Fixed Income Securities: Time Value of Money
Time value of money is the concept of determining the value of all the future likely streams of income as of today due to fall in value of money with time. The reasons for this decrease are:
Inflation in the economy
Risks/uncertainty involved in delayed receipts of cash or financial transactions
Opportunity cost of capital delayed
Prospective bond buyers use this concept to determine the bond prices and yields in order to make investing decisions. The Yield to Maturity is determined which is the internal rate of return of an investment in the bond made at the observed price. YTM assumes that the bond is held till maturity, payments are made as per schedule and are reinvested at the same rate. The coupons expected in future years are discounted at this YTM rate to arrive at the present value and to make buying decisions accordingly.
Let’s find the value of a corporate bond with an annual interest rate of 5%, making semi-annual interest payments for 2 years, after which the bond matures and the principal must be repaid. Assume a YTM of 3%.
F = $1000 for corporate bond; Coupon rate annual = 5%, therefore, Coupon rate semi-annual = 5%/2 = 2.5%
C = 2.5% x $1000 = $25 per period
t = 2 years x 2 = 4 periods for semi-annual coupon payments
T = 4 periods
Present value of semi-annual payments = 25/(1.03)^1 + 25/(1.03)^2 + 25/(1.03)^3 + 25/(1.03)^4 = 24.27 + 23.56 + 22.88 + 22.21 = 92.93
Present value of face value = 1000/(1.03)^4 = 888.49
Therefore, value of bond = $92.93 + $888.49 = $981.42