13. A bond problem. A bond is a financial device that is very interesting, in th

Question

13. A bond problem. A bond is a financial device that is very interesting, in that it has two types of cash flows--the interest payments and the face value at maturity. For example, suppose Johnson Company issues $100,000 of 3-year bonds, with 6% interest paid annually. From the investor's standpoint, the cash flows for this bond would be sketched as follows:

Time Period 0

Time Period 1

Time Period 2

Time Period 3

Pay How Much?

Receive $6,000

Receive $6,000

Receive $6,000

Receive $100,000

Question: is this an annuity, a lump sum, or both? Answer: both--the interest is $6,000 per year, an annuity. The receipt of face value at maturity is a lump sum of $100,000.

Question: How much should Gina pay to get this bond, assuming Gina demands a rate of return (yield) of 8% on her investment? Hint: discount the annuity at 8% using the annuity table; then discount the lump sum at 8% using the PV of $1 table--then add the two amounts together. Note that it is possible to earn an 8% return on a 6% bond if you pay sufficiently less than face value to acquire the investment.

14. Same bond as in Question 13. How much should Gina pay to acquire the bond, assuming that she only earns a 5% yield on her investment? Hint: it will be more than $100,000.

15. Same bond as in Question 13. How much should Gina pay to acquire the bond, assuming she earns 6% on this 6% bond? Does the answer surprise you?

Comment: looking at Questions 13, 14, and 15, the interest payments on a bond are fixed. However, because the price of a bond is allowed to fluctuate, the rate of return (yield) of the bond may not be identical to the contractual rate printed on the bond.

Time Period 0

Time Period 1

Time Period 2

Time Period 3

Pay How Much?

Receive $6,000

Receive $6,000

Receive $6,000

Receive $100,000

Explanation / Answer

1)   Amount paid: If rate of return is 8   %

     Annual Interest    6,000/-

     Annuity factor of 8 % for 3 years 2.5771

     Present value of interest payment:   6,000 * 2.5771   =   15,463 /-

     Face value at maturity : 100,000/-

    Present value factor @ 8 % at the end of year 3   .7938

     Present value of maturity:   79,383/-

    Amount to be paid to acquire the bond:   79,383 + 15,463 = 94,846/-

    (Since market rate is 8 % and bond is paynig only 6 % interest definitly the issue of bond at discount)

2. Amount paid: If rate of return is 5 %

     Annual Interest    6,000/-

     Annuity factor of 5 % for 3 years 2.7232

     Present value of interest payment:   6,000 * 2.7232 =   16,340/-

     Face value at maturity : 100,000/-

    Present value factor @ 8 % at the end of year 3   .8638

     Present value of maturity:   86,384/-

    Amount to be paid to acquire the bond:   86,384 + 16,340 = 102,724/-

    (Since market rate is 5% and bond is paynig 6 % interest definitly the issue of bond at premium)

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