Valuation¶

Debt¶

It is the rate of return the firm’s lenders demand when they loan money to the firm.

Forms of Borrowing¶

Type
Private	Bank Loan
Public	Bond/Debenture

Bond¶

Certificate of

Term	Fixed?	Meaning	Formula	Unit
Face/PAR/Book Value	✅	Listing price of the security	\(\text{PAR } = \frac{\text{Total Amount}}{\text{No of bonds}}\)	Currency
Coupon Rate	✅	Interest rate		% of face value
Time to Maturity/ Time to Expiry	✅	Bounding time period by which face value will be repayed (at every payment instant, we only pay the coupon amount)
Credit Rating	Partially
YTM (Yield-to-Maturity)		IRR of the bond Actual return for the buyer of the bond

Bond Traded at	Purchase	Returns
PAR	Market Value = Face Value	YTM = Coupon rate
Premium	Market Value > Face Value	YTM < Coupon rate
Discount	Market Value < Face Value	YTM > Coupon rate

Bond Price¶

\[ \text{Bond Price} = \sum_{t=1}^T \frac{\text{Coupon } t}{(1+\text{YTM})^t} + \frac{\text{PAR}}{(1+\text{YTM})^T} \]

\[ \text{Bond Price } \propto \frac{1}{\text{Interest Rate}} \]

This is because, if interest rate increases, lenders will go to loan market, and everyone will sell their bonds.

Misc¶

Run-on-the-bank¶

Banks should have minimum liquidity, to ensure that

If a private bank falls show on SLR, they can request from government, using Rapport
If a govt bank falls show on SLR, they can request from government, using Reverse Rapport

Rapport¶

Repurchase agreement

Reverse Rapport¶

Why are Govt Bonds Risk-Free?¶

Chance of default is lowest.

Preference Shares¶

Hybrid of debt and common shares
Fixed dividends
Deferrable dividends
They don’t have voting rights
There is no expiration date
It is the only real example of perpetuity
Usually higher return than bonds

\[ k_p = \frac{d_p}{p_p} \quad \left(\frac{c}{r} \text{ from Perpetuity} \right) \]

Common Shares¶

Returns

Dividends
Capital Gains

Difficult to estimate pricing, as there are so many variables in play

Unsure cashflows
Life of investment is infinite
No way to calculate required rate of return

It is frowned upon for a corporation to reduce dividends. Hence, if it increases dividends, it does so very carefully.

Book value Method¶

Most appropriate for established companies

Dividend Growth Model¶

\[ \begin{aligned} g &= \text{ROE} \times \text{Retention Rate} \\ D_t &= D_{t-k} \times (1+g)^k \\ \implies P_t &= \frac{D_{t+1}}{k_\text{CS} - g} \quad \cancel{+ \frac{P_\infty}{(1+r)^\infty}} \end{aligned} \]

where

\(g =\) dividend growth rate
non-zero constant percentage change of dividend from one year to next. If non-constant, we take average \(g\) over a few years
\(g = \text{ROE} \times b\)
- \(\text{ROE \%}=\) Return on Equity
- \(b \% =\) Retention rate, Plowback rate
- \(b \% = 1-\text{Payout Rate}\)
\(k=\) market discount rate

Dividend Growth	\(g\)
No	\(0\)	Perpetuity
Constant	\(\ge 0\)

Limitations¶

Assumes constant growth
Only works when \(g \ne 0\)

CAPM¶

Capital Asset Pricing Model

Describes relation between systematic risk and expected rate of return of risky investments.

Expected return on a risk investment depends on

Risk-free rate (return rate of bond)
Risk premium, depending on \(\beta\), where \(\beta\) is the sensitivity of the stock wrt the market

\[ \begin{aligned} k &= r_\text{min} \\ &= r_f + \beta \Big( E(r_m) - r_f \Big) \end{aligned} \]