Suppose Alex purchases a 10-year,zero-coupon bond with a yield to maturity of 7.5% and face value of $10,000.If he sold it 3 years later,what would be the rate of return of his investment,given that the yield to maturity is now 6%?

Question

Quizplus · Accepted Answer

To calculate the rate of return, we need to determine the price of the bond after 3 years using the new yield to maturity of 6%. We can use the following formula to do this:

Price = Face Value / (1 + Yield)^Time

where Yield is the yield to maturity and Time is the time to maturity in years.

After 3 years, the Time to maturity will be 7 years (original time - time elapsed). Plugging in the values:

Price = 10,000 / (1 + 0.06)^7
Price = 10,000 / 1.5034
Price = 6,648.33

So, Alex would be able to sell the bond for $6,648.33 after 3 years. He originally purchased the bond for $10,000, so his capital loss would be $3,351.67.

The rate of return would be the total return (capital loss plus any coupon payments) divided by the original investment. In this case, there are no coupon payments since it is a zero-coupon bond.

Rate of Return = (Ending Value - Beginning Value) / Beginning Value
Rate of Return = ($6,648.33 - $10,000) / $10,000
Rate of Return = -0.335167 or -33.52%

However, we need to adjust for the fact that interest rates have fallen from 7.5% to 6% over the 3-year period. This means that the bond has become more valuable because its yield is now higher than the prevailing interest rate.

To calculate the adjusted rate of return, we can use the following formula:

Adjusted Rate of Return = (Ending Value - Beginning Value + Interest Earned) / Beginning Value

where Interest Earned is the interest that would have been earned if the original yield to maturity of 7.5% had been maintained. We can calculate this interest as follows:

Interest Earned = Beginning Value * Yield * Time
Interest Earned = $10,000 * 0.075 * 3
Interest Earned = $2,250

Plugging in the values:

Adjusted Rate of Return = ($6,648.33 - $10,000 + $2,250) / $10,000
Adjusted Rate of Return = -$1,101.67 / $10,000
Adjusted Rate of Return = -0.110167 or -11.02%

So the adjusted rate of return is -11.02%, which is closest to choice D (11.08%).

Suppose Alex Purchases a 10-Year,zero-Coupon Bond with a Yield to Maturity