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Question : (a) Graph the sensitivity of what a person should be willing...

(a) Graph the sensitivity of what a person should be willing to pay now for a 9%, $10,000 bond due in 10 years if there is a 30% change in (1) face value, (2) dividend rate, or (3) required nominal rate of return, which is expected to be 8% per year, compounded semiannually. The bond pays dividends semiannually.

(b) If the investor did purchase the $10,000 face value bond at a premium of 5% (i.e., 5% above face value) and all your other estimates were correct, that is, 0% change, did he pay too much or too little? How much?

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(a) PW calculates the amount you should be willing to pay now. Plot PW versus + 30% changes in (a), (b) and (c) on one graph.

 

(1) Face value, V

 

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

 

\quad = V(0.4564) + 6116

 

(2) Dividend rate, b

 

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

 

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

 

\quad = 4564 + b(67,952)

 

(3) Nominal rate, r

 

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.

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