# Time value of money

Figure 2: time value of money (PV to FV)

Before we begin with the investment instruments an essential principle needs to be understood: the time value of money (TVM). This is a fancy term for interest and the concepts of present value (PV) and future value (FV). The rate of interest for the relevant period is applied to the PV in order to calculate the FV. Figure 2 depicts the TVM.

This simply means that if an amount of LCC30 100 000 (= PV) is invested now for a year at a rate of 10% pa it will have a FV of:

Conversely (see Figure 3), if an investment has a FV of LCC 110 000, and the applicable interest rate (now called discount rate) is 10% pa, it has a PV of:

The TVM principle applies in all the financial markets, in respect of valuation of financial instruments, as we will see shortly and again later.

Figure 3: time value of money (FV to PV)

# Money market instruments

A reminder of the money market and its instrumentals presented in Figure 4.

Figure 4: money market

This information may also be presented (more elucidatory) as in Table 1.

Table 1: Money market instruments / securities

The household sector will not be familiar with all these money market investments (or will not invest in them). In general, the household sector will tend to invest in bank deposits in the form of NNCDs, and some may purchase small-denomination TBs.

As is well known, bank deposits yield interest, and here the PV-FV concept applies. If you deposit LC 100 000 (= PV) with a bank at 10% pa for 180 days the bank will present you a NNCD that states you will get back an amount of LCC 104 931.51 (= FV) after 180 days, calculated as follows:

Figure 5: money market investments for the individual investor

TBs and some other money market instruments work a little differently. They pay back a round amount (called the nominal or face value) at maturity (= FV). If the nominal value is LCC 100 000 (= FV), the term is 180 days and the discount rate is 10% pa, you pay for the TB (= PV):

You will earn LCC 100 000 - LCC 95 300.26 = LCC 4 699.40 on the investment. An example of a TB is presented in Box 1.

# Bond market instruments

A reminder of the bond market and its instruments is presented in Figure 6 and Table 2 (for interest Table 2 also lists LTNMD). From these it will be seen that there are 5 categories of bonds issuers:

- Corporate sector (private).

- Public enterprises (which are incorporated).

- Government sector (central & local).

- Foreign sector (called foreign bonds).

- Special purpose vehicles (called SPV bonds).

Table 2: Bond market instruments / securities

Figure 6: bond market instruments

Worldwide, there is a wide variety of bond-types as follows:

- Plain vanilla bonds.

- Bearer bonds versus registered bonds.

- Perpetual bonds versus fixed-term bonds.

- Floating rate bonds versus fixed-rate bonds.

- Zero coupon bonds versus coupon bonds.

- Call bonds.

- STRIPS.

- Convertible bonds.

- Exchangeable bonds.

- Bonds with share warrants attached.

- General obligation bonds.

- Revenue bonds.

- Serial bonds.

- Catastrophe bonds.

- Asset-backed bonds.

- Senior, subordinated, junior and mezzanine bonds.

- Junk bonds.

- Guaranteed bonds.

- Pay-in-kind bonds.

- Split coupon bonds.

- Extendable bonds.

- Islamic bonds.

- Foreign bonds.

- Eurobonds.

- Global bonds.

- Retail bonds.

Figure 7: example of plain vanilla bond (3-year maturity; nominal value LLC 100 000; coupon 10% pa)

The most common bond is the first-mentioned: the plain vanilla bond (PVB). Probably 95% of bonds are of this variety. It has a fixed maturity date and pays a fixed rate of interest called a coupon. This is the bond that the household sector will tend to invest in because it is available in small denominations. The PVB bond issued by government will be favored because the rate earned is called the risk-free-rate (rfr). It is called this because government has the power to tax and raise revenue to repay these bonds (and the coupon rate). A simplified example is called for (see Figure 7 and Box 2):

Nominal / face value: LCC 100 000

Term to maturity: 3 years

Coupon: 10% pa

Interest payable: annually in arrears.

If you buy this bond you will be paid interest pa of LCC 10 000 (= 10% pa on LCC 100 000), irrespective of the rate at which the bond trades in the secondary market after issue. Just like in the case of shares, bonds are bought and sold and price (rate) discovery takes place in the secondary market which is a function of supply and demand [and of course the central bank's (CB's) key interest rate (KIR) which determines the start of the yield curve]. Two issues need to be elaborated upon here:

- The term rate of interest does not apply in the case of bonds. Rather, because of multiple cash flows in the future (all are FVs), the secondary market rate that applies here is an average rate earned over the life of the bond, which is called the yield to maturity (ytm).

- It will be evident that if you buy the bond at an ytm of 10% pa (which equals the coupon of 10% pa, the price of the bond will be 1.0 (i.e. you will pay LCC 100 000 for it). However, if you sell the bond in the secondary market at an ytm lower than the coupon rate (remember it is fixed), then the price of the bond will be higher than 1.0, and you will make a capital gain. Conversely, if you sell the bond are an ytm higher than the coupon rate, the price will be lower than 1.0, and you will make a capital loss.

In this way, bonds are similar to shares. The holding period return (HPR) on a PVB over a will be (P0 = purchase price of bond; P1 = selling price of bond):

HPR = (P1 - P0) x nominal value of bond.

Any coupon income is incorporated in the valuation formula, as we will see later.