a) George has been offered the opportunity to purchase a 9%, $10,000 bond due in 10 years. The bond dividend is paid semiannually. George expects an 8% per year, compounded semiannually return on his investments. Use a spreadsheet to graph the sensitivity in PW value if there is a ±30% change in (1) face value, (2) dividend rate, or (3) required nom­inal rate of return. (b) If George purchases the $10,000 face-value bond at a premium of 5%, and all other es­timates are correct, that is, 0% change, did he pay too much or too little? By how much?

Question

What will be an ideal response?

Answer 1

(a) PW calculates the amount you should be willing to pay now. Plot PW versus ±30% changes in (1), (2) and (3) on one graph.

(1) V = face value; r is 4% per 6-month period



PW = V(P/F,4%,20) + 450(P/A,4%,20)

= V(0.4564) + 6116



(2) b = dividend rate; r is 4% per 6-month period



PW = 10,000(P/F,4%,20) + (10,000/2)(b)(P/A,4%,20)

= 10,000(0.4564) + b(5000)(13.5903)

= 4564 + b(67,952)

(3) r = nominal rate per 6-month period



PW = 10,000(P/F,r,20) + 450(P/A,r,20)



(b) Amount paid is 10,000(1.05) = $10,500



For 0% change, PW = $10,680. Therefore, $180 less was paid than the investor was willing to pay to make a nominal 8% per year, compounded semiannually.