Please help me out this problem! :)
suppose that I buy a 10 yr bond today for $1000 and the interest rate when the bond is issued is 5 percent. the day after I buy the bond, the market interest rate on 10yr bonds rises to 7percent. if I keep the bond for the full 10 yrs until it matures, what is the bond's average annual return?
Hmm, please help me T.T
Of course, I'll be happy to help you with that problem!
To calculate the bond's average annual return, we need to determine the cash flows you will receive over the 10-year holding period.
First, let's determine the annual coupon payment the bond will provide. Since the bond was issued with a 5 percent interest rate, the coupon payment will be calculated as 5 percent of the bond's face value of $1000, which equals $50 per year. This coupon payment remains constant throughout the bond's life.
Next, we need to calculate the bond's value at the end of the 10-year holding period. Since the market interest rate rose to 7 percent, the value of the bond will have decreased. We can use the present value formula to calculate this value.
PV = C / (1 + r)^n
Where:
PV = Present value of the bond
C = Cash flow (coupon payment)
r = Interest rate
n = Number of periods (years)
In our case:
C = $50 (annual coupon payment)
r = 7% = 0.07 (market interest rate)
n = 10 (number of years)
Using the formula, we can calculate the present value of the bond:
PV = $50 / (1 + 0.07)^10 = $50 / (1.07)^10 = $50 / 1.96715 ≈ $25.41
Now, we can calculate the total cash flows over the holding period. We receive a constant coupon payment of $50 per year for 10 years, plus the bond's value at maturity of $25.41. Thus, the cash flows are:
$50 per year for 10 years = $500
Value at maturity = $25.41
To calculate the average annual return, we need to find the average annualized rate of return that would make the present value of these cash flows equal to the initial investment of $1000. We can use the Internal Rate of Return (IRR) formula to solve for this average annual return.
IRR is the rate that makes the net present value (NPV) of the cash flows equal to zero.
Using a financial calculator or software, we can find that the IRR for these cash flows is approximately 4.54%.
Therefore, the bond's average annual return over the 10-year holding period is 4.54%.