Business Finance · Chapter 6
Study notes aligned to the official NEB syllabus.
The value of any financial asset is the present value of the cash flows the investor expects to receive from it, discounted at the return the investor requires. This single idea underlies the valuation of both bonds and stocks. A bond promises fixed interest and a fixed repayment, so its cash flows are easy to write down. A share promises uncertain dividends, so its valuation needs a model of how those dividends behave. This chapter applies the present-value idea to both.
A bond is a long-term debt instrument that pays the holder a fixed coupon interest each period and repays its face (par) value at maturity. Its value today is the present value of all the coupon payments plus the present value of the face value:
$$ V_B = \sum_{t=1}^{n} \frac{I}{(1+k_d)^t} + \frac{M}{(1+k_d)^n} $$
Here $I$ is the annual coupon interest in rupees, $M$ is the face value repaid at maturity, $k_d$ is the required rate of return (yield) per period, and $n$ is the number of periods to maturity. The first term is an annuity of the coupons and the second is a single lump sum.
Consider a bond of face value Rs. 1,000 carrying a 10 percent annual coupon, with 3 years to maturity, when investors require a 12 percent return. The annual coupon is $I = 10% \times 1,000 = \text{Rs. } 100$. Discounting each cash flow at 12 percent:
$$ \begin{aligned} V_B &= \frac{100}{(1.12)^1} + \frac{100}{(1.12)^2} + \frac{100}{(1.12)^3} + \frac{1,000}{(1.12)^3} \ V_B &= 89.29 + 79.72 + 71.18 + 711.78 \ &= \text{Rs. } 951.97 \end{aligned} $$
Because the required return (12 percent) exceeds the coupon rate (10 percent), the bond sells below par at about Rs. 952. Whenever the required return is above the coupon rate the bond trades at a discount; when it is below, the bond trades at a premium; when the two are equal the bond sells at par.
The value of any financial asset is the present value of the cash flows the investor expects to receive from it, discounted at the return the investor requires. This single idea underlies the valuation of both bonds and stocks. A bond promises fixed interest and a fixed repayment, so its cash flows are easy to write down. A share promises uncertain dividends, so its valuation needs a model of how those dividends behave. This chapter applies the present-value idea to both.
A bond is a long-term debt instrument that pays the holder a fixed coupon interest each period and repays its face (par) value at maturity. Its value today is the present value of all the coupon payments plus the present value of the face value:
Here is the annual coupon interest in rupees, is the face value repaid at maturity, is the required rate of return (yield) per period, and is the number of periods to maturity. The first term is an annuity of the coupons and the second is a single lump sum.
Consider a bond of face value Rs. 1,000 carrying a 10 percent annual coupon, with 3 years to maturity, when investors require a 12 percent return. The annual coupon is . Discounting each cash flow at 12 percent:
Because the required return (12 percent) exceeds the coupon rate (10 percent), the bond sells below par at about Rs. 952. Whenever the required return is above the coupon rate the bond trades at a discount; when it is below, the bond trades at a premium; when the two are equal the bond sells at par.