Unit 2
Shares and Mutual Funds
Share is the smallest unit of the capital of a company. In other words, A unit of ownership, that represents an equal proportion of a company’s capital is called as shares.
The share is regarded as unit of account that can represent several monetary instruments such as stocks, mutual funds, etc.
Share market is the aggregation of buyers and sellers of stock shares or stock.
Any stock exchange is for trading the stocks.
There are two stock exchanges in India-
- National stock exchange
- Bombay stock exchange
Note- if a person owns the shares of a company’s stock is known as shareholder.
Here we study two types of shares-
Ordinary shares or common stock-
These types of shares entitle the shareholder to share in the earnings of the company as and when they occur and to cast a vote at the company’s annual general meeting’s and other official meetings.
Note- if the share is ordinary in the course of company’s business then it is called equity share.
Preference shares or preferred stock-
These types of shares entitle the shareholder to a fixed periodic income or interest but generally do not give him or her voting rights.
These types of shares are cumulative, non-cumulative, convertible etc.
Face value or nominal value-
It is the original cost of the stock shown on certificate.
Dividend-
Dividend is declared by the company on the face value of a share. When the company makes profit, we receive a part of it and it is the primary source of income.
Bonus shares-
Bonus shares are additional shares given to the shareholder without anyadditional cost; based on the number of shares that a shareholder own.
Brokerage-
Brokerage is the commission charged by broker for buying and selling of shares from buyer or seller.
Important formulae-
Note-
- Buying: Actual price of the share = Market value + Brokerage per share
- Selling: Actual price of the share = Market value - Brokerage per share
Example: How many shares of market price of Rs.130 each, can be purchased for Rs.50150 with brokerage being 0.5%?
Solution
It is given that-
Market price for one share = Rs. 130
Total amount invested = Rs.50,150
And brokerage = 0.5
Brokerage per share = 0.5% of market price
Purchased price for one share = Market price + Brokerage
= 130+0.65 = 130.65
Example: There are two investments given below, then find out which investment is better?
7% of Rs. 100 shares at Rs. 120 or 8% of Rs. 10 shares at Rs. 13.50?
Solution
Suppose the investment amount is = Rs. X
First situation-
It is given that- rate of dividend = 7%
F.V = 100, and Market value = Rs. 120
Second situation-
It is given that- rate of dividend = 8%
F.V = 10, and Market value = Rs. 13.50
Here we see that the dividend in second situation is more than the first situation.
Hence we conclude that the second situation is more profitable for investment.
Example: Mrs. Kapoor invested to Rs. 80,000 to purchase equity shares of Reliance Company at market value of Rs. 210 each through a broker, charging 1% brokerage. The face value of a share is Rs. 10. How many shares did saptak purchase?
Solution
It is given that-
Total Investment = 80,000
M.V. = Rs. 210, F.V. = Rs. 10, Brokerage = 1%
Now, Brokerage per share = 1% of M.V.
So that, Purchase price of 1 share = M.V. + Brokerage
= 210 + 2.1 = 212.10
Example: Amandeep purchased 150 shares of BOB at Rs. 210 on 3rd Jan 2019. On 13th Feb. 2019, the company decided to split all the shares of company so that the face value of the share becomes Rs. 10 from Rs. 20 per share. The market price as on 30th July, 2019 is Rs. 300. Find number of shares held by Amandeep as on 30th July 2019. Also Find gain as on 30th July 2019.
Solution
It is given that-
Total number of shares = 150
M.V. = Rs. 210, F.V. =Rs. 20.
Total amount invested = Number of shares × M.V.
= 150 × 210
= 31,500
Number of shares held on 30th July 2019
Actual value of shares on 30th July 2014
= 300 × 300
= 90,000
Profit = 90,000 – 31,500
= 58,500
Key takeaways-
- Share is the smallest unit of the capital of a company.
- If a person owns the shares of a company’s stock is known as shareholder.
- if the share is ordinary in the course of company’s business then it is called equity share
- Dividend is declared by the company on the face value of a share
Mutual Fund is a pool of money collected from investors and invests in stocks.”
In other words- An investment programme funded by shareholder’s, that trades in diversified holding and professionally managed is called as mutual funds.
A mutual fund is basically at less risk as compared to shares. All the profits or losses of the fund are shared by all the investors in the same proportion as the amount of contribution made by them.
Mutual fund investments are subject to market risk.
There are many mutual funds but all mutual funds are of two types- open ended funds and closed ended funds.
Open-ended Fund-
There is no limit to the number of units purchased and sold in open ended fund
It has no fixed maturity period.
A number called Net Asset Value is used to determine the value of a share in open-ended fund at any time.
Investor can buy and sells his units at Net Asset Value (NAV)which are declared on a daily basis.
Closed-ended Fund-
In closed-ended fund will issue a fixed number of shares are issued tothe public. The price of share in a closed-ended fund is determined by market-demand.
These types of funds are not redeemable.
Net Asset Value-
A mutual funds price per share or unit is called Net Asset Value or N.A.V. All mutual funds buy and sells, orders are processed at the N.A.V of the trade date
Entry Load and Exit load-
Entry load and Exit load are the brokerage while buying and selling the mutual fund respectively.
Entry load is charged at the time, an investor purchases the units and exit load is charged at the time of sale of all units.
Note-
- Buying: Actual price of the Mutual fund = N.A.V + Entry load per share
- Selling: Actual price of the Mutual fund = N.A.V - Exit load per share.
Example: Amit invests Rs. 65,000 in ABC mutual fund where N.A.V. of Rs. 98. How many units he bought, if entry load is 2%.
Solution
Amount Invested = Rs. 65,000
N.A.V. = Rs. 98, Entry Load = 2%
Actual Purchase amount of 1 unit = NAV + Entry load
Example: If a ICICI M.F. had a N.A.V. of Rs. 60 at the beginning of the year and if percentage increase in NAV during the year was 15% Find absolute change in N.A.V.
Solution
NAV at the beginning of the year = Rs. 60
Percent change in NAV = 15%
Absolute change in NAV = (% change in NAV) × (NAV at beginning of year)
NAV at the end of the year = (Absolute change in NAV) + (NAV at beginning of the year)
= 9 + 60 = 69
Example: Rakhi invested Rs. 25,000 in LPU M.F. with entry load 1%. Find the N.A.V. if the number of units purchased was 120.
Solution
Let N.A.V. of 1 unit = Rs. X
Purchase price of 1 unit = NAV + Entry load
It is given that-
Amount investment = Rs. 25,000
No. of unit purchase = 120.
From equation (1) and (2), we get-
1.01 X = 208.33
Example: Mr. Sharma purchased 500 units of Bajaj M.F. at Rs. 8,000 and sold all the units after 2 months when NAV of Rs. 35. The short term gain tax was 10% of the profit. Find his net profit or loss.
Solution
It is given that-
No. of unit purchased = 500
Purchase Amount = Rs. 8,000
Now selling Price of all the units
= 35 × 500 = 17,500
So that
Profit = SP – Purchasing Price = 17,500 – 8,000 = 9,500
Short term gain tax = 10% of profit
Net profit = 9,500 – 950 = Rs. 8,550
Key takeaways-
- Mutual Fund is a pool of money collected from investors and invest in stocks.
This is plan where investors make regular, equal payment into a mutual fund. In this plan, investor can benefit by buying more units when the price falls and less units when the price rises. This scheme helps reduce the average cost per unit of investment, through a method called Average Rupee cost or Rupee cost Averaging. Also, in this plan investor may choose to increase or decrease the investment amount. In India, a recurring payment can be set for SIP using Electronic Clearing Services (ECS). SIP is like a recurring deposit in a bank, where you put a fixed amount every month.
Examples
Nana invested 2,000 every month for 4 month in SBI Gold systematic Investment plan (SIP). The N.A.V.’s on these particular dates were 25, 28, 26.75 and 30 respectively. After 1 year, he sold all the units when N.A.V. was 29. Find average (mean) price of one unit and his net profit or loss.
Note: there was no entry and exit load
Solution
Amount Investment = 2,000 per month.
No Entry load-------Given
Month | Amount invested | NAV | No. of unit purchased |
1 | 2000 | 25 | 2000/25 = 80 |
2 | 2000 | 28 | 71.42 |
3 | 2000 | 26.75 | 74.76 |
4 | 2000 | 30 | 66.66 |
| 8000 |
| 292.661 |
Average (mean) price of 1 unit
= Total no. of unit purchased/ Total Amount Invested
= 8,000/292.861 = 27.3166
Given: selling price of 1 unit = 29
S.P. of all units = 29 × 292.861
= 8,492.9806
Net profit = S.P. – purchase price
= 8,492.9806 – 8,000 = 492.9806
Example
Ms. Lalita invested 5,000 every month for 5 months in BIRLA systematic investment plan (SIP) with N.A.V. of 35, 41, 40, 45 and 50 respectively the entry load was 2%. After 9 months she sold all the units when N.A.V. of 48.
Solution
Amount invested every month = 5,000.
Entry Load = 2%. Exit Load = Nil.
Selling price of 1 unit = 48
Month | NAV | Entry load | purchased price of 1 unit | No. of unit purchased |
1 | 35 | 0.70 | 35.7 | 5000/35.70 = 140.056 |
2 | 41 | 0.82 | 41.82 | 119.56 |
3 | 40 | 0.80 | 40.8 | 122.549 |
4 | 45 | 0.90 | 45.9 | 108.932 |
5 | 50 | 1.00 | 51 | 98.039 |
|
|
| 215.22 | 589.136 |
Average price of 1 unit = Total Amount Invested/Total no. of unit purchased
= 25,000/589.136
= 42.435
Average (mean) price of 1 unit = Total amount/5
=215.22/5
= 43.044
Total S.P. = 48 × 589.136
= 28,278.528
Gain = S.P. – Purchase price
= 28,278.528 – 25,000 = 3,278.528
Example
An investor joined the S.I.P scheme, for a mutual fund, under which he would invest Rs. 750 for 4 months. If the N.A.Vs for each month are Rs.75,Rs.60,Rs.25 and Rs.50, find the average unit cost using Rupee Cost Averaging method and compare it with Arithmetic Mean of prices if the entry load was 2% throughout, correct to 4 decimal places.
Solution
Month | sum insured | NAV | Entry load | purchased price of 1 unit | No. of unit |
1 | 750 | 75 | 1.50 | 76.5 | 9.8039 |
2 | 750 | 60 | 1.20 | 61.2 | 12.2549 |
3 | 750 | 25 | 0.50 | 25.5 | 29.4118 |
4 | 750 | 50 | 1.00 | 51 | 14.7059 |
| 3000 |
|
| 214.2 | 66.1765 |
Rupee cost average = total amount invested/total number of units=3000/66.1765 = 45.3333
A.M. of prices =sum of all shares/number of months =214.2/4 = 53.55
Thus the average price using Rupee cost method is less than A.M of prices.
Example
Mr. Patil invested in a SIP of a M.F. , a fixed sum of Rs. 10,000/- on 5th of every month , for 4 months . The NAV on these dates were Rs. 34.26 , 46.12 , 39.34 and 41.85 . The entry load was 2.25 % throughout the period. Find the average price, including the entry load , using the Rupee cost-Averaging method .How does it compare with the Arithmetic mean of the prices ? (Calculations are correct to 4 digits decimal)
Solution
Month | NAV | Entry load = 2.25% | Total price | No. of unit= 1000/total price |
1 | 34.2600 | 0.7708 | 35.0308 | 285.4627 |
2 | 46.1200 | 1.0377 | 47.1577 | 212.0544 |
3 | 39.3400 | 0.8851 | 40.2252 | 248.6006 |
4 | 41.8500 | 0.9141 | 42.7916 | 233.6906 |
|
|
| 165.205 | 979.8083 |
By using Rupee-cost-Averaging method :-
Avg Price = Total amount/ Total No. of units
= 40,000/979.8083 = 40 .8243
A.M. of price = Total price/ 4= 165.2053/ 4= 41.3013
∴ Avg. price using Rupee-cost- Averaging method is less than A.M. of prices .
Key takeaways –
- The scheme helps reduce the average cost per unit of investment, through a method called Average Rupee cost or Rupee cost Averaging
References
- Practical business mathematics by S.A Bari
- Mathematics of commerce by K. Selvakumar
- Business mathematics with application by Dinesh Khattar and S.R Arora
- Statistical methods by Gupta SP