Question

Explain please

Note: The circled answer is wrong

10. (3.0 pts) You purchase ten $1,000 bonds at par value with a bond rate of 12% compounded quarterly for 4 years. Which of the following calculations is correct, if you want a rate of return of 12% per quarter by selling it in the end of the second year before maturity? a. $10,000 = $10,000(0.03)(PIA 12%, 8) + F(PIF 12%, 8) b. P = $10,000(0.12)(P|A 12%, 2) + $10,000(P|F 12%, 2) c. P = $10,000(0.03)(PIA 3%, 8) + $10,000(PIF 3%, 8) d. $10,000 = $10,000(0.12)(P|A3%, 8) + F(P|F 3%, 8)

Answer 1

Correct Option:

$\textup{a. \$10,000 = \$10,000(0.03)(P/A 12\%,8)+F(P/F 12\%,3)}$

Current Price of Bond is equals to the Present value of Future Cash Flow of Bond at required rate of return.

In the given case,

Required rate of return = 12% per quarter

Annual coupon rate = 12%

Quarterly coupon rate = 12%/4 = 3% = 0.03

Current Price of Bond (Par value) = $10,000

thus,

Quarterly Coupon Amount = $10,000*0.03

Sale Price of Bond at end of second year = F

Quarters in 2 years = 8

(P/A,i,n) = Find present value of uniform series of payment

(P/F,i,n) = Find present value of single future payment

Coupon payment = uniform series of payment

Sale Price at end of 2nd year = Single future payment.

thus,  

Current price of Bond = Coupon payment*(P/A,12%,8) + F*(P/F,12%,8)

$10,000 = 10,000*0.03*(P/A,12%,8)+F*(P/F,12%,8)

Please note: Required return in question i.e 12% is for quarter period, no need to convert to quarterly.

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.