Exactly one year ago, an investor purchased a $100 face value zero coupon bond with 4 years to maturity. The market yield to maturity at that time was 6% p.a. compounded semi-annually. Now, one year later, with the market yield to maturity decreases to 5% p.a., the same investor purchases another security that pays a stream of cash flows of $3 every six months for 3 years and with no face value. The combined current value of both investments (i.e., the zero coupon bond bought one year ago and the new security bought today) based on the current market yield to maturity is likely to be:A.ZeroB.Greater than the par valueC.Less than the par valueD.Equal to the par value

To answer this question, we need to calculate the current value of both investments based on the current market yield to maturity.

Step 1: Calculate the current value of the zero coupon bond A zero coupon bond does not pay any interest and is redeemed at its face value at maturity. Its price is the present value of its face value, discounted at the yield to maturity. One year ago, the bond had 4 years to maturity and was purchased when the yield to maturity was 6%. Now, one year later, the bond has 3 years to maturity and the yield to maturity has decreased to 5%. The decrease in yield will increase the price of the bond. The current value of the bond is $100 / (1 + 0.05/2)^(2*3) =$86.38.

Step 2: Calculate the current value of the new security The new security pays a stream of cash flows of $3 every six months for 3 years and has no face value. The current value of this security is the present value of these cash flows, discounted at the current yield to maturity. This is$3 / (1 + 0.05/2) + $3 / (1 + 0.05/2)^2 + ... +$3 / (1 + 0.05/2)^(2*3) = $16.53.

Step 3: Calculate the combined current value of both investments The combined current value of both investments is the sum of the current values of the zero coupon bond and the new security. This is $86.38 +$16.53 = $102.91.

Therefore, the combined current value of both investments based on the current market yield to maturity is greater than the par value. So, the answer is B. Greater than the par value.

First, let's calculate the current value of the zero-coupon bond.

A zero-coupon bond does not pay interest but is sold at a discount and redeemed at face value. The price of a zero-coupon bond can be calculated using the formula:

Price = Face Value / (1 + r/n)^(nt)

Where: r = annual yield (as a decimal) n = number of compounding periods per year t = time to maturity in years

When the bond was purchased, the yield was 6% compounded semi-annually, so n = 2, r = 0.06, and t = 4. However, one year has passed, so now t = 3. The current yield is 5%, so r = 0.05.

Price = 100 / (1 + 0.05/2)^(2*3) Price = 100 / (1.025)^6 Price = 100 / 1.15927407 Price = $86.23

Next, let's calculate the present value of the new security. This security pays $3 every six months for 3 years, so it's an annuity. The present value of an annuity can be calculated using the formula:

PV = C * [(1 - (1 + r/n)^(-nt)) / (r/n)]

Where: C = cash payment per period

PV = 3 * [(1 - (1 + 0.05/2)^(-2*3)) / (0.05/2)] PV = 3 * [(1 - 1/1.15927407) / 0.025] PV = 3 * [0.13772593 / 0.025] PV = $16.53

The combined current value of both investments is $86.23 +$16.53 = $102.76.

Therefore, the correct answer is:

B. Greater than the par value.