 # Valuation of shares Figure 19: approaches to share valuation

There are a number of valuation techniques for shares, as indicated in Figure 19. The balance sheet valuation methods provide information on the replacement / liquidation value of a company, and the relative valuation methods are used for comparisons, but they do not provide the FVP of shares (except to the extent that comparisons can be made). This is left to the discounted cash flow methods. In these the futures cash flows (dividends and free cash flows, which are recurring = FVs) are discounted to PV using appropriate discount rates.

In the case of the discounting of dividends (ordinary shares), the pricing formula may be written as (D = dividend): Because the dividend flows are perpetual, the formula simplifies to [recall that rrr is the required rate of return from the CAPM: rrr = rfr +P(mr - rfr)]: The shares that have a constant annual rate of growth in dividends (Dg) are the easiest to value and the formula becomes:  Figure 20: short-term banking rates & yield curve government securities

In the case of fee cash flow (FCF), assuming a constant growth rate in FCF (FCFg) the formula is (WACC = weighted average cost of capital): Note the significance of the money market in the valuation of shares: the rfr. Figure 20 provides the context of the rfr: it is all the points of the curve and the curve (called the yield curve and the term structure of interest rates) is a representation of the relationship between the many rfr on the curve and term to maturity at a specific time (i.e. it is like a snapshot). In the valuation of shares the 3-month rfr is usually used.

# Valuation of fixed-interest securities

Money market assets have less than a year to maturity and one interest payment. In this case the well known formula applies (assumptions: t = 91 days to maturity, ir = 8.0% pa) (price per unit of 1.0): As we saw above, when we have periods of a year and more than a year (and multiple interest payments apply), compounding interest comes into play. The formula for each cash flow is [cp = compounding period (annually = 1, semi-annually = 2); y = number of years]:  Figure 21: valuation of fixed-interest securities (FV to PV): multiple periods: fixed-rate bond

For a 3-year bond (coupon payment = 1 = compounding period) the calculation is (coupon rate = cr = 9.0% pa; market rate = ytm = 8.0% pa) (price per unit of 1.0): This is illustrated in Figure 21 (keep in mind that ytm = yield to maturity = the correct name for the market rate in the case of bonds).

# Valuation of futures and options

The TVM also applies in the case of futures. The FVP of a futures contract is equal to the spot price (SP) of the underlying asset, plus the cost-of-carry or carry cost [financing cost (usually the risk free rate46 is used here) plus other costs (OC) such as insurance and storage] (CC) less any income earned (I) (CC - I = net carry cost, NCC) expressed as a proportion of the SP. This may be written as follows (t = remaining term of contract in days / 365): Options pricing is more involved [because of the rights of the option holder (and no obligation), and the term to expiry date] but one of the main inputs is the TVM.

# Valuation of income-producing property

In the case of rental property, rental income after tax (FV) is discounted to PV at the so-called capitalization rate. The latter = rfr + an appropriate risk premium.

# Valuation of commodities

Because commodities do not have a recurring income (FVs), valuation is irrelevant. Their value is the market prices at which they trade, and these are available at all times in the case of most commodities.

# Valuation of other real assets

It will be recalled that "other real assets" includes real assets other than property and commodities, for example antique furniture, rare stamps, rare books and art. The above comments apply, except that it is not easy to establish prices, and this is so because the markets for them are not efficient, i.e. price discovery is inefficient. The prices for these assets are usually established at auctions.

# Valuation of participation interests

As discussed, most individuals hold a large proportion of their assets in the form of their dwellings and PIs in retirement funds (an investment vehicle). To the extent that they hold other financial investments, these are usually in the form of the other investment vehicles, such as SUTs and ETFs. It will be recalled that investment vehicles hold assets in the form of the ultimate investments: shares, bonds, money market and real assets, and they issue PIs which are held by individuals in the main. The valuation of PIs reflects the market prices of the ultimate investments mentioned. As these are usually available at all times, the valuation of PIs are available at all times. Good examples are SUTs and ETFs.