impacted
(e) The following are the problems in financial statement analysis
There is no underlying theory It is difficult to find suitable benchmarks for conglomerate firms Firms may resort to window dressing Financial statements do not reflect price level changes Diversity of accounting policies may vitiate financial statement analysis It is somewhat difficult to judge whether a certain ratio is ‘good’ or ‘bad’
(f) The qualitative factors relevant for evaluating the performance and prospects of a company are as follows:
Are the company’s revenues tied to one key customer? To what extent are the company’s revenues tied to one key product? To what extent does the company rely on a single supplier? What percentage of the company’s business is generated overseas? How will competition impact the company? What are the future prospects of the firm? What could be the effect of the changes in the legal and regulatory environment?
124
Chapter 5BREAK-EVEN ANALYSIS AND LEVERAGES
1. a. EBIT = Q(P-V)-F = 20,000(10-6)-50,000 = Rs.30,000
(b) Profit when the quantity is 3000 bags Profit =3,000(30-16)-10000 = Rs.3200010 per cent increase in production means that the quantity is 3300 bagsAt that productionProfit = 3,300(30-16)-10,000 = Rs.36200So, the percentage change in profit is :
36200-32000 = 13.1%
32000
(c) A 10 per cent increase in selling price means that P= Rs.33Break-even point when P= Rs.33
10,000Q = = 588.2 bags
33-16
(d) A 50 per cent increase in fixed costs means that F=Rs.15,000Break-even point when F= Rs.15,000 15,000Q = = 882.4 bags 33-16
(e) If V= Rs.20, the break-even point is : 10,000
Q = = 1000 bags 30-20
8. A B C D Selling price per unit Rs.10 Rs.16.66 Rs.20 Rs.10 Variable cost per unit Rs.6 Rs.8.33 Rs.12 Rs.5
127
Contribution margin per unit Rs.4 Rs.8.33 Rs.8 Rs.5 Contribution margin ratio 0.4 0.5 0.4 0.5 Total fixed costs Rs.16000 Rs.100000 Rs.160000 Rs.60000 Break-even point in units 4000 12000 20000 12000 Break-even sales(Rs.) Rs.40000 Rs.200000 Rs.400000 Rs.120000 Net income(loss)before tax Rs.30000 Rs.80000 Rs.(40000) Rs.40000 No.of units sold 11500 21600 15000 20000
9. (a) Break-even point for product P 30,000
= 3,000 units 30-20
Break-even point for product Q100,000
= 5,000 units 50-30
Break-even point for product R200,000
= 5,000 units 80-40
(b) The weighted contribution margin is : 5000 8,000 6,000
x Rs.10 + x Rs.20 + x Rs.40 = Rs.23.68 19000 19000 19000
10. EBITDFL =
Dp
EBIT – I -T
at Q = 20000EBIT= 20000(Rs.40-Rs.24)=Rs.320,000
Rs.320,000DFL(Q=20,000) =
Rs.10,000Rs.320,000-Rs.30,000 -
(1-.5)
128
= 1.185
11. (a) EBIT = Q(P-V) – F
Firm A : 20,000(Rs.20-Rs.15) – Rs.40,000 = Rs.60,000 Firm B : 10,000(Rs.50-Rs.30) - Rs.70,000 = Rs.130,000
Firm C : 3,000(Rs.100-Rs.40)- Rs.100,000 = Rs.80,000(EBIT-I) (1-T) - Dp
(b) EPS = n
(Rs.60,000-Rs.10,000)(1-.4)-Rs.5,000 Firm A : = Rs.1.9
10,000
(Rs.130,000-Rs.20,000)(1-.5)-Rs.5,000 Firm B : = Rs.4.17
12,000
(Rs.80,000-Rs.40,000)(1-.6)-Rs.10,000 Firm C : = Rs.0.40
15,000F + I
(c) BEP =P – V
Rs.40,000 + Rs.10,000 Firm A : = 10,000 units
Rs.20 – Rs.15
Rs.70,000 + Rs.20,000Firm B : = 4,500 units
Rs.50 – Rs.30
Rs.100,000 + Rs.40,000Firm C : = 2,333 units
Rs.100 – Rs.40
Q(P-V) (d) DOL =
Q(P-V)-F
20,000(Rs.20-Rs.15)
129
Firm A : = 1.6720,000(Rs.20-Rs.15)- Rs.40,000
10,000(Rs.50-Rs.30)Firm B : = 1.54
10,000(Rs.50-Rs.30)-Rs.70,000
3,000(Rs.100-Rs.40)Firm C : = 2.25
3,000(Rs.100-Rs.40)-Rs.100,000
EBIT (e) DFL = Dp
EBIT – I - (1-T)
Rs.60,000Firm A : = 1.44
Rs.5000Rs.60,000-Rs.10,000 -
(1-.4)
Rs.130,000Firm B : = 1.30
Rs.5,000Rs.130,000-Rs.20,000 -
(1-.5)
Rs.80,000Firm C : = 5.333
Rs.10,000Rs.80,000-Rs.40,000-
(1-.6) (f) DTL = DOL x DFL
Firm A : 1.67 x 1.44 = 2.40Firm B : 1.54 x 1.30 = 2.00Firm C : 2.25 x 5.333 = 12.00
130
Chapter 6FINANCIAL PLANNING AND BUDGETING
1. The proforma income statement of Modern Electronics Ltd for year 3 based on the per cent of sales method is given below
Average per cent Proforma income statement of sales for year 3 assuming sales of
1020
Net sales 100.0 1020.0Cost of goods sold 76.33 778.57Gross profit 23.67 241.43Selling expenses 7.40 75.48General & administration expenses 6.63 67.63Depreciation 6.75 68.85Operating profit 2.90 29.58Non-operating surplus/deficit 1.07 10.91Earnings before interest and taxes 3.96 40.39Interest 1.24 12.65Earnings before tax 2.72 27.74Tax 1.00 10.20Earnings after tax 1.72 17.54Dividends (given) 8.00Retained earnings 9.54
131
2. The proforma income statement of Modern Electronics for year 3 using the the combination method is given below :
Average per cent Proforma income statementof sales for year 3
Net sales 100.0 1020.0Cost of goods sold 76.33 778.57Gross profit 23.67 241.43Selling expenses 7.40 75.48General & administration expenses Budgeted 55.00Depreciation Budgeted 60.00Operating profit 50.95Non-operating surplus/deficit 1.07 10.91Earnings before interest and taxes 61.86 Interest Budgeted 12.0Earnings before tax 49.86 Tax 1.00 10.20Earnings after tax 39.66Dividends (given) Budgeted 8.00Retained earnings 31.66
132
3. The proforma balance sheet of Modern Electronics Ltd for year 3 is given below
Average of percent Projections for year 3 of sales or some based on a forecast other basis sales of 1400
Net sales 100.0 1020.0
ASSETSFixed assets (net) 40.23 410.35Investments No change 20.00
Current assets, loans & advances :Cash and bank 1.54 15.71Receivables 22.49 229.40Inventories 21.60 220.32
Prepaid expenses 5.09 51.92Miscellaneous expenditure & losses No change 14.00
961.70
LIABILITIES :
Share capital :Equity No change 150.00Reserves & surplus Proforma income 160.66
statement
Secured loans:Term loans No change 175.00Bank borrowings No change 199.00
Current liabilities :Trade creditors 17.33 176.77Provisions 5.03 51.31
133
External funds requirement Balancing figure 48.96
961.7
A L4. EFR = - S – m S1 (1-d)
S S
800 190 = - 300 – 0.06 x 1,300 (1-0.5)
1000 1000
= (0.61 x 300) – (0.06) x 1,300 x (0.5)
= 183 – 39 = Rs.144.
Projected Income Statement for Year Ending 31st December , 2001
Sales 1,300Profits before tax 195Taxes 117Profit after tax (6% on sales) 78Dividends 39Retained earnings 39
Therefore, mS1(1-d) – - S represents surplus funds S S
Given m= 0.06, S1 =11,000, d= 0.6 , L= 3,000 S= 10,000 and surplus funds = 150 we have
A 3,000(0.06) 11,000 (1-0.6) - - 1,000 = 150
10,000 10,000
138
A – 3,000= (0.06) (0.4) (11,000) – 150 = 114
10
or A = (1,140 + 3,000) = 4,140
The total assets of Videosonics must be 4,140
9. m= .05 , d = 0.6 , A/E = 2.5 , A/S = 1.4
m (1-d)A/E .05 (1-0.6) 2.5 (a) g = = = 3.70 per cent
A/S –m(1-d)A/E 1.4 -.05 (1-0.6) 2.5
.05 (1-0.6) x A/E(b) 0.5 = A/E = 3.33
2.4 - .05 (1-0.6) A/E
d = 0.466The dividend payout ratio must be reduced from 60 per cent to 46.6 per cent
.05 (1-0.6) x A/E(c) .05 = A/E = 3.33
1.4 -.05 (1-0.6) A/E
The A/E ratio must increase from 2.5 to 3.33
m (1-0.6) 2.5(d) .06 = m = 7.92 per cent
1.4 – m (1-0.6) x 2.5
The net profit margin must increase from 5 per cent to 7.92 per cent
.05 (1-0.6) 2.5(e) .06 = A/S = .883
A/S - .05 (1-0.6) 2.5
The asset to sales ratio must decrease from 1.4 to 0.883
139
Chapter 32 CORPORATE VALUATION
1. (a) The calculations for Hitech Limited are shown below :Year 2 Year3
EBIT PBT 86 102+ Interest expense 24 28- Interest income (10) (15)- Non-operating income (5) (10) EBIT 95 105
Tax on EBIT Tax provision on income statement 26 32+ Tax shield on interest expense 9.6 11.2- Tax on interest income (4) (6)- Tax on non-operating income (2) (4) Tax on EBIT 29.6 33.2
Present value of the operating cash flow = 147Residual value = 264 / 0.15 = 1760Present value of residual value = 1760 / (1.15)4 = 1007Total shareholder value = 147 + 1007 = 1154Pre-strategy value = 168/0.15 = 1120Value of the strategy = 1154 – 1120 = 34
2. According to the Marakon approachM r – g =B k – g
9. Investment = Rs.100 millionNet working capital = Rs.20 millionLife = 8 yrsSalvage value = Rs.20 million (Net working capital)Annual cash flow = Rs.21.618 millionCost of capital = 15%Straight line depreciation = Rs.10 million per year
80 80Economic depreciation = = = Rs.5.828 million
FVIFA(8, 15%) 13.727
Year 1 Year 4 Profit after tax 11.618 11.618 Depreciation 10.000 10.000 Cash flow 21.618 21.618 Book capital100 70 (Beginning) ROCE 11.62% 16.59% ROGI 21.62% 21.62% CFROI 15.79% 15.79%
148
Chapter 34 MERGERS, ACQUISITIONS AND RESTRUCTURING
1. The pre-amalgamation balance sheets of Cox Company and Box Company and the post-amalgamation balance sheet of the combined entity, Cox and Box Company, under the ‘pooling’ method as well as the ‘purchase’ method are shown below :
Before Amalgamation After Amalgamation Cox & Box Company
4. Let A stand for Ajeet and J for JeetPVA = Rs.60 x 300,000 = Rs.18 millionPVJ = Rs.25 x 200,000 = Rs.5 millionBenefit = Rs.4 millionPVAJ = 18 + 5 + 4 = Rs.23 millionExchange ratio = 0.5The share of Jeet in the combined entity will be :
100,000= = 0.25
300,000 + 100,000
a) True cost to Ajeet Company for acquiring Jeet CompanyCost = PVAB - PVB
= 0.25 x 27 - 5 = Rs.1.75 million
b) NPV to Ajeet= Benefit - Cost= 4 - 1.75 = Rs.2.25 million
c) NPV to Jeet = Cost = Rs.1.75 million
5. a) PVB = Rs.12 x 2,000,000 = Rs.24 millionThe required return on the equity of Unibex Company is the value of k in the equation.
150
Rs.1.20 (1.05)Rs.12 =
k - .05
k = 0.155 or 15.5 per cent.
If the growth rate of Unibex rises to 7 per cent as a sequel to merger, the intrinsic value per share would become :
1.20 (1.07)= Rs.15.11
0.155 - .07
Thus the value per share increases by Rs.3.11 Hence the benefit of the acquisition is
2 million x Rs.3.11 = Rs.6.22 million
(b) (i) If Multibex pays Rs.15 per share cash compensation, the cost of the merger is 2 million x (Rs.15 – Rs.12) = Rs.6 million.
(ii) If Multibex offers 1 share for every 3 shares it has to issue 2/3 millionshares to shareholders of Unibex.
So shareholders of Unibex will end up with
0.667 = 0.1177 or 11.77 per cent
5+0.667
shareholding of the combined entity,The present value of the combined entity will be
PVAB = PVA + PVB + Benefit= Rs.225 million + Rs.24 million + Rs.6.2 million = Rs.255.2 million
So the cost of the merger is :Cost = PVAB - PVB
= .1177 x 255.2 - 24 = Rs.6.04 million
6. The expected profile of the combined entity A&B after the merger is shown in the last column below.
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A B A&BNumber of shares 5000 2000 6333Aggregate earnings Rs.45000 Rs.4000 Rs.49000Market value Rs.90000 Rs.24000 Rs.114000P/E 2 6 2.33
7. (a) The maximum exchange ratio acceptable to shareholders of Vijay Limited is :
S1 (E1+E2) PE12
ER1 = - + S2 P1S2
12 (36+12) 8= - + = 0.1
8 30 x 8
(b) The minimum exchange ratio acceptable to shareholders of Ajay Limited is : P2 S1
ER2 = (PE12) (E1+E2) - P2 S2
9 x 12 = = 0.3
9 (36+12) - 9 x 8
(c) 12 (48) PE12
ER1 = - + 8 240
9 x 12 ER2 =
PE12 (48) - 72
Equating ER1 and ER2 and solving for PE12 gives, PE12 = 9 When PE12 = 9 ER1 = ER2 = 0.3Thus ER1 and ER2 intersect at 0.3
8. The present value of FCF for first seven years is 16.00 14.30 9.7 0
PV(FCF) = - - - + (1.15) (1.15)2 (1.15)3 (1.15)4
152
0 10.2 16.7 + + +
(1.15)5 (1.15)6 (1.15)7
= - Rs.20.4 millionThe horizon value at the end of seven years, applying the constant growth model is
FCF8 18 V4 = = = Rs.257.1 million
0.15-0.08 0.15 – 0.08
1 PV (VH) = 257.1 x = Rs.96.7 million
(1.15)7
The value of the division is :- 20.4 + 96.7 = Rs.76.3 million
MINICASE
Solution:(a)
Modern Pharma Magnum Drugs Exchange Ratio
Book value per share 2300 650 = Rs.115 = Rs.65 20 10
65
115Earnings per share 450 95
= Rs.22.5 = Rs.9.5 20 10
9.5
22.5Market price per share Rs.320 Rs.102 102
320
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Exchange ratio that gives equal weightage to book value per share, earnings per share, and market price per share
(b) An exchange ratio based on earnings per share fails to take into account the following:
(i) The difference in the growth rate of earnings of the two companies.(ii) The gains in earnings arising out of merger.(iii) The differential risk associated with the earnings of the two companies.
(c) Current EPS of Modern Pharma 450= = Rs.22.5
20
If there is a synergy gain of 5 percent, the post-merger EPS of Modern Pharma is
(450 + 95) (1.05)
20 + ER X 10Equating this with Rs.22.5, we get
(450 + 95) (1.05) = 22.5
20 + 10ERThis gives ER = 0.54
Thus the maximum exchange ratio Modern Pharma should accept to avoid initial dilution of EPS is 0.54
(d) Post-merger EPS of Modern Pharma if the exchange ratio is 1:4, assuming no synergy gain:
450 + 95 = Rs.24.2 20 + 0.25 x 10
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(e) The maximum exchange ratio acceptable to the shareholders of Modern Pharma if the P/E ratio of the combined entity is 13 and there is no synergy gain
-S1 (E1 + E2) P/E12
ER1 = + S2 P1 S2
- 20 (450 + 95) 13 = + = 0.21
10 320 x 10
(f) The minimum exchange ratio acceptable to the shareholders of Magnum Drugs if the P/E ratio of the combined entity is 12 and the synergy benefit is 2 percent
P2S1
ER2 = (P/E12) (E1 + E2) (1 + S) – P2S2
102 x 20 =
12 (450 + 95) (1.02) – 102 X 10 = 0.36
(g) The level of P/E ratio where the lines ER1 and ER2 intersect.
To get this, solve the following for P/E12
- S1 (E1 + E2) P/E12 P2S1
+ = S2 P1S2 P/E12 (E1 + E2) – P2S2
- 20 (450 +95) P/E12 102 x 20 + = 10 320 x 10 P/E12 (450 +95) – 1020
Given a rupee discount rate of 20 per cent, the NPV in rupees is :
2408.5 3530.8 4753.8NPV = -9200 + + +
(1.18)2 (1.18)3 (1.18)4
5807.6 4633.6 + +
(1.18)5 (1.18)6
= Rs.3406.2 million
The dollar NPV is : 3406.2 / 46 = 74.05 million dollars
5. Forward rate 1 + domestic interest rate =
Spot rate 1 + foreign interest rate
F 1 + .015 =
1.60 1 + .020F = $ 1.592 / £
6. Expected spot rate a year from now 1 + expected inflation in home country=
Current spot rate 1 + expected inflation in foreign country
Expected spot rate a year from now 1.06 =
Rs.70 1.03
So, the expected spot rate a year from now is : 72 x (1.06 / 1.03) = Rs.72.04
7. (a) The spot exchange rate of one US dollar should be :
158
12000= Rs.48
250(b) One year forward rate of one US dollar should be :
13000= Rs.50
260
8. (1 + expected inflation in Japan)2
Expected spot rate = Current spot rate x2 years from now (1 + expected inflation in UK)2
(1.01)2
= 170 x = 163.46 yen / £ (1.03)2
9. (i) Determine the present value of the foreign currency liability (£100,000) by using 90-day money market lending rate applicable to the foreign country. This works out to :
£100,000 = £ 98522
(1.015)(ii) Obtain £98522 on today’s spot market(iii) Invest £98522 in the UK money market. This investment will grow to
£100,000 after 90 days
10. (i) Determine the present value of the foreign currency asset (£100,000) by using the 90-day money market borrowing rate of 2 per cent.
100,000 = £98039
(1.02)
(ii) Borrow £98039 in the UK money market and convert them to dollars in the spot market.
(iii) Repay the borrowing of £98039 which will compound to £100000 after 90 days with the collection of the receivable
11. A lower interest rate in the Swiss market will be offset by the depreciation of the US dollar vis-à-vis the Swiss franc. So Mr.Sehgal’s argument is not tenable.
159
Chapter 40CORPORATE RISK MANAGEMENT
1. (a) The investor must short sell Rs.1.43 million (Rs.1 million / 0.70) of B(b) His hedge ratio is 0.70(c) To create a zero value hedge he must deposit Rs.0.43 million