Question

1. A 10-year maturity mortgage-backed bond is issued. The bond is a zero coupon bond that promises to pay $10,000 (par) after 10 years. At issue, bond market investors require a 15 percent interest rate on the bond. What is the initial price on the bond? (A)
2. 1. $2,252
   2. $2,472
   3. $8,696
   4. $10,000

Answer is A but I don't know how to do it. Please explain using financial calculator step.

Answer 1

ANSWER

• The Bond Price at the time of Issue will be $ 2472 and not option (A). I'll explain you how :

• The Price of anything in general is the "Present Value" of the benefits we get from that particular thing in future. Same thing we do in Capital Budgeting problems when we find net present values of the Project.

• Now, in case of Zero Coupon Bonds, we do not get any coupons throughout the tenure of the Bond. All we get is the Matured Amount at the end of Maturity. Such Bonds are basically issue at a price lower than its Par Value so the difference between issue price and Maturity value is our Income.

• So the Value of such Bond is the "PRESENT VALUE" of the "MATURITY AMOUNT" which is the PAR VALUE itself.

• We just have to discount the PAR VALUE at 15% Discount Rate for 10th year.

• BOND INITIAL PRICE = MATURITY VALUE * PVF(at 15%, for 10th year)

​​​​​​​= $ 10000 * 0.2472

= $ 2472

• ​​​​​​​PVF(at 15%, for 10th year) can be calculated on calculator by pressing:

1/1.15 then equal to 10 times