### What is Capital Market Line (CML)?

Capital Market Line:
It shows the relationship between risk (standard deviation) and return of risk free asset and market portfolio (All the financial investment available in proportion of they are available in a market). The slope of the Capital Market Line shows the price of market risk. The efficient portfolio is a reward for waiting and bearing a risk of holding that portfolio for specified period.

In the above diagram standard deviation is shown in X axis and expected return and risk free asset. The curve shown in the diagram is known as efficient frontier curve.  If the investors prefer less risk then they must lying between risk free asset points to market portfolio point. Between these two points investor can lend money to government by buying treasury bills, government bonds on risk. If the investors are interested in taking more risk to earn high return, then those investors lying beyond the market portfolio point. And beyond the market portfolio point the investor can borrow funds on risk free rate for buying risky assets.

Difference between Capital Market Line and Security Market Line:
·         The CML shows the total risk as standard deviation while the SML shows market risk as beta.
·         The efficient frontier curve shown in CML only while inefficient portfolio shown in SML.
·         The capital market line shows risk and return relationship as a whole market while the relationship of risk and return of single stock is shown by security market line.

Formula:
E(Rp) = Rf + σp ((Rm – Rf) / σm)

Where,
E(Rp) = Expected return of a portfolio
Rf = Risk free rate of return
σp = Standard deviation of a portfolio
σm = Standard deviation of market
Rm = Market rate of return
Example: Find out the expected return of a portfolio if the market standard deviation is 23% and risk free rate is 4%. The market return is 12% and the standard deviation of portfolio is 5%.
Solution:
E(Rp) = Rf + σp ((Rm – Rf) / σm)
= 4 + 5 ((12 – 4) / 23
= 4 + 5*0.35
= 4 + 1.75
= 5.75%

Example: Find out the expected return of given portfolio with the help of given information:

 Portfolio Standard deviation of portfolio (in %) Risk free rate in %) Expected market return Standard deviation of market portfolio A 2 3 13 5 B 8 3 18 4 C 4 3 9 8 D 6 3 11 2

Solution:
E (Rp) = Rf + σp ((Rm – Rf) / σm)
Portfolio A:
= 3 + 2 ((13 – 3) / 5)
= 3 + 2*2
= 3 + 4
= 7%
Portfolio B:
= 3 + 8 ((18 -3) /4)
= 3 + 8*3.75
= 3 + 30
= 33%
Portfolio C:
= 3 + 4((9 – 3) / 8)
= 3 + 4*0.75
= 3 + 3
= 6%
Portfolio D:
= 3 + 6((11 -3) / 2)
= 3 + 6*4
= 3 + 24
= 27%

Example: Find out which portfolio gives higher return from the given information:

 Portfolio Standard deviation of portfolio (in %) Risk free rate in %) Expected market return Standard deviation of market portfolio P 6 4 11 3 Q 1 4 12 2 R 5 4 10 7

Solution: E (Rp) = Rf + σp ((Rm – Rf) / σm)
Portfolio P:
= 4 + 6((11 - 4) / 3)
= 18%
Portfolio Q:
= 4 + 1((12 - 4) / 2)
= 8%
Portfolio R:
= 4 + 5((10 -4) / 7)
= 8.29%

Portfolio P has higher expected return in comparison to portfolio Q and R.

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### How to calculate Cost of Preference Share Capital?

Cost of Preference Share Capital: An amount paid by company as dividend to preference shareholder is known as Cost of Preference Share Capital. Preference share is a small unit of a company’s capital which bears fixed rate of dividend and holder of it gets dividend when company earn profit. Dividend payable is not a tax deductible amount. So, there is no tax adjustments required for comparing with cost of debt.
Formula for Cost of Preference Share:
Irredeemable Preference Share Redeemable Preference Share Kp = Dp/NP Kp = Dp+((RV-NP)/n )/ (RV+NP)/2
Where, Kp = Cost of Preference Share Dp = Dividend on preference share NP = Net proceeds from issue of preference share (Issue price – Flotation cost) RV = Redemption Value N = Period of preference share
Example: A company issues 20,000 irredeemable preference share at 8% whose face value is Rs.50 each at 4% discount. Find out the Cost of Preference Share Capital.
Solution: Dividend on Preference share (Dp) = 50*8/100 = 4 Discount = 50*4/100 = 2 Net Proce…

### What is Certainty-Equivalent Cash Flows?

Certainty-Equivalent: It is a method in which uncertain cash flows are converted into certain cash flows by multiplying with probability of occurrence such cash flows .Certainty coefficient assumes value between 0 and 1. In this method risk free rate are used instead of risk-adjusted discount rate. We would use either IRR or NPV for evaluation of a project.

By using NPV method: NPV > 0 project accepted NPV < 0 project rejected NPV = 0 project may be accepted or rejected
By using IRR method: IRR > r project accepted IRR < r project rejected IRR = 0 project may be accepted or rejected
Formula of Certainty Coefficient:
Certainty Coefficient = Expected Cash Flows (Certain cash Flows) / Risky Cash Flows
= Expected Cash Flows (Certain cash Flows)/ (1+risk premium rate)
Example: In below table 5 years cash inflows and certainty coefficient are given which shows the probability of occurrence of cash flows.
Year Cash inflows Certainty Coefficient 1 28,000 0.8 2 32,000 0.6 3 46,000 0.4 4

### What is Perpetuity and Deferred Perpetuity?

Perpetuity:
It is a fixed series of payments received in infinite periods.
Example: Console bond has no maturity period and it pays fixed coupon.
Growing Perpetuity: It is a fixed series of payments receives at a constant growth rate for infinite periods.

Deferred Perpetuity: It is fixed series of cash flows received at a future date.
Perpetuity Vs Annuity: In perpetuity payment received for infinite period and in annuity payment received for fixed period.The formula to calculate perpetuity and annuity is also different, in annuity the formula is  C[1-(1/(1+r)n/r) and the formula for perpetuity is C/r.
Formula:

Simple
perpetuity Growing
Perpetuity Deferred
Perpetuity Deferred Growing
Perpetuity PV C1/r C1/r-g PVp /(1+r) t PV GP /(1+r) t

Where, C1= Initial cash flow R= rate per period G= growth rate PVP=Preset Value of perpetuity