Question

1. A 5 year bond (with $1,000 face value) was issued with an unusual coupon payment schedule. The company promises to pay the following amounts as coupon interest each year:

Time 1      $45

Time 2      $55

Time 3      $65

Time 4      $75

Time 5     $85 (The company will also pay back the face value in time 5).

(a) Find the exact bond price if YTM = 6.5%. Show your work

(b ) Explain using time value of money principles why the bond in part (a) does not sell for exactly $1,000.

2. You have won a contest that pays an award of $100,000 paid over a number of years. Consider the following three choices are given three choices for receiving the award:

A. receive 50,000 in time 0 and 50,000 in time 5

B. receive $10,000 each year from time 0 through time 9

C. receive 20,000 in each year from time 0 through 4

Assuming r > 0, rank the choices with the highest first and the lowest last. Explain your rankings

Answer 1

1]

a]

Price of a bond is the present value of its cash flows.

Present value of each cash flow = cash flow / (1 + discount rate)ⁿ

where n = number of years after which the cash flow is received

discount rate = YTM of bond

Bond price = $987.32

b]

As per time value of money, an amount received in the future is worth less than the same amount received today. Conversely, an amount received today is worth more than the same amount received in the future.

This is because if money is received earlier, it can be invested to earn a return. Hence, there is an "opportunity cost" to receiving money later rather than earlier. This "opportunity cost" is called the time value of money.

The bond does not sell for $1,000 because the YTM is 6.5%, whereas the weighted average coupon rate of the bond is less than 6.5%. That is, the value of the coupons received are less when discounted at the market rate of 6.5%. Hence, the bond sells for less than $1,000