Subject: Financial Management

Question – A (1) Mr. Nimish holds the following portfolio.

Share Beta Investment

Alpha 0.9 Rs.12, 00,000

Beta 1.5 Rs. 3, 50,000

Carrot 1.0 Rs. 1, 00,000

What is the expected rate of return on his portfolio, if the risk rate is 7 per cent and the expected return on the market portfolio is 16 per cent?

Answer – A (1): For given bata (β), the required rate of return is obtained as

E(rp) = rf + β (rm – rf)

E(rp) = Expected return from portfolio

rf = Risk free rate of return (Note: individual investments may consider as

risk free)

β = Systematic risk of asset, beta

rm = Expected rate on market portfolio

(rf = 7% = 0.07, rm = 16% = 0.16)

Therefore, E(rp) = 0.07 + β (0.16 – 0.07) = 0.07 + 0.09 β

Share Beta E(r) = rf + β(rm-rf)Investment

(Rs.)Weight

Weighted Return

Alpha 0.9 0.151 12,00,000 0.727 0.110Beta 1.5 0.205 3,50,000 0.212 0.043Carrot 1.0 0.160 1,00,000 0.061 0.010Portfolio 1.033 0.163 16,50,000 1.000 0.163

Portfolio Beta is the simple weighted average of the betas of three shares.

ie, β portfolio = 0.9 X 0.727 + 1.5 X 0.212 + 1 X 0.061 = 1.033

Question – A (2) A share is selling for Rs.60 on which a dividend of Rs.4 per share is expected at the end of the year. The expected market price after dividend declaration is to be Rs.70. Compute the following: -

(i) The return on investment ® in shares.(ii) Dividend yield (iii) Capital Gain Yield

Answer – A (2):

(i) Return on Investment per share = Net profit after taxes – Dividend X 100Average ordinary share or net worth

(70 – 60) – 4 X 100 = 10 % 60

(ii) Dividend Yield = Dividend per ordinary share (DPS) X 100Market Value per Share

= 4 X 100 = 5.714 % 70

(iii) Capital Gain Yield = Earnings per share (EPS) X 100 Market value per share

= 60 X 10% X 10070

= 8.571 %

Question – B: DIC Ltd. provides the following data:

Comparative trial balance March 31 year 2 March 31 year 1 Increase(Decrease)

Debit Balance Cash 20 10 10Working capital (other than cash) Rs.190 Rs. 90 Rs.100Investment (Long term) 100 200 (100)Building and equipment 500 400 100Land 40 50 (10)

Total 850 750 100

CreditAccumulated Depreciation 200 160 40Bonds 150 100 50Reserves 350 350 ---Equity Shares 150 140 10

Total 850 750 100

Income StatementFor the period ending March 31, year 2

(Amount in Rs lakh)

Sales Rs.1000Cost of Goods Sold 500Selling Expense Rs.50Administrative Expenses 50 100Operating Income 400Other charges

Gain on sale of building and equipment Rs 5Loss on sale of investments (10)Interest (6)Taxes (189) (200)

Net Income after taxes 200

Notes: (a) The depreciation charged for the year was Rs.60 Lakh(b) The Book value of the building and equipment disposed was Rs 10 Lakh

Prepare a Cash Flow Statement (Based on AS-3)

Answer – B:

Cash Flow Statement of DIC Limited (Indirect Method)

Particulars Amount in Rs. Lakh

Cash flow from operating activities:

Net profit before taxation and extraordinary items 389 Adjustment for Depreciation 60 Gain on sale of building and equipment (5) Interest expense 6 Loss on sale of Investments 10 Operating profit before working capital changes 460 Increase in working capital (100) Cash generated from operation 360 Income tax paid 189

Net cash from operating activities 171

Cash flow from investing activities:

Proceeds from sale of long term Investments (working notes 1) 90 Proceeds from sale of land 10 Proceeds from sale of building and equipment (Rs.10 lakh + Rs.5 lakh gain) 15 Purchase of building and equipment (working notes 2) (130)

Net cash used in investing activities (15)

Cash flow from financing activities:

Proceeds from issuance of bonds (150 – 100) 50 Proceeds from issuance of equity shares (150 – 140) 10 Interest (6) Dividend to equity share holders (working notes 3) (200)

Net cash used in financing activities (146)

Net increase in cash 10

Cash at the beginning of year – 2 10

Cash at the end of year – 2 20

Working Notes

1) Proceeds from sale of long term investments: (Amount in Rs. Lakh)

Investments at beginning of year – 2 200Less investment of year – 2 end 100Book value of investment sold 100Less loss on sale of investments (10)Sale proceeds 90

2) Purchase of building and equipment: (Amount in Rs. Lakh)

Original cost of building and equipment at the beginning of year – 2 400

Less original cost of building and equipment sold daring year – 2 (book value Rs. 10 lakh + accumulated depreciation Rs. 20 lakh) (30)

370Original cost of building and equipment at year – 2 end 500Difference represents purchases of building and equipment 130

3) Dividend to equity share holders:

Since there is no increase in reserves (Rs. 350 lakhs), the entire net income after taxes of Rs. 200 lakhs represent payment of dividend to equity shareholders.

Accumulated depreciation account (Amount in Rs. Lakh)

Particulars Amount Particulars Amount

To Building & Equipment (accumulated depreciation on sale, balancing figure)

20 By Balance b/f 160

To Balance c/d 200By Profit and Loss account (depreciation of current year)

60

220 220

Question – C (1) - A. Ltd. produces a product which has a monthly demand of 4,000 units. The product requires a component X which is purchased at Rs.20. For every finished product one

unit of component is required. The ordering cost is Rs.120 per order and the holding cost is 10 per cent per annum. You are required to calculate:

(i) Economic order quantity(ii) If the minimum lot size to be supplied is 4, 000 units, what is the extra cost, the

company has to incur?(iii) What is the minimum carrying cost, the company has to incur?

Answer – C (1):

(i) Determination of EOQ

EOQ = 2 AB A = Annual usage of inventory (units) C B = Buying cost per order

C = Carrying cost per unit

A = 4,000 units per month & 12 months = 48,000 unitsB = Rs. 120C = Rs. 20 cost per unit X 0.10 = Rs. 2 per unit per annum

Therefore, EOQ = 2 X 48,000 X 120 2

= 2,400 Units

(ii) Determination of Extra cost when lot size is 4,000 units

Sl. No. ParticularsCost when lot size is

4,000 units 2,400 units

1 Annual usage (units) 48,000 48,0002 Size of order 4,000 2,4003 Number of orders (1 + 2) 12 204 Cost per order Rs. 120 Rs. 1205 Total ordering costs (3 X 4) 1,440 2,4006 Carrying cost per unit per annum 2 27 Average inventory (size of order/2) 2,000 1,2008 Total carrying cost (6 X 7) 4,000 2,4009 Total costs (5 + 8) 5,400 4,800

Extra costs to be incurred is Rs. 640 (Rs. 5,440 – Rs. 4,800), when the order size is 4,000 units.

(iii) There is a positive relationship between the total carrying cost the firm incurs and the size of the average inventory it carries; this average size of inventory, in turn, is positively related to the size of order. In view of these facts, the minimum carrying costs the firm is to incur is Rs. 2,400 (corresponding to EOQ of 2,400 units and the average inventory level of 1,200 units).

Question – D - A stock is currently trading for Rs.29. The risk less interest is 7 % p.a continuously compounded. Estimate the value of European call option with a strike price of

Rs.30 and a time of expiration of 4 months. The standard deviation of the stock’s annual return is 0.45. Apply BS model.

Answer – D:

Spot price of the share S Rs. 29.00

Exercise price of the call option E Rs. 30.00

Risk free interest rate r 0.07

Time remaining for expiration = 4 months = 4/12 (year) t 0.33

Volatility of the stock σ 0.45

The value of European call option can be obtained by using Black-scholes option pricing model.

C = S N(d1) – Ee-rt N(d2)

Computation of call option essentially requires calculation of three values, viz., d1, d2 and present value of the exercise price (Ee

-rt).

d1 = In S/E + (r + σ 2 /2) t

σ t

Substituting values from the information given above we get

d1 = In (29/30) + (0.07 + (0.45) 2 / 2) 0.33

0.45 0.33

d1 = In (0.9667) + (0.07 + 0.1013) 0.33 0.45 (0.5744)

In (0.9667) = Log10 (0.9667) X 2.3026 = (-1.9853) X 2.3026 = (-1 + 0.9853) X 2.3026 = -2.3026 X 2.2688

In (0.9667) = -0.0338

d1 = -0.0338 + 0.0565 0.2585

d1 = 0.0227 0.2585

d1 = 0.0879

d2 = d1 – σ t

d2 = 0.0879 – (0.45) 0.33

d2 = 0.0879 – (0.45) 0.5744

d2 = 0.0879 – 0.2585

d2 = -0.1706

and Ee-rt = 30 e-(0.07 X 0.33) = 30 e

-0.02

Ee-rt = 30 e-0.22 {e

-0.22 = 0.9802 as per Table A – 7)

Ee-rt = 30 (0.9802)

Ee-rt = 29.406

The equation of call option looks like C = 29 N(0.0879) – 29.406 N(-0.1706)

The next step is to look up the values of a cumulative standardized normal probability distribution at (0.0879) and (-0.1706)

N(0.0879) = N(0.08) + 0.79 [ N(0.09) – N(0.08) ] = 0.5319 + 0.79 (0.5359 – 0.5319)

= 0.5319 + 0.79 (0.004)= 0.5319 + 0.00316= 0.53506

N(-0.1706) = N(-0.17) – 0.06 [ N(-0.17) – N(-0.18) ]= 0.4325 – 0.06 (0.4325 – 0.4286)= 0.4325 – 0.06 (0.0039)= 0.4325 – 0.000234= 0.432266

[Values as per cumulative standardized normal distribution table]

Therefore, C = 29 (0.53506) – 29.406 (0.432266) = 15.51674 – 12.71121 = 2.8055

Thus, the value of European call option is Rs. 2.81.