Question

An investor wants to buy a zero-coupon bond with face value $100, maturity date is 12 months (1 Year), market price is $50 and the annual inflation rate is 5%.

What is the nominal zero-coupon bonds yield to maturity? What is the real bond price?

Answer 1

Given in the question,

Face value = $100

Years to Maturity = 1 year

Present value = $ 50

Annual Inflation Rate = 5%

Calculation of yield to maturity

A zero coupon bond is a bond that does not pay dividends (coupons) per period, but instead is sold at a discount from the face value. For example, an investor purchases one of these bonds at $500, which has a face value at maturity of $1,000. Although no coupons are paid periodically, the investor will receive the return upon maturity or upon sell.

In the given question n = 1 year,

Yield To Maturity (YTM) = (100/50) ^ (1/2) – 1

YTM = 0.41 years or 5 Months

Calculation of Real bond price

Since Zero coupon bond does not pay dividends (coupons) per period, the difference between the maturity Value and purchase price is the return for the investor. This return actually covers only the inflation risk.

So Inflation rate given in this question is 5%, and the return is $ 50 (difference between maturity value and purchase price)

Therefore the nominal value per Bond = 50/5% = $ 1000

Real Value per Bond = Nominal Value - Inflation Value = 1000 - 50 = $ 950