If the purchase price of an investment is positive and all subsequent cash flows are positive, show how there can only be a single yield to maturity.

Answer:

The yield to maturity takes into accounts two aspects: The capital gain from the sale of the asset and the regular return. Since it takes into account both these, there is only one single yield to maturity.

Let us take an example of a bond. Suppose you bought a bond at a face value of $1,000 and sold it at $1,020 in a year with a coupon of 5% or $50.

Your total yield to maturity = Capital Gain + subsequent coupon payment

Yield to maturity = (1020-1000) + 50 = $70

Yield to maturity = 70/1000 = 7%

Since Yield to maturity combines the affect of the capital gain on the purchase price and the subsequent cash flows, there is only a single yield to maturity.