Question

3.Consider Fulton Manufacturing Company's 8.75 percent bonds that mature on April 15, 2028. Assume that the interest on these bonds is paid and compounded annually. Determine the value of a $1,000 denomination Fulton bond as of April 15, 2016, to an investor who holds the bond until maturity and whose required rate of return is: ANS: 9 percent FV =1000 NPER-6 RATE =9.00 PMT=98.75 PV =$1,039.25

show the working

9 percent

Answer 1

Value or Price of the bond can be calculated by the following formula:

Bond price = Present value of interest payment + Present value of bond payment at maturity

Bond interest = 8.75% * $1000 = $87.5

Bond interest payments will be same every year, so it is an annuity. Bond payment at maturity is a one time payment. The interest rate that will be used in calculating the required present values will be the required rate, which is 9% with 12 (i.e. 2028 - 2016) periods.

Now,

First we will calculate the present value of interest payments:

For calculating the present value, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $87.5, r is the rate of interest = 9% and n is the time period = 12

Now, putting these values in the above formula, we get,

PVA = $87.5 * (1 - (1 + 9%)^-12 / 9%)

PVA = $87.5 * (1 - ( 1+ 0.09)^-12 / 0.09)

PVA = $87.5 * (1 - ( 1.09)^-12 / 0.09)

PVA = $87.5 * ((1 - 0.3555347251 / 0.09)

PVA = $87.5 * (0.6444652749 / 0.09)

PVA = $87.5 * 7.160725276666667

PVA = $626.5634

Next, we will calculate the present value of bond payment at maturity:

For calculating present value, we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $1000, PV = Present value, r = rate of interest = 9%, n= time period = 12

now, putting theses values in the above equation, we get,

$1000 = PV * (1 + 9%)¹²

$1000 = PV * (1 + 0.09)¹²

$1000 = PV * (1.09)¹²

$1000 = PV * 2.81266478178

PV = $1000 / 2.81266478178

PV = $355.5347

Now,

Bond price = Present value of interest payment + Present value of bond payment at maturity

Bond price = $626.5634 + $355.5347 = $982.10

So, value of the bond is $982.10