Question

A 3 year coupon bond, issued at $946.54, pays annual coupon and has a face value of $1000. Use the standard amortization table below to answer these questions:

period	coupon	interest revenue	Balance addition	Carrying Balance
0				$946.54
1	$40	?	$16.71	$946.33
2	$40	$57.80	?	Cell E4
3	$40	$58.87	?	$1,000,000

Fill the missing number in E4

a. $941.13 b.$980.12 c. $981.13 d. 986.54 e. $1,005.41

A speculator purchased the bond for $946.54 at issuance, pocketed the first coupon at t=1 and then immediately sold the bond at its actual market price, which was different from $963.33. He managed to earn higher than YTM for his 1-year holding price. What must be the YTM for the buyer who took over the bond from the speculator, assume this buyer holds the bond for the remaining 2 years till maturity? Select the most accurate answer?

A. <7% b. <6% c. 5-6% d. 4% e. >3%

Answer 1

Answer 1:

Correct answer is:

c. $981.13

Explanation:

The bond maturity is 3 years. As given in the table, interest revenue for year 3 is $58.87 and coupon is $40.

Hence discount amortized in year 3 is (58.87 - 40=) $18.87

As such carrying value at the end of year 2 (missing number in E4) = 1000 - 18.87 = $981.13

Hence:

Option c is correct and other options a, b and d are incorrect.

Answer 2:

Correct answer is:

b. <6%

Explanation:

From explanation of answer 1 above, we find

Coupon rate = 40/1000 * 100 = 4%

YTM = 58.87 / 981.13 * 100 = 6%

Hence:

The amortization schedule is as follows:

Now since the seller earned higher YTM (as he sold the bond at value higher that $963.33 at the end of year 1), the buyer will have lesser than 6% YTM for the balance 2 years.

As such the buyer's YTM is <6% and option b is correct.

Option e is incorrect since it is possible that buyer's YTM is less than 3%.

Between option a and option b, option b is most appropriate since buyer's YTM cannot be higher than 6%.

Option d could be correct. But the buyer's YTM will depend on what exact amount (higher than $963.33) he bought and option b is most appropriate.