Star Corp. purchases a $100,000 face value bond which matures in two years. The coupon rate is 6% and the market rate is 7%. At what amount will the bond be recorded (rounded)?

Question

Quizplus · Accepted Answer

To calculate the amount at which the bond will be recorded, we need to find the present value of the bond's future cash flows (coupon payments and face value payment at maturity) using the market rate of interest of 7%.

First, we need to find the amount of each coupon payment. Since the coupon rate is 6%, the annual coupon payment will be $6,000 ($100,000 x 6%). Since the bond pays semi-annual coupons, we need to divide the annual coupon payment by 2 to get the semi-annual coupon payment of $3,000.

Next, we need to find the present value of each semi-annual coupon payment for each of the 4 payment periods (2 years x 2 payment periods per year). We can use the formula PV = FV/(1 + r)^n, where PV is the present value of the cash flow, FV is the future value of the cash flow, r is the market rate of interest, and n is the number of periods.

For the first coupon payment, n = 1 (since it's in 6 months), r = 7%/2 = 3.50% (since it's a semi-annual rate), and FV = $3,000. Plugging in these values, we get PV = $2,941.18.

For the second coupon payment (in 12 months), n = 2, r = 7%/2 = 3.50%, and FV = $3,000. Plugging in these values, we get PV = $2,886.88.

For the third coupon payment (in 18 months), n = 3, r = 7%/2 = 3.50%, and FV = $3,000. Plugging in these values, we get PV = $2,833.61.

For the fourth coupon payment (at maturity in 2 years), n = 4, r = 7%/2 = 3.50%, and FV = $3,000 + $100,000 (face value). Plugging in these values, we get PV = $101,470.74.

Finally, we need to find the present value of the face value payment at maturity. Using the same formula as above with n = 4, r = 7%/2 = 3.50%, and FV = $100,000, we get PV = $88,536.59.

The total present value of all the bond's cash flows is the sum of the present values of the coupon payments and face value payment at maturity:
PV = $2,941.18 + $2,886.88 + $2,833.61 + $101,470.74 + $88,536.59
PV = $198,668.99

Therefore, the bond will be recorded at $98,192 (rounded to the nearest dollar).

Star Corp Purchases a $100,000 Face Value Bond Which Matures in in Two