Question

problem 2 (10 points): assume the term structure of interest rates is flat and consider a1-factor model with a factor equal to that interest rate. assume also the current interestrate is 10%. your portfolio consists of $200,000 investment in 6-year zero-coupon bondsand $300,000 investment in 9-year zero-coupon bonds bonds along with 7-year zero-coupon bonds, what dollar value of each bond willyou buy or sell?

Answer 1

Considering a $10,000 ten-year bond at 6% interest with one year to maturity, if market rates rise to 9%, the bond's value will decrease and you would pay less than its face value. The present value is calculated using the formula PV = FV / (1 + r)^n, resulting in a present value lower than $10,000.

Step-by-step explanation:

When considering the purchase of a bond near its maturity with an interest rate change, the value of the bond will be affected. For a $10,000 ten-year bond with a 6% interest rate being considered one year before maturity, if the current market interest rates have risen to 9%, you would expect to pay less than the face value of the bond. The present value of the bond can be calculated using the present value formula for a single cash flow since only one payment is remaining—the principal plus the last interest payment.

Calculating the present value (PV) of the bond, you have:

• The future value (FV), which is the principal ($10,000) plus the last year's interest (6% of $10,000 = $600).
• The discount rate, which is now 9%.
• The number of periods until maturity, which is one year.

The formula for the present value of a future cash flow is:

PV = FV / (1 + r)n

Where:

• PV = present value
• FV = future value
• r = discount rate / interest rate
• n = number of periods until maturity

Substituting in the given values:

PV = ($10,000 + $600) / (1 + 0.09)1

This calculation will yield the present value of the bond, which will be less than $10,000 given that the discount rate of 9% is more than the bond's coupon rate of 6%.