M/S. ABC limited is expected to pay RS. 18 every year on a share of its stock what is present value of a share if money worth is 9% compounded annually
Solution of the above question
Well, let me put on my clown wig and calculate that for you! *Honk honk*
To find the present value of the share, we need to use the formula for the present value of an ordinary annuity. The formula is:
PV = P * (1 - (1 + r)^-n) / r
Where PV is the present value, P is the payment per period, r is the interest rate, and n is the number of periods.
In this case, the payment per period is RS. 18, the interest rate is 9%, and since the company is expected to pay every year, the number of periods is also 1.
Plugging in the values, we get:
PV = 18 * (1 - (1 + 0.09)^-1) / 0.09
Calculating that out, the present value of a share of M/S. ABC Limited stock is approximately RS. 16.51. So, grab your clown shoes and RS. 16.51, and let's go invest in some laughs! *Squirt*
To calculate the present value of a share, we can use the formula for present value of a future cash flow:
Present Value = Cash Flow / (1 + r)^n
Where:
Cash Flow = the annual payment of RS. 18
r = the interest rate or money worth rate, which is 9% or 0.09
n = the number of years, which would be in perpetuity
Now, since the annual payment is constant and paid indefinitely, we can use the formula for the present value of a perpetuity:
Present Value of Perpetuity = Cash Flow / r
Substituting in the values, we have:
Present Value of Perpetuity = 18 / 0.09
Calculating this, we get:
Present Value of Perpetuity = 200
Therefore, the present value of a share is RS. 200.
To calculate the present value of a share, we need to use the formula for the present value of an annuity:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
PMT = Payment per period (RS. 18 in this case)
r = Interest rate per period (9% or 0.09 in decimal form)
n = Number of periods (assuming the dividend is paid indefinitely, we can use a large number such as 100)
Let's calculate the present value of a share using this formula:
PV = 18 * (1 - (1 + 0.09)^(-100)) / 0.09
Here are the steps to calculate it manually:
1. Calculate (1 + r)^(-n):
(1 + 0.09)^(-100) = 0.13439
2. Subtract this value from 1:
1 - 0.13439 = 0.86561
3. Divide PMT by r:
18 / 0.09 = 200
4. Multiply step 2 by step 3:
0.86561 * 200 = 173.122
Therefore, the present value of a share is approximately RS. 173.122.
.09x = 18
Solve for x.