Question

4. You h ave purchased a 10,000-dollar bond par value for 9400 dollars. You purchased interest payment. The it immediately after the previous owner received a quarterly bond rate is 8 % per year payable quarterly. You will hold the bond 5 years and sell ayment at that time. You desire a yield of 16 % per immediately after receiving thep -compounded quarterly. What will be the minimum selling price of the bond to achieve this goal?

Answer 1

Purchase value = 9400

Par value = 10000

Coupon rate = 8% payable quarterly

quarter payments = 8%*10000/4 = 200

Bond holding period =5 yrs = 5*4 quarters = 20 quarters

return desired = 16% per year compounded quarterly = 16%/4 = 4% per quarter

Let S be the selling price after 5 year then as per the condition given in the question at 16% per compunded quarterly present value should be equal to zero

Now,

Present worth = -9400 + 200 *(P/A, 4%,20) + S *(P/F, 4%,20)

-9400 + 200 *(P/A, 4%,20) + S *(P/F, 4%,20) = 0

S *(P/F, 4%,20) = 9400 - 200 *(P/A, 4%,20)

S *0.4563869 = 9400 - 200 * 13.590326

S = 6681.9348 / 0.4563869

S = 14640.94

This is the minimum selling price to make 16% return