Time valu of money ppt Unit 4 Part 5.pptx

1. Future Value of an Annuity

Meaning: An annuity is a series of equal payments made at regular intervals (like EMIs, insurance premiums).

Formula:

𝐹
𝑉
=
𝐴
×
(
1
+
𝑟
)
𝑛
−
1
𝑟
FV=A×
r
(1+r)
n
−1
​


where
𝐴
=
A= annuity (payment),
𝑟
=
r= interest rate,
𝑛
=
n= periods.

Example: If you invest ₹1,000 every year for 5 years at 10% interest, FV = ₹6,105 approx.

2. Present Value of an Annuity

Meaning: What is today’s worth of future regular payments?

Formula:

𝑃
𝑉
=
𝐴
×
1
−
(
1
+
𝑟
)
−
𝑛
𝑟
PV=A×
r
1−(1+r)
−n
​


Example: You will receive ₹5,000 per year for 3 years, discount rate = 12%. PV = ₹11,635 approx.

3. Perpetuity

Meaning: An annuity that goes on forever (no end).

Formula:

𝑃
𝑉
=
𝐴
𝑟
PV=
r
A
​


Example: A company promises to pay ₹1,000 every year forever, interest rate = 10%. PV = ₹10,000.

4. Annuity Due

Meaning: Payments made at the beginning of each period (e.g., house rent, insurance premiums).

Formula Relation:

𝐹
𝑉
𝑎
𝑛
𝑛
𝑢
𝑖
𝑡
𝑦
 
𝑑
𝑢
𝑒
=
𝐹
𝑉
𝑜
𝑟
𝑑
𝑖
𝑛
𝑎
𝑟
𝑦
 
𝑎
𝑛
𝑛
𝑢
𝑖
𝑡
𝑦
×
(
1
+
𝑟
)
FV
annuitydue
​

=FV
ordinaryannuity
​

×(1+r)
𝑃
𝑉
𝑎
𝑛
𝑛
𝑢
𝑖
𝑡
𝑦
 
𝑑
𝑢
𝑒
=
𝑃
𝑉
𝑜
𝑟
𝑑
𝑖
𝑛
𝑎
𝑟
𝑦
 
𝑎
𝑛
𝑛
𝑢
𝑖
𝑡
𝑦
×
(
1
+
𝑟
)
PV
annuitydue
​

=PV
ordinaryannuity
​

×(1+r)
5. Compounding More Than Once a Year (Quarterly, Monthly, etc.)

Formula:

𝐹
𝑉
=
𝑃
𝑉
×
(
1
+
𝑟
𝑚
)
𝑛
×
𝑚
FV=PV×(1+
m
r
​

)
n×m

where
𝑚
=
m= number of compounding periods per year.

Example: ₹10,000 invested @12% compounded quarterly for 2 years → FV = ₹12,682 approx.

6. Effective Annual Rate (EAR)

Meaning: The true annual interest rate after considering compounding.

Formula:

𝐸
𝐴
𝑅
=
(
1
+
𝑟
𝑚
)
𝑚
−
1
EAR=(1+
m
r
​

)
m
−1

Example: 12% interest compounded monthly → EAR = 12.68%.

1. Measurement of Specific Costs-Cost of Equity Shares Unit 4 Part 5 Financial Management Rashid Usman Ansari Reference Financial Management Khan & Jain 6th Edition

2. Measuring cost of equity is conceptually most difficult. There is no contractual obligation as far as payment of return on equity shares is concerned. Due to the absence of any contractual obligation, it is difficult to calculate cost of equity. However, equity does not come for free. The basis of calculating cost of equity is the return expected by the shareholders. The cost of equity is highest amongst all sources as the return on equity is not fixed and is paid after all obligations are met. Equity shareholders demand more return to compensate for the higher risk involved. Therefore, cost of equity is the rate at which investors discount the expected dividends of the firm to determine its value. Cost of Equity Capital

3. Dividend Valuation Model assumes that the value of a share equals the present value of all the future dividends that is expected to be provided over an indefinite period. This model can take the following forms: Constant growth in dividends model. Growth in dividends at different rates Calculating Cost of Equity-Dividend Valuation Model

4. When the dividends are expected to grow at a constant rate perpetually, the cost of equity is calculated as follows: k e = (D 1 / P ) + g Where, k e = Cost of Equity D 1 = Expected Dividend Per Share P = Current market price of share g = Growth in expected dividends Constant Growth in Dividends Model

5. The calculation of cost of equity in this model is based on following assumptions: The market value of share depends upon the expected dividends. Investors can formulate subjective probability distribution of dividends per share expected to be paid in various future periods. The initial dividend, D , is greater than zero. The dividend payout ratio is constant. Investor can accurately measure the riskiness of the firm so as to agree on the rate at which to discount the dividends. Assumptions of the Constant Growth Model

6. Suppose that dividend per share of a firm is expected to be Re. 1 per share next year and is expected to grow at 6% per year perpetually. Determine the cost of equity assuming market price per share to be Rs. 25. Solution k e = (D 1 / P ) + g = (1/25) + .06 = .04 + .06 = 10% This approach can be used to find the expected market value of shares in different years: P 1 = D 2 / (k e - g) = 1.06/ (.10 - .06 ) = Rs. 26.50 Similarly we can find P 2 and P 3 and so on. Illustration on the Constant Growth Model

7. A company is foreseeing a growth rate of 12% per annum in the next 2 years. The growth rate is likely to fall to 10% for the next two years. After that the growth rate is expected to stabilize at 8% per annum. If the last dividend was Rs. 1.50 per share and the investors’ required rate of return is 16%, find out the intrinsic value per share of the company. Solution Intrinsic Value of Share =(PV of dividends payments during years 1-4 + PV of Expected Market price at the end of year 4) Illustration on Variable Growth in Dividends Years Dividend ( Adjust for growth Rate) PVIF ( @ 16%) Total PV 1 1.68 .862 1.45 2 1.88 .743 1.40 3 2.07 .641 1.33 4 2.28 .552 1.26 Total PV 5.44 P 4 D 5 / (k e – g) = 2.28 ( 1.08 ) / ( .16 - .08) = Rs. 30.78 PV of P 4 30.78 x .552 = Rs. 16.99 Intrinsic Value = 5.44 + 16.99 = Rs. 22.43

8. As discussed earlier, retained earnings involve opportunity cost. It is the opportunity cost in terms of the dividends foregone by/withheld from equity shareholders. Another way to look at it is the external-yield criterion. It means that that if the earnings have been retained it may be invested by the firm itself. As the retained earnings are used by the firm, the earnings on the external investment forgone is also an opportunity cost. Therefore, cost of retained earnings is equivalent to cost of equity less the flotation cost. Cost of Retained Earnings