Valuation of Bond or Debenture

Valuation of Bond or Debenture.

It is relatively easy to determine the intrinsic value of a bond or a debenture. If there is no risk of default, there is no difficulty in estimating the cash flows associated with a bond. The expected cash flows consist of the annual interest payments plus the principal amount to be recovered at maturity or sooner. The appropriate capitalization or discount rate to be applied will depend upon the riskiness of the bond. The risk in holding a government bond is less than that associated with a debenture issued by a company. Consequently, a lower discount rate would be applied to the cash flows of the government bond and a higher rate to the cash flows of the debenture.

Valuation of Bond or Debenture

1. Bond with Single Maturity Period

When a bond or a debenture has a finite maturity, to determine its value we will consider the annual interest payments plus its terminal or maturity value. Using the present value concept, the discounted value of these flows will be calculated. By comparing the present value of a bond with its current market value, it can be determined whether the bond is overvalued or undervalued. The following formula can be used in determining the value of a bond:

V_d = R₁/ (1 + k_d) + R₂/ (1 + k_d)² + ……. +  R_n / (1 + k_d)ⁿ + M_n / (1 + k_d)ⁿ

_n  

= ∑ R_t/ (1 + k_d)^t + M_n/ (1 + k_d)ⁿ

                                ^{t = 1}

where,

V_d = value of bond or debenture

R = annual interest

k_d = required rate of return

M = terminal or maturity value

n = number of years to maturity. Valuation of Bond or Debenture

2. Bond in Perpetuity

The bond which will never mature is known as a perpetual bond. This type of bond or debenture is rarely found in practice. In case of perpetual bonds, the value of the same would simply the discounted value of the infinite stream of interest flows. The value of a perpetual bond can be determined by using the following formula:

V_d = R₁/ (1 + k_d) + R₂/ (1 + k_d)² + …… +  R∞/ (1 + k_d)∞

∞

= ∑ R_t/ (1 + k_d)^t = R/k_d                             

                                 ^{t = 1}

where,

V_d = value of bond or debenture

R = constant annual interest

k_d = required rate of return

The above equation is an infinite series of R taka per year and the value of a perpetual bond is simply the discounted sum of the infinite series.

3. Valuation of Preferred Share

Preferred share may be issued with or without a maturity period. The holders of preference shares get dividends at a fixed rate. Like bond, it is relatively easy to estimate the cash inflows associated with the preference shares. The following formula is to be used in determining the value of preference share:

V_p = D_p1/ (1 + k_P) + D_p2/ (1 + k_P)² + …… +  D_pn + M_n/ (1 + k_p)ⁿ

_n  

= ∑ D_t/ (1 + k_P)^t + = M_n/ (1 + k_p)^t

                               ^{t = 1}

where,

V_p = value of preferred share

D_p = preferred dividends

k_P = required rate on preferred share

M_n = terminal value of preference share.

The value of a preference share considered as perpetuity can be determined by dividing annual dividend by expected return. The following formula is used to calculate the value of a preference share:

V_p = D_p/k_p

4. Valuation of Equity Share

The valuation of equity share is relatively more difficult. The difficulty arises because of two factors viz.,

1. the estimates of the amount and timing of the cash flows expected by investors are more uncertain. In the case of debentures and preference shares, the rate of interest and dividend is known with certainty. It is, therefore, easy to make forecasts of cash flows associated with them.
2. the earnings and dividends on equity shares are generally expected to grow unlike the interest on debentures and preference dividend. These features of equity shares make the calculation of shares difficult.

Valuation of Bond or Debenture