What is the present value of the following payment stream, discounted at 8% annu

Question

What is the present value of the following payment stream, discounted at 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3? A corporation has promised to pay $1,000 20 years from today for each bond sold now. No interest will be paid on the bonds during the 20 years, and the bonds are discounted at an interest rate of 7%, compounded semiannually. Approximately how much should an investor pay for each bond? How much would an investor expect to pay for a $1,000 par value bond with a 9% annual coupon that matures in 5 years if the interest rate is 7%?

Explanation / Answer

17) Calculation of present value

= 1000/(1.08) + 2000/(1.08)2+3000/(1.08)3

= 5,022.1 (A)

18) 7% compounded semi annually hence effective rate is 3.5% per half year.

As per PV table for 3.5% for 20 years is coming to 14.18 annuity factor

Present value = $1000 / 14.18 = $70 (A)

19) Given the current market rate of 7.000% for a similar bond, a bond with a face value of $1,000.00 and paying a coupon rate of 9.000% (compounding Annually), should be selling for $1,082.00 (selling at a premium) (C)

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