Question

Suppose you purchase a​ 30-year, zero-coupon bond with a yield to maturity of

3 %

.

You hold the bond for five years before selling it.

a. If the​ bond's yield to maturity is

3 %

when you sell​ it, what is the internal rate of return of your​ investment?

b. If the​ bond's yield to maturity is

4 %

when you sell​ it, what is the internal rate of return of your​ investment?

c. If the​ bond's yield to maturity is

2 %

when you sell​ it, what is the internal rate of return of your​ investment?

d. Even if a bond has no chance of​ default, is your investment risk free if you plan to sell it before it​ matures? Explain.

​Note: Assume annual compounding.

Answer 1

Steps to Solve:

1. Find the purchase price using the financial calculator

2. Find selling price using the financial calculator

3. Find the IRR using purchase price and selling price using financial calculator

Purchase Price

Feed N = 30

PMT = 0

FV = 1000

iY = 3

Compute PV we get 411.99

We find the selling price using financial calculator

Using Selling price as FV and Purchase price as PV, N = 5 and PMT = 0 we find the I.Y which is the IRR we get

d) We observe that as we are selling the bond before maturity our returns are sensitive to the changes in market rates. Selling price of the bond depends on the future expected return. If future expected return increases, bond prices decreases and we have to sell at a lower price thereby reducing our effective return. Hence, bonds are sensitive to interest rate changes which is the interest rate risk.